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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : LAT303+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n015.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 07:47:07 AM UTC 2026

% Result   : Theorem 169.12s 46.13s
% Output   : Refutation 174.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      : 1033
% Syntax   : Number of formulae    : 3491 ( 648 unt;   0 typ;  67 def)
%            Number of atoms       : 18734 (3379 equ;   0 cnn)
%            Maximal formula atoms :   58 (   5 avg)
%            Number of connectives : 61745 (5087   ~;2776   |;6409   &;42438   @)
%                                         ( 227 <=>;4808  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  328 ( 325 usr;  79 con; 0-9 aty)
%            Number of variables   : 7734 (  53   ^;7277   !; 337   ?;7734   :)
%                                         (   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(m2_filter_2_decl,type,
    m2_filter_2: $i > $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(v3_filter_0_decl,type,
    v3_filter_0: $i > $o ).

thf(v4_lattices_decl,type,
    v4_lattices: $i > $o ).

thf(v5_lattices_decl,type,
    v5_lattices: $i > $o ).

thf(v6_lattices_decl,type,
    v6_lattices: $i > $o ).

thf(v7_lattices_decl,type,
    v7_lattices: $i > $o ).

thf(v8_lattices_decl,type,
    v8_lattices: $i > $o ).

thf(v9_lattices_decl,type,
    v9_lattices: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(l2_struct_0_decl,type,
    l2_struct_0: $i > $o ).

thf(v2_struct_0_decl,type,
    v2_struct_0: $i > $o ).

thf(k7_domain_1_decl,type,
    k7_domain_1: $i > $i > $i > $i ).

thf(v1_finset_1_decl,type,
    v1_finset_1: $i > $o ).

thf(k5_finsub_1_decl,type,
    k5_finsub_1: $i > $i ).

thf(v1_lattice2_decl,type,
    v1_lattice2: $i > $o ).

thf(k13_nat_lat_decl,type,
    k13_nat_lat: $i ).

thf(k3_binop_1_decl,type,
    k3_binop_1: $i > $i > $i ).

thf(k2_subset_1_decl,type,
    k2_subset_1: $i > $i ).

thf(m2_nat_lat_decl,type,
    m2_nat_lat: $i > $i > $o ).

thf(a_2_2_domain_1_decl,type,
    a_2_2_domain_1: $i > $i > $i ).

thf(a_2_0_domain_1_decl,type,
    a_2_0_domain_1: $i > $i > $i ).

thf(r8_relat_2_decl,type,
    r8_relat_2: $i > $i > $o ).

thf(k1_subset_1_decl,type,
    k1_subset_1: $i > $i ).

thf(k4_subset_1_decl,type,
    k4_subset_1: $i > $i > $i > $i ).

thf(r3_relat_2_decl,type,
    r3_relat_2: $i > $i > $o ).

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

thf(v16_lattices_decl,type,
    v16_lattices: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(v17_lattices_decl,type,
    v17_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(m2_lattice4_decl,type,
    m2_lattice4: $i > $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(a_0_0_domain_1_decl,type,
    a_0_0_domain_1: $i ).

thf(f1_s7_domain_1_decl,type,
    f1_s7_domain_1: $i ).

thf(k8_setwiseo_decl,type,
    k8_setwiseo: $i > $i > $i > $i > $i ).

thf(k5_setwiseo_decl,type,
    k5_setwiseo: $i > $i > $i > $i ).

thf(k2_setwiseo_decl,type,
    k2_setwiseo: $i > $i > $i ).

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

thf(k7_filter_2_decl,type,
    k7_filter_2: $i > $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(r1_filter_2_decl,type,
    r1_filter_2: $i > $i > $i > $o ).

thf(k14_filter_2_decl,type,
    k14_filter_2: $i > $i > $i ).

thf(r2_lattices_decl,type,
    r2_lattices: $i > $i > $i > $o ).

thf(u2_struct_0_decl,type,
    u2_struct_0: $i > $i ).

thf(k10_domain_1_decl,type,
    k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).

thf(r1_lattice2_decl,type,
    r1_lattice2: $i > $i > $i > $o ).

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

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

thf(a_3_2_domain_1_decl,type,
    a_3_2_domain_1: $i > $i > $i > $i ).

thf(a_2_0_lattice4_decl,type,
    a_2_0_lattice4: $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(k13_filter_2_decl,type,
    k13_filter_2: $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(k3_filter_2_decl,type,
    k3_filter_2: $i > $i > $i ).

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

thf(k16_filter_2_decl,type,
    k16_filter_2: $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

thf(k15_filter_2_decl,type,
    k15_filter_2: $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(k18_filter_2_decl,type,
    k18_filter_2: $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(sk265_decl,type,
    sk265: $i ).

thf(sk278_decl,type,
    sk278: $i ).

thf(sk282_decl,type,
    sk282: $i ).

thf(sk295_decl,type,
    sk295: $i ).

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

thf(sk312_decl,type,
    sk312: $o ).

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

thf(sk314_decl,type,
    sk314: $i ).

thf(sk318_decl,type,
    sk318: $o ).

thf(sk319_decl,type,
    sk319: $i ).

thf(sk320_decl,type,
    sk320: $i ).

thf(sk322_decl,type,
    sk322: $i ).

thf(sk325_decl,type,
    sk325: $i ).

thf(sk326_decl,type,
    sk326: $o ).

thf(sk327_decl,type,
    sk327: $i ).

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

thf(sk331_decl,type,
    sk331: $i > $i ).

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

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

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

thf(sk347_decl,type,
    sk347: $i > $i > $i ).

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

thf(sk352_decl,type,
    sk352: $o ).

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

thf(sk354_decl,type,
    sk354: $i ).

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

thf(sk393_decl,type,
    sk393: $i ).

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

thf(sk432_decl,type,
    sk432: $o ).

thf(sk433_decl,type,
    sk433: $i ).

thf(sk434_decl,type,
    sk434: $i ).

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

thf(sk458_decl,type,
    sk458: $i ).

thf(sk1_def,definition,
    ( sk1
    = ( @+[A: $i] :
          ~ ( ( ( A @ l3_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ! [B: $i] :
                ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
               => ( ( A @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m2_filter_2 ) )
                 => ( A @ v13_lattices ) ) ) ) ) ) ).

thf(sk2_def,definition,
    ( sk2
    = ( @+[A: $i] :
          ~ ( ( sk1 @ u1_struct_0 @ ( A @ m1_subset_1 ) )
           => ( ( sk1 @ ( A @ ( sk1 @ u1_struct_0 @ k6_domain_1 ) @ m2_filter_2 ) )
             => ( sk1 @ v13_lattices ) ) ) ) ) ).

thf(sk4_def,definition,
    ( sk4
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( C @ ( D @ r2_hidden ) )
           => ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ).

thf(sk5_def,definition,
    ( sk5
    = ( ^ [A: $i,B: $i,C: $i,D: $i,E: $i] :
        @+[F: $i] :
          ~ ( ( E @ ( F @ m1_subset_1 ) )
           => ~ ( ( A
                  = ( F @ ( B @ k1_funct_1 ) ) )
                & ( C @ ( F @ r2_hidden ) ) ) ) ) ) ).

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

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

thf(sk8_def,definition,
    ( sk8
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( C @ ( D @ m1_subset_1 ) )
           => ! [E: $i] :
                ( ( C @ ( E @ m1_subset_1 ) )
               => ( ( ( E @ ( D @ ( C @ ( B @ ( A @ sk7 ) ) @ ( A @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
                    = ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) )
                  & ( ( E @ ( D @ ( A @ k1_binop_1 ) ) @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) )
                    = ( E @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( D @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) ) ) ) ) ) ) ).

thf(sk9_def,definition,
    ( sk9
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( C @ ( D @ m1_subset_1 ) )
           => ( ( ( D @ ( C @ ( B @ ( A @ sk8 ) ) @ ( C @ ( B @ ( A @ sk7 ) ) @ ( A @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
                = ( D @ ( C @ ( B @ ( A @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( D @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) )
              & ( ( D @ ( C @ ( B @ ( A @ sk8 ) ) @ ( A @ k1_binop_1 ) ) @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) )
                = ( D @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ ( A @ sk8 ) ) @ ( C @ ( B @ ( A @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ k1_binop_1 ) ) ) ) ) ) ) ) ).

thf(sk10_def,definition,
    ( sk10
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ! [D: $i] :
              ( ( ( A @ k1_relat_1 @ ( D @ r2_hidden ) )
                & ( B @ k1_relat_1 @ ( C @ r2_hidden ) ) )
             => ( ( ( ( D @ ( A @ k1_funct_1 ) )
                    = C )
                 => ( ( C @ ( B @ k1_funct_1 ) )
                    = D ) )
                & ( ( ( C @ ( B @ k1_funct_1 ) )
                    = D )
                 => ( ( D @ ( A @ k1_funct_1 ) )
                    = C ) ) ) ) ) ) ).

thf(sk11_def,definition,
    ( sk11
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
              & ( B @ k1_relat_1 @ ( B @ ( A @ sk10 ) @ r2_hidden ) ) )
           => ( ( ( ( C @ ( A @ k1_funct_1 ) )
                  = ( B @ ( A @ sk10 ) ) )
               => ( ( B @ ( A @ sk10 ) @ ( B @ k1_funct_1 ) )
                  = C ) )
              & ( ( ( B @ ( A @ sk10 ) @ ( B @ k1_funct_1 ) )
                  = C )
               => ( ( C @ ( A @ k1_funct_1 ) )
                  = ( B @ ( A @ sk10 ) ) ) ) ) ) ) ) ).

thf(sk12_def,definition,
    ( sk12
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( B @ ( C @ m1_subset_1 ) )
           => ( ( C @ ( C @ ( A @ k1_binop_1 ) ) )
              = C ) ) ) ) ).

thf(sk13_def,definition,
    ( sk13
    = ( @+[A: $i > $i > $i] :
        ! [B: $i,C: $i] :
          ( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
          = B ) ) ) ).

thf(sk14_def,definition,
    ( sk14
    = ( @+[A: $i] :
          ( ! [B: $i] :
              ( ( A @ ( B @ m1_subset_1 ) )
             => ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
          & ~ ( A @ v1_xboole_0 ) ) ) ) ).

thf(sk15_def,definition,
    ( sk15
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ( ~ ? [D: $i] :
                ( ( C
                  = ( D @ ( A @ k1_funct_1 ) ) )
                & ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
          & ( B @ ( C @ r2_hidden ) ) ) ) ) ).

thf(sk18_def,definition,
    ( sk18
    = ( ^ [A: $i] :
        @+[B: $i] :
          ~ ( ( ( B @ v1_funct_1 )
              & ( B @ v1_relat_1 ) )
           => ! [C: $i] :
                ( ( ( C @ v1_funct_1 )
                  & ( C @ v1_relat_1 ) )
               => ( ( ( ( C @ k1_relat_1 )
                      = A )
                    & ( ( B @ k1_relat_1 )
                      = A ) )
                 => ( B = C ) ) ) ) ) ) ).

thf(sk19_def,definition,
    ( sk19
    = ( ^ [A: $i] :
        @+[B: $i] :
          ~ ( ( ( B @ v1_funct_1 )
              & ( B @ v1_relat_1 ) )
           => ( ( ( ( B @ k1_relat_1 )
                  = A )
                & ( ( A @ sk18 @ k1_relat_1 )
                  = A ) )
             => ( ( A @ sk18 )
                = B ) ) ) ) ) ).

thf(sk25_def,definition,
    ( sk25
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( ( C @ v1_funct_1 )
              & ( C @ v1_relat_1 ) )
           => ~ ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
                & ( A
                  = ( C @ k1_relat_1 ) ) ) ) ) ) ).

thf(sk71_def,definition,
    ( sk71
    = ( @+[A: $i] :
          ( ( A @ v1_xboole_0 )
          & ( A @ v2_funct_1 )
          & ( A @ v1_funct_1 )
          & ( A @ v1_relat_1 ) ) ) ) ).

thf(sk80_def,definition,
    ( sk80
    = ( ^ [A: $i] :
        @+[B: $i] :
          ( ~ ? [C: $i] :
                ( ~ ( B @ ( C @ r2_hidden ) )
                & ~ ( B @ ( C @ r2_tarski ) )
                & ( B @ ( C @ r1_tarski ) ) )
          & ~ ? [C: $i] :
                ( ~ ? [D: $i] :
                      ( ! [E: $i] :
                          ( ( C @ ( E @ r1_tarski ) )
                         => ( D @ ( E @ r2_hidden ) ) )
                      & ( B @ ( D @ r2_hidden ) ) )
                & ( B @ ( C @ r2_hidden ) ) )
          & ! [C: $i,D: $i] :
              ( ( ( C @ ( D @ r1_tarski ) )
                & ( B @ ( C @ r2_hidden ) ) )
             => ( B @ ( D @ r2_hidden ) ) )
          & ( B @ ( A @ r2_hidden ) ) ) ) ) ).

thf(sk81_def,definition,
    ( sk81
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ( ! [D: $i] :
              ( ( A @ ( D @ r1_tarski ) )
             => ( C @ ( D @ r2_hidden ) ) )
          & ( B @ sk80 @ ( C @ r2_hidden ) ) ) ) ) ).

thf(sk94_def,definition,
    ( sk94
    = ( @+[A: $i] :
          ( ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ( A @ v3_lattices )
          & ~ ( A @ v3_struct_0 )
          & ( A @ l3_lattices ) ) ) ) ).

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

thf(sk110_def,definition,
    ( sk110
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ( ( C @ v1_funct_1 )
          & ( C @ v1_relat_1 )
          & ( A @ ( B @ ( C @ m1_relset_1 ) ) ) ) ) ) ).

thf(sk111_def,definition,
    ( sk111
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ( ( A @ ( B @ ( C @ v1_funct_2 ) ) )
          & ( C @ v1_funct_1 )
          & ( C @ v1_relat_1 )
          & ( A @ ( B @ ( C @ m1_relset_1 ) ) ) ) ) ) ).

thf(sk118_def,definition,
    ( sk118
    = ( @+[A: $i] :
          ( ( A @ v1_lattice2 )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ~ ( A @ v3_struct_0 )
          & ( A @ l3_lattices ) ) ) ) ).

thf(sk138_def,definition,
    ( sk138
    = ( @+[A: $i] :
          ( ( A @ v2_funct_1 )
          & ( A @ v1_funct_1 )
          & ( A @ v1_relat_1 ) ) ) ) ).

thf(sk152_def,definition,
    ( sk152
    = ( @+[A: $i] :
          ( ( A @ v1_relat_1 )
          & ( A @ v1_xboole_0 ) ) ) ) ).

thf(sk157_def,definition,
    ( sk157
    = ( @+[A: $i] :
          ( ( A @ v14_lattices )
          & ( A @ v13_lattices )
          & ( A @ v12_lattices )
          & ( A @ v11_lattices )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ( A @ v3_lattices )
          & ~ ( A @ v3_struct_0 )
          & ( A @ l3_lattices ) ) ) ) ).

thf(sk187_def,definition,
    ( sk187
    = ( @+[A: $i] :
          ( ( A @ v15_lattices )
          & ( A @ v14_lattices )
          & ( A @ v13_lattices )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ( A @ v3_lattices )
          & ~ ( A @ v3_struct_0 )
          & ( A @ l3_lattices ) ) ) ) ).

thf(sk188_def,definition,
    ( sk188
    = ( @+[A: $i] :
          ( ( A @ v3_filter_0 )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ( A @ v3_lattices )
          & ~ ( A @ v3_struct_0 )
          & ( A @ l3_lattices ) ) ) ) ).

thf(sk195_def,definition,
    ( sk195
    = ( ^ [A: $i] :
        @+[B: $i] : ( A @ ( B @ r2_hidden ) ) ) ) ).

thf(sk196_def,definition,
    ( sk196
    = ( @+[A: $i] :
          ( ( A @ v16_lattices )
          & ( A @ v15_lattices )
          & ( A @ v14_lattices )
          & ( A @ v13_lattices )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ( A @ v3_lattices )
          & ~ ( A @ v3_struct_0 )
          & ( A @ l3_lattices ) ) ) ) ).

thf(sk197_def,definition,
    ( sk197
    = ( @+[A: $i] :
          ( ( A @ v1_lattice2 )
          & ( A @ v3_filter_0 )
          & ( A @ v13_lattices )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ( A @ v3_lattices )
          & ~ ( A @ v3_struct_0 )
          & ( A @ l3_lattices ) ) ) ) ).

thf(sk207_def,definition,
    ( sk207
    = ( @+[A: $i] :
          ( ( A @ v1_funct_1 )
          & ( A @ v1_relat_1 ) ) ) ) ).

thf(sk216_def,definition,
    ( sk216
    = ( @+[A: $i] :
          ( ( A @ v1_funct_1 )
          & ( A @ v1_xboole_0 )
          & ( A @ v1_relat_1 ) ) ) ) ).

thf(sk218_def,definition,
    ( sk218
    = ( @+[A: $i] :
          ( ( A @ v1_relat_1 )
          & ~ ( A @ v1_xboole_0 ) ) ) ) ).

thf(sk235_def,definition,
    ( sk235
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( A @ ( D @ r2_hidden ) )
           => ( ( D = B )
              | ( D = C ) ) ) ) ) ).

thf(sk236_def,definition,
    ( sk236
    = ( ^ [A: $i,B: $i,C: $i] :
        @+[D: $i] :
          ~ ( ( ( D = B )
              | ( D = C ) )
           => ( A @ ( D @ r2_hidden ) ) ) ) ) ).

thf(sk249_def,definition,
    ( sk249
    = ( ^ [A: $i] :
        @+[B: $i] :
          ( ( B @ v1_xboole_0 )
          & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).

thf(sk265_def,definition,
    ( sk265
    = ( @+[A: $i] :
          ( ~ ( A @ v3_struct_0 )
          & ( A @ l1_struct_0 ) ) ) ) ).

thf(sk278_def,definition,
    ( sk278
    = ( @+[A: $i] : ( A @ v1_xboole_0 ) ) ) ).

thf(sk282_def,definition,
    ( sk282
    = ( @+[A: $i] : ( A @ l1_struct_0 ) ) ) ).

thf(sk295_def,definition,
    ( sk295
    = ( @+[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(sk297_def,definition,
    ( sk297
    = ( @+[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(sk313_def,definition,
    ( sk313
    = ( @+[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(sk314_def,definition,
    ( sk314
    = ( @+[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(sk319_def,definition,
    ( sk319
    = ( @+[A: $i] :
          ~ ( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
           => ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) ) ) ) ).

thf(sk320_def,definition,
    ( sk320
    = ( @+[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(sk322_def,definition,
    ( sk322
    = ( @+[A: $i] : ( A @ l1_lattices ) ) ) ).

thf(sk325_def,definition,
    ( sk325
    = ( @+[A: $i] :
          ( ( A @ v3_lattices )
          & ( A @ l3_lattices ) ) ) ) ).

thf(sk327_def,definition,
    ( sk327
    = ( @+[A: $i] :
          ~ ( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
           => ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) ) ) ) ).

thf(sk328_def,definition,
    ( sk328
    = ( @+[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(sk331_def,definition,
    ( sk331
    = ( ^ [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(sk337_def,definition,
    ( sk337
    = ( @+[A: $i] : ( A @ l2_struct_0 ) ) ) ).

thf(sk338_def,definition,
    ( sk338
    = ( @+[A: $i] : ( A @ l2_lattices ) ) ) ).

thf(sk341_def,definition,
    ( sk341
    = ( @+[A: $i] :
          ~ ( A @ v1_xboole_0 ) ) ) ).

thf(sk347_def,definition,
    ( sk347
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( A @ ( C @ r2_hidden ) )
           => ( C = B ) ) ) ) ).

thf(sk348_def,definition,
    ( sk348
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ~ ( ( C = B )
           => ( A @ ( C @ r2_hidden ) ) ) ) ) ).

thf(sk353_def,definition,
    ( sk353
    = ( @+[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(sk354_def,definition,
    ( sk354
    = ( @+[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(sk366_def,definition,
    ( sk366
    = ( ^ [A: $i] :
        @+[B: $i] : ( A @ ( B @ m1_subset_1 ) ) ) ) ).

thf(sk393_def,definition,
    ( sk393
    = ( @+[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(sk410_def,definition,
    ( sk410
    = ( @+[A: $i] :
          ( ~ ( A @ v3_struct_0 )
          & ( A @ l2_struct_0 ) ) ) ) ).

thf(sk433_def,definition,
    ( sk433
    = ( @+[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(sk434_def,definition,
    ( sk434
    = ( @+[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(sk445_def,definition,
    ( sk445
    = ( @+[A: $i] :
          ( ( A @ v3_lattices )
          & ~ ( A @ v3_struct_0 )
          & ( A @ l3_lattices ) ) ) ) ).

thf(sk458_def,definition,
    ( sk458
    = ( @+[A: $i] : ( A @ l3_lattices ) ) ) ).

thf(196,axiom,
    ? [A: $i] :
      ( ( A @ v10_lattices )
      & ( A @ v9_lattices )
      & ( A @ v8_lattices )
      & ( A @ v7_lattices )
      & ( A @ v6_lattices )
      & ( A @ v5_lattices )
      & ( A @ v4_lattices )
      & ( A @ v3_lattices )
      & ~ ( A @ v3_struct_0 )
      & ( A @ l3_lattices ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_lattices) ).

thf(2153,plain,
    ? [A: $i] :
      ( ( A @ v10_lattices )
      & ( A @ v9_lattices )
      & ( A @ v8_lattices )
      & ( A @ v7_lattices )
      & ( A @ v6_lattices )
      & ( A @ v5_lattices )
      & ( A @ v4_lattices )
      & ( A @ v3_lattices )
      & ~ ( A @ v3_struct_0 )
      & ( A @ l3_lattices ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(2154,plain,
    ( ( sk94 @ v10_lattices )
    & ( sk94 @ v9_lattices )
    & ( sk94 @ v8_lattices )
    & ( sk94 @ v7_lattices )
    & ( sk94 @ v6_lattices )
    & ( sk94 @ v5_lattices )
    & ( sk94 @ v4_lattices )
    & ( sk94 @ v3_lattices )
    & ~ ( sk94 @ v3_struct_0 )
    & ( sk94 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[2153]) ).

thf(2163,plain,
    sk94 @ v4_lattices,
    inference(cnfConj,[status(thm)],[2154]) ).

thf(729,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( B @ ( A @ k7_lattices ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_lattices) ).

thf(5116,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)],[729]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ v1_relat_1 )
     => ~ ( ( ( A @ ( B @ k9_relat_1 ) )
            = k1_xboole_0 )
          & ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
          & ( A != k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t152_relat_1) ).

thf(1022,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(1023,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)],[1022]) ).

thf(1024,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)],[1023]) ).

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

thf(1633,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(516,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( C @ ( F @ m1_subset_1 ) )
                           => ( ( D @ ( F @ r2_hidden ) )
                             => ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) )
                       => ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
                          | ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_lattice2) ).

thf(4022,plain,
    ! [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)],[516]) ).

thf(25,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
     => ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
        = ( C @ ( B @ k4_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).

thf(1081,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(1082,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)],[1081]) ).

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

thf(525,axiom,
    ? [A: $i] : ( A @ v1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(4082,plain,
    ? [A: $i] : ( A @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(4083,plain,
    sk278 @ v1_xboole_0,
    inference(cnf,[status(esa)],[4082]) ).

thf(368,axiom,
    ? [A: $i] :
      ( ( A @ v1_relat_1 )
      & ~ ( A @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).

thf(3253,plain,
    ? [A: $i] :
      ( ( A @ v1_relat_1 )
      & ~ ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(3254,plain,
    ( ( sk218 @ v1_relat_1 )
    & ~ ( sk218 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[3253]) ).

thf(3255,plain,
    ~ ( sk218 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[3254]) ).

thf(8636,plain,
    ( ( ( sk278 @ v1_xboole_0 )
     != ( sk218 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4083,3255]) ).

thf(8637,plain,
    ( ( sk278 @ v1_xboole_0 )
   != ( sk218 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8636]) ).

thf(8646,plain,
    sk278 != sk218,
    inference(simp,[status(thm)],[8637]) ).

thf(45,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ v1_relat_1 )
     => ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_relat_1) ).

thf(1178,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(1179,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
      | ~ ( B @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[1178]) ).

thf(933,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
        <=> ( A @ k1_lattice2 @ ( B @ m1_filter_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_filter_2) ).

thf(6014,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)],[933]) ).

thf(682,axiom,
    ! [A: $i] :
      ~ ( A @ k1_tarski @ v1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).

thf(4904,plain,
    ! [A: $i] :
      ~ ( A @ k1_tarski @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

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/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).

thf(2250,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(322,axiom,
    ? [A: $i] :
      ( ( A @ v1_lattice2 )
      & ( A @ v3_filter_0 )
      & ( A @ v13_lattices )
      & ( A @ v10_lattices )
      & ( A @ v9_lattices )
      & ( A @ v8_lattices )
      & ( A @ v7_lattices )
      & ( A @ v6_lattices )
      & ( A @ v5_lattices )
      & ( A @ v4_lattices )
      & ( A @ v3_lattices )
      & ~ ( A @ v3_struct_0 )
      & ( A @ l3_lattices ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_lattice2) ).

thf(2998,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)],[322]) ).

thf(2999,plain,
    ( ( sk197 @ v1_lattice2 )
    & ( sk197 @ v3_filter_0 )
    & ( sk197 @ v13_lattices )
    & ( sk197 @ v10_lattices )
    & ( sk197 @ v9_lattices )
    & ( sk197 @ v8_lattices )
    & ( sk197 @ v7_lattices )
    & ( sk197 @ v6_lattices )
    & ( sk197 @ v5_lattices )
    & ( sk197 @ v4_lattices )
    & ( sk197 @ v3_lattices )
    & ~ ( sk197 @ v3_struct_0 )
    & ( sk197 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[2998]) ).

thf(3001,plain,
    sk197 @ v13_lattices,
    inference(cnfConj,[status(thm)],[2999]) ).

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

thf(1919,plain,
    ? [A: $i] :
      ( ( A @ v1_xboole_0 )
      & ( A @ v2_funct_1 )
      & ( A @ v1_funct_1 )
      & ( A @ v1_relat_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(1920,plain,
    ( ( sk71 @ v1_xboole_0 )
    & ( sk71 @ v2_funct_1 )
    & ( sk71 @ v1_funct_1 )
    & ( sk71 @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[1919]) ).

thf(1922,plain,
    sk71 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[1920]) ).

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

thf(1000,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(1001,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)],[1000]) ).

thf(1002,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)],[1001]) ).

thf(1003,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)],[1002]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( A @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m2_filter_2 ) )
           => ( A @ v13_lattices ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_filter_2) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ( A @ l3_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ( ( A @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m2_filter_2 ) )
             => ( A @ v13_lattices ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(968,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)],[2]) ).

thf(969,plain,
    ( ~ ( sk1 @ v13_lattices )
    & ( sk1 @ ( sk2 @ ( sk1 @ u1_struct_0 @ k6_domain_1 ) @ m2_filter_2 ) )
    & ( sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
    & ( sk1 @ l3_lattices )
    & ( sk1 @ v10_lattices )
    & ~ ( sk1 @ v3_struct_0 ) ),
    inference(cnf,[status(esa)],[968]) ).

thf(970,plain,
    ~ ( sk1 @ v13_lattices ),
    inference(cnfConj,[status(thm)],[969]) ).

thf(6459,plain,
    ! [B: $i,A: $i] :
      ( ( A != sk1 )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( A @ ( B @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
      | ~ ( B @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1003,970]) ).

thf(6460,plain,
    ! [A: $i] :
      ( ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ ( A @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[6459:[bind(A,$thf( sk1 ))]]) ).

thf(6622,plain,
    ! [A: $i] :
      ( ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ ( A @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[6460]) ).

thf(6898,plain,
    ! [A: $i] :
      ( ( ( sk71 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1922,6622]) ).

thf(6899,plain,
    ! [A: $i] :
      ( ( ( sk71 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[6898]) ).

thf(6900,plain,
    ( ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[6899:[bind(A,$thf( sk71 ))]]) ).

thf(7362,plain,
    ( ( ( sk197 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3001,6900]) ).

thf(7363,plain,
    ( ( ( sk197 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7362]) ).

thf(7375,plain,
    ( ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7363]) ).

thf(325,axiom,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_subset_1) ).

thf(3019,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(3020,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[3019]) ).

thf(3021,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[3020]) ).

thf(860,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k3_filter_2 ) @ m1_filter_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_filter_2) ).

thf(5686,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)],[860]) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ! [E: $i] :
                    ( ( A @ ( E @ m1_subset_1 ) )
                   => ! [F: $i] :
                        ( ( A @ ( F @ m1_subset_1 ) )
                       => ( ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
                            = ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
                          & ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
                            = ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_binop_1) ).

thf(1031,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(1032,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
        | ( ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
         != ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
        | ( ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) )
         != ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        | ~ ( B @ v1_funct_1 ) )
      & ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
        | ( A @ ( A @ ( B @ ( C @ sk9 ) ) @ m1_subset_1 ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        | ~ ( B @ v1_funct_1 ) )
      & ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
        | ( A @ ( A @ ( B @ ( C @ sk8 ) ) @ m1_subset_1 ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        | ~ ( B @ v1_funct_1 ) )
      & ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
        | ( A @ ( A @ ( B @ ( C @ sk7 ) ) @ m1_subset_1 ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        | ~ ( B @ v1_funct_1 ) )
      & ( ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
          = ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
        | ~ ( A @ ( F @ m1_subset_1 ) )
        | ~ ( A @ ( E @ m1_subset_1 ) )
        | ~ ( A @ ( D @ m1_subset_1 ) )
        | ~ ( C @ ( B @ ( A @ r6_binop_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        | ~ ( B @ v1_funct_1 ) )
      & ( ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
          = ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
        | ~ ( A @ ( F @ m1_subset_1 ) )
        | ~ ( A @ ( E @ m1_subset_1 ) )
        | ~ ( A @ ( D @ m1_subset_1 ) )
        | ~ ( C @ ( B @ ( A @ r6_binop_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        | ~ ( B @ v1_funct_1 ) ) ),
    inference(cnf,[status(esa)],[1031]) ).

thf(1036,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
      | ( A @ ( A @ ( B @ ( C @ sk7 ) ) @ m1_subset_1 ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
      | ~ ( B @ v1_funct_1 ) ),
    inference(cnfConj,[status(thm)],[1032]) ).

thf(554,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( B @ ( F @ m1_subset_1 ) )
                           => ( ( C @ ( F @ r2_hidden ) )
                             => ( F @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
                       => ( ( E @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
                          | ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_lattice2) ).

thf(4201,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)],[554]) ).

thf(7364,plain,
    ( ( ( sk197 @ v13_lattices )
     != ( sk1 @ v13_lattices ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3001,970]) ).

thf(7365,plain,
    ( ( sk197 @ v13_lattices )
   != ( sk1 @ v13_lattices ) ),
    inference(simp,[status(thm)],[7364]) ).

thf(7373,plain,
    sk197 != sk1,
    inference(simp,[status(thm)],[7365]) ).

thf(257,axiom,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_subset_1) ).

thf(2557,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(2558,plain,
    ! [A: $i] :
      ( ( A @ k1_subset_1 )
      = ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
    inference(cnf,[status(esa)],[2557]) ).

thf(2559,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) )
      = ( A @ k1_subset_1 ) ),
    inference(lifteq,[status(thm)],[2558]) ).

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

thf(2474,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(2475,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = A ),
    inference(cnf,[status(esa)],[2474]) ).

thf(2476,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = A ),
    inference(lifteq,[status(thm)],[2475]) ).

thf(45907,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k3_subset_1 ) )
      = k1_xboole_0 ),
    inference(rewrite,[status(thm)],[2559,2476,3021]) ).

thf(69,axiom,
    ! [A: $i,B: $i] :
      ~ ( ! [C: $i] :
            ( ( ( C @ v1_funct_1 )
              & ( C @ v1_relat_1 ) )
           => ~ ( ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
                & ( B
                  = ( C @ k1_relat_1 ) ) ) )
        & ~ ( ( B != k1_xboole_0 )
            & ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_1) ).

thf(1317,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(1318,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)],[1317]) ).

thf(1319,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ sk25 ) @ k2_relat_1 @ r1_tarski ) )
        | ( B != k1_xboole_0 ) )
      & ( ( B
          = ( A @ ( B @ sk25 ) @ k1_relat_1 ) )
        | ( B != k1_xboole_0 ) )
      & ( ( A @ ( B @ sk25 ) @ v1_funct_1 )
        | ( B != k1_xboole_0 ) )
      & ( ( A @ ( B @ sk25 ) @ v1_relat_1 )
        | ( B != k1_xboole_0 ) )
      & ( ( A @ ( A @ ( B @ sk25 ) @ k2_relat_1 @ r1_tarski ) )
        | ( A = k1_xboole_0 ) )
      & ( ( B
          = ( A @ ( B @ sk25 ) @ k1_relat_1 ) )
        | ( A = k1_xboole_0 ) )
      & ( ( A @ ( B @ sk25 ) @ v1_funct_1 )
        | ( A = k1_xboole_0 ) )
      & ( ( A @ ( B @ sk25 ) @ v1_relat_1 )
        | ( A = k1_xboole_0 ) ) ),
    inference(cnf,[status(esa)],[1318]) ).

thf(1321,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ sk25 ) @ v1_relat_1 )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1319]) ).

thf(1336,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ sk25 ) @ v1_relat_1 )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1321]) ).

thf(1337,plain,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ sk25 ) @ v1_relat_1 ),
    inference(simp,[status(thm)],[1336]) ).

thf(806,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v16_lattices )
              & ( A @ v11_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C
                    = ( B @ ( A @ k7_lattices ) ) )
                <=> ( B @ ( C @ ( A @ r2_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d21_lattices) ).

thf(5469,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)],[806]) ).

thf(501,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ ( B @ v1_filter_0 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( B @ ( C @ r2_hidden ) )
                <=> ~ ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_filter_0) ).

thf(3944,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)],[501]) ).

thf(723,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v13_lattices )
       => ( A @ ( A @ k5_lattices @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m2_filter_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_filter_2) ).

thf(5088,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)],[723]) ).

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

thf(1237,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(1238,plain,
    ! [A: $i] :
      ( ( ( A = k1_xboole_0 )
        | ( ( A @ sk18 )
         != ( A @ sk19 ) ) )
      & ( ( A = k1_xboole_0 )
        | ( ( A @ sk19 @ k1_relat_1 )
          = A ) )
      & ( ( A = k1_xboole_0 )
        | ( ( A @ sk18 @ k1_relat_1 )
          = A ) )
      & ( ( A = k1_xboole_0 )
        | ( A @ sk19 @ v1_funct_1 ) )
      & ( ( A = k1_xboole_0 )
        | ( A @ sk19 @ v1_relat_1 ) )
      & ( ( A = k1_xboole_0 )
        | ( A @ sk18 @ v1_funct_1 ) )
      & ( ( A = k1_xboole_0 )
        | ( A @ sk18 @ v1_relat_1 ) ) ),
    inference(cnf,[status(esa)],[1237]) ).

thf(1243,plain,
    ! [A: $i] :
      ( ( A = k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(cnfConj,[status(thm)],[1238]) ).

thf(1246,plain,
    ! [A: $i] :
      ( ( A @ sk18 @ v1_funct_1 )
      | ( A = k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1243]) ).

thf(29779,plain,
    ! [A: $i] :
      ( ( A != sk197 )
      | ( sk1 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,7373]) ).

thf(29780,plain,
    ( ( sk1 != k1_xboole_0 )
    | ( sk197 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[29779:[bind(A,$thf( sk197 ))]]) ).

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

thf(1369,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(671,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( B @ ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
                       => ! [F: $i] :
                            ( ( C @ ( F @ m1_subset_1 ) )
                           => ( ( D @ ( F @ r2_hidden ) )
                             => ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_lattice2) ).

thf(4835,plain,
    ! [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)],[671]) ).

thf(302,axiom,
    ? [A: $i] :
      ( ( A @ v3_filter_0 )
      & ( A @ v10_lattices )
      & ( A @ v9_lattices )
      & ( A @ v8_lattices )
      & ( A @ v7_lattices )
      & ( A @ v6_lattices )
      & ( A @ v5_lattices )
      & ( A @ v4_lattices )
      & ( A @ v3_lattices )
      & ~ ( A @ v3_struct_0 )
      & ( A @ l3_lattices ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_filter_0) ).

thf(2883,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)],[302]) ).

thf(2884,plain,
    ( ( sk188 @ v3_filter_0 )
    & ( sk188 @ v10_lattices )
    & ( sk188 @ v9_lattices )
    & ( sk188 @ v8_lattices )
    & ( sk188 @ v7_lattices )
    & ( sk188 @ v6_lattices )
    & ( sk188 @ v5_lattices )
    & ( sk188 @ v4_lattices )
    & ( sk188 @ v3_lattices )
    & ~ ( sk188 @ v3_struct_0 )
    & ( sk188 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[2883]) ).

thf(2889,plain,
    sk188 @ v3_lattices,
    inference(cnfConj,[status(thm)],[2884]) ).

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

thf(1187,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(1188,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)],[1187]) ).

thf(1189,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)],[1188]) ).

thf(1190,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ r2_hidden ) )
      | ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) ),
    inference(cnfConj,[status(thm)],[1189]) ).

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

thf(1165,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(1166,plain,
    ! [A: $i] :
      ( ( ~ ( A @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
        | ~ ( sk14 @ ( A @ m1_subset_1 ) ) )
      & ~ ( sk14 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[1165]) ).

thf(1168,plain,
    ! [A: $i] :
      ( ~ ( A @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
      | ~ ( sk14 @ ( A @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[1166]) ).

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/sandbox/benchmark/theBenchmark.p',rc1_lattice2) ).

thf(2341,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(330,axiom,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_relat_1) ).

thf(3051,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(3052,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[3051]) ).

thf(3053,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[3052]) ).

thf(531,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k1_tarski @ r1_tarski ) )
    <=> ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).

thf(4101,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)],[531]) ).

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/sandbox/benchmark/theBenchmark.p',t27_lattice2) ).

thf(2336,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(3008,plain,
    sk197 @ v10_lattices,
    inference(cnfConj,[status(thm)],[2999]) ).

thf(191,axiom,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset_1) ).

thf(2108,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(2109,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
    inference(cnf,[status(esa)],[2108]) ).

thf(568,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ k2_tarski ) )
      = ( A @ k1_tarski ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).

thf(4262,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k2_tarski ) )
      = ( A @ k1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(771,axiom,
    ( ( f3_s11_funct_2 != f4_s11_funct_2 )
   => ? [A: $i] :
        ( ! [B: $i] :
            ( ( f1_s11_funct_2 @ ( B @ m1_subset_1 ) )
           => ~ ( ( ( B @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
                 != ( B @ f7_s11_funct_2 ) )
                & ( B != f4_s11_funct_2 )
                & ( B != f3_s11_funct_2 ) ) )
        & ( ( f4_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
          = f6_s11_funct_2 )
        & ( ( f3_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
          = f5_s11_funct_2 )
        & ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ m2_relset_1 ) ) )
        & ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ v1_funct_2 ) ) )
        & ( A @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s11_funct_2) ).

thf(5321,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)],[771]) ).

thf(5322,plain,
    ! [A: $i] :
      ( ( ( ( A @ ( sk393 @ ( 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 @ ( sk393 @ ( 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 @ ( sk393 @ ( 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 @ ( sk393 @ m2_relset_1 ) ) )
        | ( f3_s11_funct_2 = f4_s11_funct_2 ) )
      & ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk393 @ v1_funct_2 ) ) )
        | ( f3_s11_funct_2 = f4_s11_funct_2 ) )
      & ( ( sk393 @ v1_funct_1 )
        | ( f3_s11_funct_2 = f4_s11_funct_2 ) ) ),
    inference(cnf,[status(esa)],[5321]) ).

thf(5323,plain,
    ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk393 @ m2_relset_1 ) ) )
    | ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
    inference(cnfConj,[status(thm)],[5322]) ).

thf(5329,plain,
    ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk393 @ m2_relset_1 ) ) )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(lifteq,[status(thm)],[5323]) ).

thf(168,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ~ ( B @ ( D @ r2_hidden ) )
                <=> ( C @ ( D @ r2_hidden ) ) ) )
           => ( B
              = ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_subset_1) ).

thf(1995,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(580,axiom,
    ? [A: $i] :
      ( ! [B: $i] :
          ( ( f1_s4_funct_2 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
            = ( B @ f3_s4_funct_2 ) ) )
      & ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ m2_relset_1 ) ) )
      & ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ v1_funct_2 ) ) )
      & ( A @ v1_funct_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_funct_2) ).

thf(4324,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)],[580]) ).

thf(4325,plain,
    ! [A: $i] :
      ( ( ( ( A @ ( sk295 @ ( 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 @ ( sk295 @ m2_relset_1 ) ) )
      & ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ v1_funct_2 ) ) )
      & ( sk295 @ v1_funct_1 ) ),
    inference(cnf,[status(esa)],[4324]) ).

thf(4328,plain,
    f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ),
    inference(cnfConj,[status(thm)],[4325]) ).

thf(348,axiom,
    ? [A: $i] :
      ( ( A @ v1_funct_1 )
      & ( A @ v1_relat_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).

thf(3134,plain,
    ? [A: $i] :
      ( ( A @ v1_funct_1 )
      & ( A @ v1_relat_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(3135,plain,
    ( ( sk207 @ v1_funct_1 )
    & ( sk207 @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[3134]) ).

thf(3137,plain,
    sk207 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[3135]) ).

thf(974,plain,
    sk1 @ v10_lattices,
    inference(cnfConj,[status(thm)],[969]) ).

thf(6446,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)],[1003,974]) ).

thf(6447,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ ( A @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[6446:[bind(A,$thf( sk1 ))]]) ).

thf(6617,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)],[6447]) ).

thf(8190,plain,
    ! [A: $i] :
      ( ( ( sk207 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3137,6617]) ).

thf(8191,plain,
    ! [A: $i] :
      ( ( ( sk207 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8190]) ).

thf(8192,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8191:[bind(A,$thf( sk207 ))]]) ).

thf(12054,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,8192]) ).

thf(12055,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12054]) ).

thf(12116,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk207 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[12055]) ).

thf(468,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ v14_lattices )
           => ( B @ ( A @ k8_filter_0 ) @ v14_lattices ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_filter_0) ).

thf(3798,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)],[468]) ).

thf(589,axiom,
    ? [A: $i] :
      ( ( A @ v17_lattices )
      & ( A @ v16_lattices )
      & ( A @ v15_lattices )
      & ( A @ v14_lattices )
      & ( A @ v13_lattices )
      & ( A @ v11_lattices )
      & ( A @ v10_lattices )
      & ( A @ v9_lattices )
      & ( A @ v8_lattices )
      & ( A @ v7_lattices )
      & ( A @ v6_lattices )
      & ( A @ v5_lattices )
      & ( A @ v4_lattices )
      & ( A @ v3_lattices )
      & ~ ( A @ v3_struct_0 )
      & ( A @ l3_lattices ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc13_lattices) ).

thf(4355,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)],[589]) ).

thf(4356,plain,
    ( ( sk297 @ v17_lattices )
    & ( sk297 @ v16_lattices )
    & ( sk297 @ v15_lattices )
    & ( sk297 @ v14_lattices )
    & ( sk297 @ v13_lattices )
    & ( sk297 @ v11_lattices )
    & ( sk297 @ v10_lattices )
    & ( sk297 @ v9_lattices )
    & ( sk297 @ v8_lattices )
    & ( sk297 @ v7_lattices )
    & ( sk297 @ v6_lattices )
    & ( sk297 @ v5_lattices )
    & ( sk297 @ v4_lattices )
    & ( sk297 @ v3_lattices )
    & ~ ( sk297 @ v3_struct_0 )
    & ( sk297 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[4355]) ).

thf(4370,plain,
    sk297 @ v13_lattices,
    inference(cnfConj,[status(thm)],[4356]) ).

thf(9394,plain,
    ( ( ( sk297 @ v13_lattices )
     != ( sk1 @ v13_lattices ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4370,970]) ).

thf(9395,plain,
    ( ( sk297 @ v13_lattices )
   != ( sk1 @ v13_lattices ) ),
    inference(simp,[status(thm)],[9394]) ).

thf(9409,plain,
    sk297 != sk1,
    inference(simp,[status(thm)],[9395]) ).

thf(33117,plain,
    ! [A: $i] :
      ( ( A != sk297 )
      | ( sk1 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,9409]) ).

thf(33118,plain,
    ( ( sk1 != k1_xboole_0 )
    | ( sk297 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[33117:[bind(A,$thf( sk297 ))]]) ).

thf(916,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k1_lattice4 ) )
            = ( A @ k7_grcat_1 @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_lattice4) ).

thf(5950,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)],[916]) ).

thf(399,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( A @ ( B @ m2_nat_lat ) )
          <=> ( ( ( B @ u1_lattices )
                = ( B @ u1_struct_0 @ ( A @ u1_lattices @ k1_realset1 ) ) )
              & ( ( B @ u2_lattices )
                = ( B @ u1_struct_0 @ ( A @ u2_lattices @ k1_realset1 ) ) )
              & ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_nat_lat) ).

thf(3434,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)],[399]) ).

thf(301,axiom,
    ? [A: $i] :
      ( ( A @ v15_lattices )
      & ( A @ v14_lattices )
      & ( A @ v13_lattices )
      & ( A @ v10_lattices )
      & ( A @ v9_lattices )
      & ( A @ v8_lattices )
      & ( A @ v7_lattices )
      & ( A @ v6_lattices )
      & ( A @ v5_lattices )
      & ( A @ v4_lattices )
      & ( A @ v3_lattices )
      & ~ ( A @ v3_struct_0 )
      & ( A @ l3_lattices ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc11_lattices) ).

thf(2868,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)],[301]) ).

thf(2869,plain,
    ( ( sk187 @ v15_lattices )
    & ( sk187 @ v14_lattices )
    & ( sk187 @ v13_lattices )
    & ( sk187 @ v10_lattices )
    & ( sk187 @ v9_lattices )
    & ( sk187 @ v8_lattices )
    & ( sk187 @ v7_lattices )
    & ( sk187 @ v6_lattices )
    & ( sk187 @ v5_lattices )
    & ( sk187 @ v4_lattices )
    & ( sk187 @ v3_lattices )
    & ~ ( sk187 @ v3_struct_0 )
    & ( sk187 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[2868]) ).

thf(2876,plain,
    sk187 @ v14_lattices,
    inference(cnfConj,[status(thm)],[2869]) ).

thf(407,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
     => ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_zfmisc_1) ).

thf(3477,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(443,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
     => ( ( D @ ( A @ r1_tarski ) )
       => ( C @ ( B @ ( A @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_relset_1) ).

thf(3698,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)],[443]) ).

thf(784,axiom,
    ( ( k6_nat_lat @ l3_lattices )
    & ( k6_nat_lat @ v13_lattices )
    & ( k6_nat_lat @ v10_lattices )
    & ~ ( k6_nat_lat @ v3_struct_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_nat_lat) ).

thf(5386,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)],[784]) ).

thf(5387,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)],[5386]) ).

thf(5390,plain,
    k6_nat_lat @ v13_lattices,
    inference(cnfConj,[status(thm)],[5387]) ).

thf(146,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relat_1) ).

thf(1899,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(853,axiom,
    ! [A: $i] :
      ( ( a_0_1_domain_1 @ ( A @ r2_hidden ) )
    <=> ? [B: $i] :
          ( ( B @ p1_s8_domain_1 )
          & ( A
            = ( B @ f3_s8_domain_1 ) )
          & ( f1_s8_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_1_domain_1) ).

thf(5654,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)],[853]) ).

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/sandbox/benchmark/theBenchmark.p',t26_relset_1) ).

thf(2595,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(514,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_lattices @ ( A @ k6_lattices @ ( A @ u1_struct_0 @ r3_binop_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_lattice2) ).

thf(4015,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)],[514]) ).

thf(948,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v3_filter_0 )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ? [D: $i] :
                    ( ! [E: $i] :
                        ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                       => ( ( C @ ( E @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
                         => ( D @ ( E @ ( A @ r1_lattices ) ) ) ) )
                    & ( C @ ( D @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) )
                    & ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_filter_0) ).

thf(6074,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)],[948]) ).

thf(1924,plain,
    sk71 @ v1_xboole_0,
    inference(cnfConj,[status(thm)],[1920]) ).

thf(6261,plain,
    ( ( ( sk218 @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1924,3255]) ).

thf(6262,plain,
    ( ( sk218 @ v1_xboole_0 )
   != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6261]) ).

thf(6263,plain,
    sk218 != sk71,
    inference(simp,[status(thm)],[6262]) ).

thf(706,axiom,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finsub_1) ).

thf(5027,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(5028,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
    inference(cnf,[status(esa)],[5027]) ).

thf(959,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k14_filter_2 ) @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_filter_2) ).

thf(6142,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)],[959]) ).

thf(942,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_filter_2 )
        = ( A @ k1_filter_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_filter_2) ).

thf(6057,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)],[942]) ).

thf(438,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_filter_0 ) )
        & ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k7_filter_0 ) ) )
        = ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_filter_0) ).

thf(3681,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)],[438]) ).

thf(615,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( B @ ( D @ m1_subset_1 ) )
               => ( C @ ( D @ r2_hidden ) ) )
           => ( C @ ( B @ r1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_subset_1) ).

thf(4515,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)],[615]) ).

thf(245,axiom,
    ? [A: $i] :
      ( ( A @ v2_funct_1 )
      & ( A @ v1_funct_1 )
      & ( A @ v1_relat_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).

thf(2469,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(2470,plain,
    ( ( sk138 @ v2_funct_1 )
    & ( sk138 @ v1_funct_1 )
    & ( sk138 @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[2469]) ).

thf(2472,plain,
    sk138 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[2470]) ).

thf(6901,plain,
    ! [A: $i] :
      ( ( ( sk138 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2472,6622]) ).

thf(6902,plain,
    ! [A: $i] :
      ( ( ( sk138 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[6901]) ).

thf(6903,plain,
    ( ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[6902:[bind(A,$thf( sk138 ))]]) ).

thf(10668,plain,
    ( ( ( k6_nat_lat @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5390,6903]) ).

thf(10669,plain,
    ( ( ( k6_nat_lat @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[10668]) ).

thf(10679,plain,
    ( ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[10669]) ).

thf(3012,plain,
    sk197 @ v3_lattices,
    inference(cnfConj,[status(thm)],[2999]) ).

thf(189,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ! [E: $i,F: $i] :
            ~ ( ( D
                = ( F @ ( E @ k4_tarski ) ) )
              & ( C @ ( F @ r2_hidden ) )
              & ( B @ ( E @ r2_hidden ) ) )
        & ( A @ ( D @ r2_hidden ) )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).

thf(2099,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(294,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( ( B @ v2_funct_1 )
       => ! [C: $i,D: $i] :
            ( ( ( ( C @ ( B @ k1_funct_1 ) )
                = ( D @ ( B @ k1_funct_1 ) ) )
              & ( A @ ( D @ r2_hidden ) )
              & ( A @ ( C @ r2_hidden ) ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_2) ).

thf(2837,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)],[294]) ).

thf(608,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m3_lattice4 ) )
         => ( A @ ( B @ m2_lattice4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_lattice4) ).

thf(4487,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)],[608]) ).

thf(436,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( B @ v1_xboole_0 )
      & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).

thf(3673,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)],[436]) ).

thf(3674,plain,
    ! [A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
      & ( A @ k1_zfmisc_1 @ ( A @ sk249 @ m1_subset_1 ) ) ),
    inference(cnf,[status(esa)],[3673]) ).

thf(3676,plain,
    ! [A: $i] : ( A @ sk249 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[3674]) ).

thf(1167,plain,
    ~ ( sk14 @ v1_xboole_0 ),
    inference(cnfConj,[status(thm)],[1166]) ).

thf(12941,plain,
    ! [A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( sk14 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3676,1167]) ).

thf(12942,plain,
    ! [A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( sk14 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[12941]) ).

thf(12949,plain,
    ! [A: $i] :
      ( ( A @ sk249 )
     != sk14 ),
    inference(simp,[status(thm)],[12942]) ).

thf(591,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_5_domain_1 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ( ~ ( C @ ( E @ r2_hidden ) )
            <=> ( D @ ( E @ r2_hidden ) ) )
            & ( A = E )
            & ( B @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_5_domain_1) ).

thf(4376,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)],[591]) ).

thf(80,axiom,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
     => ! [B: $i] :
        ? [C: $i] :
          ( ( ( C @ k2_relat_1 )
            = ( B @ k1_tarski ) )
          & ( ( C @ k1_relat_1 )
            = A )
          & ( C @ v1_funct_1 )
          & ( C @ v1_relat_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_1) ).

thf(1406,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(753,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ k1_lattice2 @ ( B @ ( A @ k13_filter_2 ) @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_filter_2) ).

thf(5225,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)],[753]) ).

thf(892,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v9_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
                  = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattices) ).

thf(5820,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)],[892]) ).

thf(584,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).

thf(4339,plain,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(1921,plain,
    sk71 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[1920]) ).

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

thf(998,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(999,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)],[998]) ).

thf(6343,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk71 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1921,999]) ).

thf(6344,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk71 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[6343]) ).

thf(6345,plain,
    ! [A: $i] : ( sk71 @ k1_relat_1 @ ( sk71 @ k9_relat_1 ) @ ( A @ ( sk71 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[6344:[bind(A,$thf( A )),bind(B,$thf( sk71 ))]]) ).

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

thf(1084,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(1085,plain,
    ! [A: $i] :
      ( ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) )
      | ~ ( A @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[1084]) ).

thf(1086,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_relat_1 )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(lifteq,[status(thm)],[1085]) ).

thf(15472,plain,
    ! [A: $i] :
      ( ( ( sk71 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ~ $true
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[1921,1086]) ).

thf(15473,plain,
    ! [A: $i] :
      ( ( ( sk71 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[15472]) ).

thf(15474,plain,
    ( ( sk71 @ k1_relat_1 @ ( sk71 @ k9_relat_1 ) )
    = ( sk71 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15473:[bind(A,$thf( sk71 ))]]) ).

thf(19093,plain,
    ! [A: $i] : ( sk71 @ k2_relat_1 @ ( A @ ( sk71 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[6345,15474]) ).

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

thf(1028,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(1029,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ! [C: $i] : ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(miniscope,[status(thm)],[1028]) ).

thf(1030,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ ( B @ ( A @ r1_tarski ) ) ),
    inference(cnf,[status(esa)],[1029]) ).

thf(19121,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk71 @ k2_relat_1 @ ( A @ ( sk71 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[19093,1030]) ).

thf(19122,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk71 @ k2_relat_1 @ ( A @ ( sk71 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[19121]) ).

thf(19123,plain,
    ! [B: $i,A: $i] : ( sk71 @ k2_relat_1 @ ( A @ ( B @ ( sk71 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[19122:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk71 @ k9_relat_1 ) )),bind(C,$thf( sk71 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(19142,plain,
    ! [B: $i,A: $i] : ( sk71 @ k2_relat_1 @ ( A @ ( B @ ( sk71 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[19123]) ).

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

thf(1882,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(965,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ? [B: $i] : ( A @ ( B @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_filter_0) ).

thf(6162,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)],[965]) ).

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

thf(1068,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(479,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
              = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
           => ! [C: $i] :
                ( ( A @ ( C @ m1_filter_2 ) )
               => ( B @ ( C @ m1_filter_2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_filter_2) ).

thf(3858,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)],[479]) ).

thf(472,axiom,
    ! [A: $i] :
      ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(3813,plain,
    ! [A: $i] :
      ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

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/sandbox/benchmark/theBenchmark.p',t41_zfmisc_1) ).

thf(2381,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(852,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v12_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( D @ ( B @ ( A @ r1_lattices ) ) )
                     => ( ( D @ ( C @ ( A @ k2_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
                        = ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k2_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_lattices) ).

thf(5644,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)],[852]) ).

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/sandbox/benchmark/theBenchmark.p',t69_partfun1) ).

thf(2395,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(181,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( B @ ( C @ k9_relat_1 ) )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_partfun1) ).

thf(2062,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(757,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k8_filter_2 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_filter_2) ).

thf(5242,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)],[757]) ).

thf(208,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_1) ).

thf(2221,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(2222,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
    inference(cnf,[status(esa)],[2221]) ).

thf(9400,plain,
    ( ( ( sk297 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4370,6903]) ).

thf(9401,plain,
    ( ( ( sk297 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9400]) ).

thf(9404,plain,
    ( ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9401]) ).

thf(16127,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( sk297 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,9404]) ).

thf(16128,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( sk297 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16127]) ).

thf(16241,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk138 != k1_xboole_0 )
      | ( sk297 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16128]) ).

thf(16308,plain,
    ( ( sk138 != k1_xboole_0 )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16241]) ).

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

thf(1618,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(4,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ v1_funct_1 )
        & ( C @ v1_relat_1 ) )
     => ( ( ! [D: $i] :
              ( ( A @ ( D @ r2_hidden ) )
             => ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
          & ( ( C @ k1_relat_1 )
            = A ) )
       => ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
          & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
          & ( C @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_funct_2) ).

thf(984,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(985,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        | ~ ( B @ ( A @ ( C @ sk3 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( C @ v1_relat_1 ) )
      & ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        | ~ ( B @ ( A @ ( C @ sk3 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( C @ v1_relat_1 ) )
      & ( ( C @ v1_funct_1 )
        | ~ ( B @ ( A @ ( C @ sk3 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( C @ v1_relat_1 ) )
      & ( ( B @ ( A @ ( C @ sk3 ) ) )
        | ~ ( B @ ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ k1_funct_1 ) @ r2_hidden ) )
        | ( ( C @ k1_relat_1 )
         != A )
        | ~ ( C @ v1_funct_1 )
        | ~ ( C @ v1_relat_1 ) )
      & ( ( B @ ( A @ ( C @ sk3 ) ) )
        | ( A @ ( A @ ( B @ ( C @ sk4 ) ) @ r2_hidden ) )
        | ( ( C @ k1_relat_1 )
         != A )
        | ~ ( C @ v1_funct_1 )
        | ~ ( C @ v1_relat_1 ) ) ),
    inference(cnf,[status(esa)],[984]) ).

thf(990,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ sk3 ) ) )
      | ~ ( B @ ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ k1_funct_1 ) @ r2_hidden ) )
      | ( ( C @ k1_relat_1 )
       != A )
      | ~ ( C @ v1_funct_1 )
      | ~ ( C @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[985]) ).

thf(993,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ sk3 ) ) )
      | ~ ( B @ ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ k1_funct_1 ) @ r2_hidden ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( C @ v1_relat_1 )
      | ( ( C @ k1_relat_1 )
       != A ) ),
    inference(lifteq,[status(thm)],[990]) ).

thf(994,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k1_relat_1 @ ( B @ sk3 ) ) )
      | ~ ( A @ ( B @ k1_relat_1 @ ( A @ ( B @ sk4 ) ) @ ( B @ k1_funct_1 ) @ r2_hidden ) )
      | ~ ( B @ v1_funct_1 )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[993]) ).

thf(253,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).

thf(2527,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(4371,plain,
    sk297 @ v4_lattices,
    inference(cnfConj,[status(thm)],[4356]) ).

thf(30124,plain,
    ! [A: $i] :
      ( ( A != sk297 )
      | ( k1_xboole_0 @ v4_lattices )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,4371]) ).

thf(30125,plain,
    ( ( k1_xboole_0 @ v4_lattices )
    | ( sk297 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[30124:[bind(A,$thf( sk297 ))]]) ).

thf(340,axiom,
    ( ( k1_xboole_0 @ v1_relat_1 )
    & ( k1_xboole_0 @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).

thf(3095,plain,
    ( ( k1_xboole_0 @ v1_relat_1 )
    & ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(3096,plain,
    ( ( k1_xboole_0 @ v1_relat_1 )
    & ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[3095]) ).

thf(3098,plain,
    k1_xboole_0 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[3096]) ).

thf(9388,plain,
    ( ( ( sk297 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4370,6900]) ).

thf(9389,plain,
    ( ( ( sk297 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9388]) ).

thf(9410,plain,
    ( ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9389]) ).

thf(16053,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( sk297 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,9410]) ).

thf(16054,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( sk297 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16053]) ).

thf(16216,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk71 != k1_xboole_0 )
      | ( sk297 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16054]) ).

thf(16280,plain,
    ( ( sk71 != k1_xboole_0 )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16216]) ).

thf(4263,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k2_tarski ) )
      = ( A @ k1_tarski ) ),
    inference(cnf,[status(esa)],[4262]) ).

thf(4264,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k2_tarski ) )
      = ( A @ k1_tarski ) ),
    inference(lifteq,[status(thm)],[4263]) ).

thf(583,axiom,
    ! [A: $i,B: $i] :
      ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).

thf(4336,plain,
    ! [A: $i,B: $i] :
      ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(4337,plain,
    ~ ? [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[4336]) ).

thf(4338,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[4337]) ).

thf(15636,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( C @ ( B @ k2_tarski ) @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3676,4338]) ).

thf(15637,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( C @ ( B @ k2_tarski ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[15636]) ).

thf(15650,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk249 )
     != ( C @ ( B @ k2_tarski ) ) ),
    inference(simp,[status(thm)],[15637]) ).

thf(29194,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ k2_tarski ) )
       != ( D @ ( C @ k2_tarski ) ) )
      | ( ( A @ k1_tarski )
       != ( B @ sk249 ) ) ),
    inference(paramod_ordered,[status(thm)],[4264,15650]) ).

thf(29195,plain,
    ! [B: $i,A: $i] :
      ( ( A @ k1_tarski )
     != ( B @ sk249 ) ),
    inference(pattern_uni,[status(thm)],[29194:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).

thf(22,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = k1_xboole_0 )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_zfmisc_1) ).

thf(1071,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(1072,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
       != k1_xboole_0 ) ),
    inference(cnf,[status(esa)],[1071]) ).

thf(1073,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
       != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1072]) ).

thf(280,axiom,
    ? [A: $i] :
      ( ( A @ v14_lattices )
      & ( A @ v13_lattices )
      & ( A @ v12_lattices )
      & ( A @ v11_lattices )
      & ( A @ v10_lattices )
      & ( A @ v9_lattices )
      & ( A @ v8_lattices )
      & ( A @ v7_lattices )
      & ( A @ v6_lattices )
      & ( A @ v5_lattices )
      & ( A @ v4_lattices )
      & ( A @ v3_lattices )
      & ~ ( A @ v3_struct_0 )
      & ( A @ l3_lattices ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc10_lattices) ).

thf(2660,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)],[280]) ).

thf(2661,plain,
    ( ( sk157 @ v14_lattices )
    & ( sk157 @ v13_lattices )
    & ( sk157 @ v12_lattices )
    & ( sk157 @ v11_lattices )
    & ( sk157 @ v10_lattices )
    & ( sk157 @ v9_lattices )
    & ( sk157 @ v8_lattices )
    & ( sk157 @ v7_lattices )
    & ( sk157 @ v6_lattices )
    & ( sk157 @ v5_lattices )
    & ( sk157 @ v4_lattices )
    & ( sk157 @ v3_lattices )
    & ~ ( sk157 @ v3_struct_0 )
    & ( sk157 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[2660]) ).

thf(2671,plain,
    sk157 @ v5_lattices,
    inference(cnfConj,[status(thm)],[2661]) ).

thf(281,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_tarski ) )
    <=> ? [C: $i] :
          ( ! [D: $i,E: $i,F: $i,G: $i] :
              ( ( ( C @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
                & ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
             => ( ( D = F )
              <=> ( E = G ) ) )
          & ! [D: $i] :
              ~ ( ! [E: $i] :
                    ~ ( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
                      & ( A @ ( E @ r2_hidden ) ) )
                & ( B @ ( D @ r2_hidden ) ) )
          & ! [D: $i] :
              ~ ( ! [E: $i] :
                    ~ ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
                      & ( B @ ( E @ r2_hidden ) ) )
                & ( A @ ( D @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_tarski) ).

thf(2676,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)],[281]) ).

thf(329,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
    <=> ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).

thf(3043,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)],[329]) ).

thf(3044,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)],[3043]) ).

thf(3045,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)],[3044]) ).

thf(3047,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[3045]) ).

thf(3049,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[3047]) ).

thf(3050,plain,
    k1_xboole_0 @ v1_xboole_0,
    inference(simp,[status(thm)],[3049]) ).

thf(818,axiom,
    ! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_subset_1) ).

thf(5528,plain,
    ! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(5529,plain,
    ! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
    inference(cnf,[status(esa)],[5528]) ).

thf(46816,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) )
       != ( sk14 @ ( B @ m1_subset_1 ) ) )
      | ~ ( B @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5529,1168]) ).

thf(46817,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) )
       != ( sk14 @ ( B @ m1_subset_1 ) ) )
      | ~ ( B @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[46816]) ).

thf(46818,plain,
    ~ ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[46817:[bind(A,$thf( sk14 )),bind(B,$thf( sk14 @ k8_subset_1 ))]]) ).

thf(46972,plain,
    ( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3050,46818]) ).

thf(46973,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[46972]) ).

thf(47031,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != k1_xboole_0 ),
    inference(simp,[status(thm)],[46973]) ).

thf(48317,plain,
    ! [A: $i] :
      ( ( A
       != ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,47031]) ).

thf(48318,plain,
    ! [A: $i] :
      ( ( A
       != ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[48317]) ).

thf(48319,plain,
    sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ sk18 @ v1_funct_1,
    inference(pattern_uni,[status(thm)],[48318:[bind(A,$thf( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ))]]) ).

thf(342,axiom,
    ( ( k6_nat_lat @ v10_lattices )
    & ( k6_nat_lat @ v9_lattices )
    & ( k6_nat_lat @ v8_lattices )
    & ( k6_nat_lat @ v7_lattices )
    & ( k6_nat_lat @ v6_lattices )
    & ( k6_nat_lat @ v5_lattices )
    & ( k6_nat_lat @ v4_lattices )
    & ( k6_nat_lat @ v3_lattices )
    & ~ ( k6_nat_lat @ v3_struct_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_nat_lat) ).

thf(3102,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)],[342]) ).

thf(3103,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)],[3102]) ).

thf(3108,plain,
    k6_nat_lat @ v7_lattices,
    inference(cnfConj,[status(thm)],[3103]) ).

thf(4326,plain,
    sk295 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[4325]) ).

thf(331,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_2) ).

thf(3054,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(3055,plain,
    ~ ? [A: $i] : ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[3054]) ).

thf(3056,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[3055]) ).

thf(15320,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( sk278 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4083,3056]) ).

thf(15321,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( sk278 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[15320]) ).

thf(15325,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != sk278 ),
    inference(simp,[status(thm)],[15321]) ).

thf(162,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( A @ ( C @ k9_relat_1 ) )
        = ( C @ k2_relat_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_partfun1) ).

thf(1971,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(862,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v13_lattices )
      <=> ( A @ k1_lattice2 @ v14_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_lattice2) ).

thf(5691,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)],[862]) ).

thf(8207,plain,
    ! [A: $i] :
      ( ( ( sk207 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3137,6622]) ).

thf(8208,plain,
    ! [A: $i] :
      ( ( ( sk207 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8207]) ).

thf(8209,plain,
    ( ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8208:[bind(A,$thf( sk207 ))]]) ).

thf(8896,plain,
    ( ( ( sk197 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3001,8209]) ).

thf(8897,plain,
    ( ( ( sk197 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8896]) ).

thf(8928,plain,
    ( ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8897]) ).

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

thf(1992,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(1993,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
      = ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
    inference(cnf,[status(esa)],[1992]) ).

thf(1994,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
      = ( A @ k1_tarski @ k1_zfmisc_1 ) ),
    inference(lifteq,[status(thm)],[1993]) ).

thf(15638,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3050,4338]) ).

thf(15639,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[15638]) ).

thf(15652,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[15639]) ).

thf(27678,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)],[1994,15652]) ).

thf(27679,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[27678:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(27696,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[27679]) ).

thf(1037,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
      | ( ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
       != ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
      | ( ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) )
       != ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
      | ~ ( B @ v1_funct_1 ) ),
    inference(cnfConj,[status(thm)],[1032]) ).

thf(1041,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
      | ~ ( B @ v1_funct_1 )
      | ( ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
       != ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
      | ( ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( C @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) )
       != ( A @ ( B @ ( C @ sk9 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( A @ ( B @ ( C @ sk8 ) ) @ ( A @ ( B @ ( C @ sk7 ) ) @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ),
    inference(lifteq,[status(thm)],[1037]) ).

thf(388,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
     => ( B @ v1_finset_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finsub_1) ).

thf(3382,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)],[388]) ).

thf(361,axiom,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_subset_1) ).

thf(3217,plain,
    ! [A: $i] :
      ( ( A @ k2_subset_1 )
      = ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(466,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).

thf(3794,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(500,axiom,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_zfmisc_1) ).

thf(3942,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(41,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ v1_relat_1 )
     => ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
          & ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
       => ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_relset_1) ).

thf(1163,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(1164,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)],[1163]) ).

thf(31368,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,970]) ).

thf(31369,plain,
    ( ~ ( k1_xboole_0 @ v13_lattices )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[31368:[bind(A,$thf( sk1 ))]]) ).

thf(305,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ~ ( ! [E: $i] :
              ~ ( ( ( E @ ( D @ k1_funct_1 ) )
                  = C )
                & ( A @ ( E @ r2_hidden ) ) )
          & ( ( D @ k2_relat_1 )
            = B )
          & ( B @ ( C @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_2) ).

thf(2901,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)],[305]) ).

thf(487,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
    <=> ( ( C @ ( B @ r2_hidden ) )
        & ( C @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).

thf(3895,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)],[487]) ).

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

thf(2585,plain,
    ? [A: $i] :
      ( ( A @ v1_relat_1 )
      & ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(2586,plain,
    ( ( sk152 @ v1_relat_1 )
    & ( sk152 @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[2585]) ).

thf(2587,plain,
    sk152 @ v1_xboole_0,
    inference(cnfConj,[status(thm)],[2586]) ).

thf(6275,plain,
    ( ( ( sk218 @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2587,3255]) ).

thf(6276,plain,
    ( ( sk218 @ v1_xboole_0 )
   != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6275]) ).

thf(6278,plain,
    sk218 != sk152,
    inference(simp,[status(thm)],[6276]) ).

thf(560,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( ( C @ ( B @ k1_tarski @ ( A @ k5_partfun1 ) ) )
            = ( D @ k1_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t164_funct_2) ).

thf(4234,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)],[560]) ).

thf(2588,plain,
    sk152 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[2586]) ).

thf(6351,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk152 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2588,999]) ).

thf(6352,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk152 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[6351]) ).

thf(6353,plain,
    ! [A: $i] : ( sk152 @ k1_relat_1 @ ( sk152 @ k9_relat_1 ) @ ( A @ ( sk152 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[6352:[bind(A,$thf( A )),bind(B,$thf( sk152 ))]]) ).

thf(15492,plain,
    ! [A: $i] :
      ( ( ( sk152 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ~ $true
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[2588,1086]) ).

thf(15493,plain,
    ! [A: $i] :
      ( ( ( sk152 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[15492]) ).

thf(15494,plain,
    ( ( sk152 @ k1_relat_1 @ ( sk152 @ k9_relat_1 ) )
    = ( sk152 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15493:[bind(A,$thf( sk152 ))]]) ).

thf(23383,plain,
    ! [A: $i] : ( sk152 @ k2_relat_1 @ ( A @ ( sk152 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[6353,15494]) ).

thf(23422,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk152 @ k2_relat_1 @ ( A @ ( sk152 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23383,1030]) ).

thf(23423,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk152 @ k2_relat_1 @ ( A @ ( sk152 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[23422]) ).

thf(23424,plain,
    ! [B: $i,A: $i] : ( sk152 @ k2_relat_1 @ ( A @ ( B @ ( sk152 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[23423:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk152 @ k9_relat_1 ) )),bind(C,$thf( sk152 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(23438,plain,
    ! [B: $i,A: $i] : ( sk152 @ k2_relat_1 @ ( A @ ( B @ ( sk152 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[23424]) ).

thf(112,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_funct_1 )
        & ( B @ v1_relat_1 ) )
     => ( ( ( B @ k1_relat_1 )
          = ( A @ k1_tarski ) )
       => ( ( B @ k2_relat_1 )
          = ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_1) ).

thf(1655,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(344,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ! [B: $i] :
          ( ( B @ v1_relat_1 )
         => ( ( B @ ( A @ r1_tarski ) )
          <=> ! [C: $i,D: $i] :
                ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
               => ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).

thf(3120,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)],[344]) ).

thf(831,axiom,
    ? [A: $i] :
      ( ~ ( A @ v3_struct_0 )
      & ( A @ l2_struct_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_struct_0) ).

thf(5562,plain,
    ? [A: $i] :
      ( ~ ( A @ v3_struct_0 )
      & ( A @ l2_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(5563,plain,
    ( ~ ( sk410 @ v3_struct_0 )
    & ( sk410 @ l2_struct_0 ) ),
    inference(cnf,[status(esa)],[5562]) ).

thf(5565,plain,
    ~ ( sk410 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[5563]) ).

thf(458,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( C @ v1_relat_1 )
             => ( ( C
                  = ( B @ ( A @ k10_filter_0 ) ) )
              <=> ( ! [D: $i] :
                      ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                     => ! [E: $i] :
                          ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                         => ( ( C @ ( E @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) )
                          <=> ( B @ ( E @ ( D @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) )
                  & ( A @ u1_struct_0 @ ( C @ k3_relat_1 @ r1_tarski ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_filter_0) ).

thf(3745,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)],[458]) ).

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

thf(1137,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(147,axiom,
    ( ( k1_xboole_0 @ k1_zfmisc_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).

thf(1901,plain,
    ( ( k1_xboole_0 @ k1_zfmisc_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(1902,plain,
    ( ( k1_xboole_0 @ k1_zfmisc_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(lifteq,[status(thm)],[1901]) ).

thf(3814,plain,
    ~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[3813]) ).

thf(3815,plain,
    ! [A: $i] :
      ~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[3814]) ).

thf(8638,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( sk278 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4083,3815]) ).

thf(8639,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( sk278 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8638]) ).

thf(8642,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != sk278 ),
    inference(simp,[status(thm)],[8639]) ).

thf(11398,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ( ( k1_xboole_0 @ k1_tarski )
       != sk278 ) ),
    inference(paramod_ordered,[status(thm)],[1902,8642]) ).

thf(11399,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != sk278 ),
    inference(pattern_uni,[status(thm)],[11398:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(906,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k8_filter_2 ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_filter_2) ).

thf(5906,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)],[906]) ).

thf(3004,plain,
    sk197 @ v4_lattices,
    inference(cnfConj,[status(thm)],[2999]) ).

thf(672,axiom,
    ? [A: $i] :
      ~ ( A @ v1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(4837,plain,
    ? [A: $i] :
      ~ ( A @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(4838,plain,
    ~ ! [A: $i] : ( A @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[4837]) ).

thf(4839,plain,
    ~ ( sk341 @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[4838]) ).

thf(15632,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
       != ( sk71 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1924,4338]) ).

thf(15633,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[15632]) ).

thf(15651,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) )
     != sk71 ),
    inference(simp,[status(thm)],[15633]) ).

thf(24,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
     => ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
        & ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).

thf(1077,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(1078,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)],[1077]) ).

thf(1080,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
      | ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ),
    inference(cnfConj,[status(thm)],[1078]) ).

thf(14757,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
       != ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
      | ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,1080]) ).

thf(14758,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
       != ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
      | ( B @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14757]) ).

thf(14759,plain,
    f2_s4_funct_2 @ ( sk295 @ k2_relat_1 @ r1_tarski ),
    inference(pattern_uni,[status(thm)],[14758:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk295 ))]]) ).

thf(14780,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( sk295 @ k2_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[14759,1030]) ).

thf(14781,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( sk295 @ k2_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14780]) ).

thf(14782,plain,
    ! [A: $i] : ( f2_s4_funct_2 @ ( A @ ( sk295 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[14781:[bind(A,$thf( sk295 @ k2_relat_1 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( C ))]]) ).

thf(14795,plain,
    ! [A: $i] : ( f2_s4_funct_2 @ ( A @ ( sk295 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[14782]) ).

thf(15197,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( A @ ( sk295 @ 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)],[14795,1030]) ).

thf(15198,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( A @ ( sk295 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15197]) ).

thf(15199,plain,
    ! [B: $i,A: $i] : ( f2_s4_funct_2 @ ( A @ ( B @ ( sk295 @ k2_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[15198:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk295 @ k2_relat_1 @ k4_xboole_0 ) )),bind(C,$thf( f2_s4_funct_2 )),bind(D,$thf( D ))]]) ).

thf(15217,plain,
    ! [B: $i,A: $i] : ( f2_s4_funct_2 @ ( A @ ( B @ ( sk295 @ k2_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[15199]) ).

thf(183,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ! [C: $i] :
          ~ ( ~ ( B @ ( C @ r2_hidden ) )
            & ~ ( B @ ( C @ r2_tarski ) )
            & ( B @ ( C @ r1_tarski ) ) )
      & ! [C: $i] :
          ~ ( ! [D: $i] :
                ~ ( ! [E: $i] :
                      ( ( C @ ( E @ r1_tarski ) )
                     => ( D @ ( E @ r2_hidden ) ) )
                  & ( B @ ( D @ r2_hidden ) ) )
            & ( B @ ( C @ r2_hidden ) ) )
      & ! [C: $i,D: $i] :
          ( ( ( C @ ( D @ r1_tarski ) )
            & ( B @ ( C @ r2_hidden ) ) )
         => ( B @ ( D @ r2_hidden ) ) )
      & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).

thf(2067,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(2068,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)],[2067]) ).

thf(2069,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ sk80 @ ( F @ r2_hidden ) )
        | ( A @ sk80 @ ( F @ r2_tarski ) )
        | ~ ( A @ sk80 @ ( F @ r1_tarski ) ) )
      & ( ( A @ ( D @ sk81 ) @ ( E @ r2_hidden ) )
        | ~ ( D @ ( E @ r1_tarski ) )
        | ~ ( A @ sk80 @ ( D @ r2_hidden ) ) )
      & ( ( A @ sk80 @ ( A @ ( D @ sk81 ) @ r2_hidden ) )
        | ~ ( A @ sk80 @ ( D @ r2_hidden ) ) )
      & ( ( A @ sk80 @ ( C @ r2_hidden ) )
        | ~ ( B @ ( C @ r1_tarski ) )
        | ~ ( A @ sk80 @ ( B @ r2_hidden ) ) )
      & ( A @ sk80 @ ( A @ r2_hidden ) ) ),
    inference(cnf,[status(esa)],[2068]) ).

thf(2071,plain,
    ! [A: $i] : ( A @ sk80 @ ( A @ r2_hidden ) ),
    inference(cnfConj,[status(thm)],[2069]) ).

thf(316,axiom,
    ! [A: $i] :
      ( ( A = k1_xboole_0 )
    <=> ! [B: $i] :
          ~ ( A @ ( B @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).

thf(2955,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)],[316]) ).

thf(2956,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)],[2955]) ).

thf(2957,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C = k1_xboole_0 )
        | ( C @ ( C @ sk195 @ r2_hidden ) ) )
      & ( ~ ( A @ ( B @ r2_hidden ) )
        | ( A != k1_xboole_0 ) ) ),
    inference(cnf,[status(esa)],[2956]) ).

thf(2958,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ r2_hidden ) )
      | ( A != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[2957]) ).

thf(2960,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ r2_hidden ) )
      | ( A != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[2958]) ).

thf(2961,plain,
    ! [A: $i] :
      ~ ( k1_xboole_0 @ ( A @ r2_hidden ) ),
    inference(simp,[status(thm)],[2960]) ).

thf(15291,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk80 @ ( A @ r2_hidden ) )
       != ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2071,2961]) ).

thf(15292,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk80 @ ( A @ r2_hidden ) )
     != ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[15291]) ).

thf(15297,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk80 )
       != k1_xboole_0 )
      | ( A != B ) ),
    inference(simp,[status(thm)],[15292]) ).

thf(15299,plain,
    ! [A: $i] :
      ( ( A @ sk80 )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[15297]) ).

thf(2672,plain,
    sk157 @ v13_lattices,
    inference(cnfConj,[status(thm)],[2661]) ).

thf(6953,plain,
    ( ( ( sk157 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2672,6900]) ).

thf(6954,plain,
    ( ( ( sk157 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[6953]) ).

thf(6955,plain,
    ( ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[6954]) ).

thf(16104,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( sk157 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,6955]) ).

thf(16105,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( sk157 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16104]) ).

thf(16219,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk71 != k1_xboole_0 )
      | ( sk157 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16105]) ).

thf(16283,plain,
    ( ( sk71 != k1_xboole_0 )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16219]) ).

thf(634,axiom,
    ? [A: $i] : ( A @ l1_lattices ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_lattices) ).

thf(4638,plain,
    ? [A: $i] : ( A @ l1_lattices ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(736,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ? [B: $i] : ( A @ ( B @ m1_filter_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_filter_2) ).

thf(5146,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)],[736]) ).

thf(366,axiom,
    ? [A: $i] :
      ( ( A @ v1_funct_1 )
      & ( A @ v1_xboole_0 )
      & ( A @ v1_relat_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).

thf(3241,plain,
    ? [A: $i] :
      ( ( A @ v1_funct_1 )
      & ( A @ v1_xboole_0 )
      & ( A @ v1_relat_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(3242,plain,
    ( ( sk216 @ v1_funct_1 )
    & ( sk216 @ v1_xboole_0 )
    & ( sk216 @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[3241]) ).

thf(3244,plain,
    sk216 @ v1_xboole_0,
    inference(cnfConj,[status(thm)],[3242]) ).

thf(8360,plain,
    ( ( ( sk216 @ v1_xboole_0 )
     != ( sk14 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3244,1167]) ).

thf(8361,plain,
    ( ( sk216 @ v1_xboole_0 )
   != ( sk14 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8360]) ).

thf(8370,plain,
    sk216 != sk14,
    inference(simp,[status(thm)],[8361]) ).

thf(197,axiom,
    ? [A: $i] :
      ( ( A @ v2_struct_0 )
      & ( A @ l2_struct_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_struct_0) ).

thf(2165,plain,
    ? [A: $i] :
      ( ( A @ v2_struct_0 )
      & ( A @ l2_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(2166,plain,
    ( ( sk95 @ v2_struct_0 )
    & ( sk95 @ l2_struct_0 ) ),
    inference(cnf,[status(esa)],[2165]) ).

thf(2168,plain,
    sk95 @ v2_struct_0,
    inference(cnfConj,[status(thm)],[2166]) ).

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

thf(1260,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(857,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m3_lattice4 ) )
         => ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_lattice4) ).

thf(5674,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)],[857]) ).

thf(564,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m1_struct_0 ) ) )
        <=> ( B @ ( C @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_struct_0) ).

thf(4247,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)],[564]) ).

thf(703,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v14_lattices )
      <=> ? [B: $i] :
            ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
                    = B )
                  & ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                    = B ) ) )
            & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_lattices) ).

thf(5005,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)],[703]) ).

thf(744,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
               => ( B @ ( A @ k7_lattices ) @ ( C @ ( A @ k7_lattices ) @ ( A @ r3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_lattices) ).

thf(5178,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)],[744]) ).

thf(848,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v11_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
             => ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
               => ( A @ v11_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_lattice4) ).

thf(5636,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)],[848]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                    & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                        & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ! [F: $i] :
                          ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
                            & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
                            & ( F @ v1_funct_1 ) )
                         => ( ( ( F
                                = ( B @ ( D @ k1_realset1 ) ) )
                              & ( E
                                = ( B @ ( C @ k1_realset1 ) ) ) )
                           => ( ( ( D @ ( C @ ( A @ r5_binop_1 ) ) )
                               => ( F @ ( E @ ( B @ r5_binop_1 ) ) ) )
                              & ( ( D @ ( C @ ( A @ r4_binop_1 ) ) )
                               => ( F @ ( E @ ( B @ r4_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_filter_2) ).

thf(1095,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(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/sandbox/benchmark/theBenchmark.p',t34_funct_2) ).

thf(2432,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [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(171,axiom,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).

thf(2020,plain,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(973,plain,
    ~ ( sk1 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[969]) ).

thf(908,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m3_lattice4 ) )
                 => ( ( ( D @ ( C @ r2_hidden ) )
                      & ( D @ ( B @ r2_hidden ) ) )
                   => ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_lattice4) ).

thf(5921,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)],[908]) ).

thf(535,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ( ( D @ ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
                    = ( C @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_lattice4) ).

thf(4124,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)],[535]) ).

thf(77,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
          & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
          & ( C @ v1_funct_1 ) )
       => ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
          | ( ( A != k1_xboole_0 )
            & ( B = k1_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_funct_2) ).

thf(1386,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(899,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ~ ( D @ v1_xboole_0 )
        & ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_0_filter_0 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i,F: $i] :
            ( ( D @ ( F @ r2_hidden ) )
            & ( C @ ( E @ r2_hidden ) )
            & ( A
              = ( F @ ( E @ ( B @ k4_lattices ) ) ) )
            & ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
            & ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_filter_0) ).

thf(5874,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)],[899]) ).

thf(630,axiom,
    ( ! [A: $i] :
        ( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
       => ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) )
   => ? [A: $i] :
        ( ! [B: $i] :
            ( ( f1_s12_funct_2 @ ( B @ m1_subset_1 ) )
           => ( ( B @ ( A @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
              = ( B @ f3_s12_funct_2 ) ) )
        & ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ m2_relset_1 ) ) )
        & ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ v1_funct_2 ) ) )
        & ( A @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s12_funct_2) ).

thf(4610,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)],[630]) ).

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

thf(2397,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(2398,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)],[2397]) ).

thf(2405,plain,
    k13_nat_lat @ v8_lattices,
    inference(cnfConj,[status(thm)],[2398]) ).

thf(91,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).

thf(1482,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(845,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( A @ k6_lattices @ ( B @ ( A @ r3_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_lattices) ).

thf(5621,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)],[845]) ).

thf(821,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( A @ k6_lattices @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_lattices) ).

thf(5533,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)],[821]) ).

thf(2881,plain,
    sk187 @ v13_lattices,
    inference(cnfConj,[status(thm)],[2869]) ).

thf(8689,plain,
    ! [A: $i] :
      ( ( ( sk295 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4326,6622]) ).

thf(8690,plain,
    ! [A: $i] :
      ( ( ( sk295 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8689]) ).

thf(8691,plain,
    ( ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8690:[bind(A,$thf( sk295 ))]]) ).

thf(9819,plain,
    ( ( ( sk187 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2881,8691]) ).

thf(9820,plain,
    ( ( ( sk187 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9819]) ).

thf(9830,plain,
    ( ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9820]) ).

thf(12414,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,9830]) ).

thf(12415,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12414]) ).

thf(12437,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk295 )
    | ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12415]) ).

thf(12447,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12437]) ).

thf(321,axiom,
    ? [A: $i] :
      ( ( A @ v16_lattices )
      & ( A @ v15_lattices )
      & ( A @ v14_lattices )
      & ( A @ v13_lattices )
      & ( A @ v10_lattices )
      & ( A @ v9_lattices )
      & ( A @ v8_lattices )
      & ( A @ v7_lattices )
      & ( A @ v6_lattices )
      & ( A @ v5_lattices )
      & ( A @ v4_lattices )
      & ( A @ v3_lattices )
      & ~ ( A @ v3_struct_0 )
      & ( A @ l3_lattices ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc12_lattices) ).

thf(2982,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)],[321]) ).

thf(2983,plain,
    ( ( sk196 @ v16_lattices )
    & ( sk196 @ v15_lattices )
    & ( sk196 @ v14_lattices )
    & ( sk196 @ v13_lattices )
    & ( sk196 @ v10_lattices )
    & ( sk196 @ v9_lattices )
    & ( sk196 @ v8_lattices )
    & ( sk196 @ v7_lattices )
    & ( sk196 @ v6_lattices )
    & ( sk196 @ v5_lattices )
    & ( sk196 @ v4_lattices )
    & ( sk196 @ v3_lattices )
    & ~ ( sk196 @ v3_struct_0 )
    & ( sk196 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[2982]) ).

thf(2989,plain,
    sk196 @ v13_lattices,
    inference(cnfConj,[status(thm)],[2983]) ).

thf(7160,plain,
    ( ( ( sk196 @ v13_lattices )
     != ( sk1 @ v13_lattices ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2989,970]) ).

thf(7161,plain,
    ( ( sk196 @ v13_lattices )
   != ( sk1 @ v13_lattices ) ),
    inference(simp,[status(thm)],[7160]) ).

thf(7168,plain,
    sk196 != sk1,
    inference(simp,[status(thm)],[7161]) ).

thf(3136,plain,
    sk207 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[3135]) ).

thf(50611,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk207 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3136,1179]) ).

thf(50612,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk207 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[50611]) ).

thf(50613,plain,
    ! [A: $i] : ( A @ ( sk207 @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[50612:[bind(A,$thf( A )),bind(B,$thf( sk207 ))]]) ).

thf(2342,plain,
    ( ( sk118 @ v1_lattice2 )
    & ( sk118 @ v10_lattices )
    & ( sk118 @ v9_lattices )
    & ( sk118 @ v8_lattices )
    & ( sk118 @ v7_lattices )
    & ( sk118 @ v6_lattices )
    & ( sk118 @ v5_lattices )
    & ( sk118 @ v4_lattices )
    & ~ ( sk118 @ v3_struct_0 )
    & ( sk118 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[2341]) ).

thf(2348,plain,
    sk118 @ v4_lattices,
    inference(cnfConj,[status(thm)],[2342]) ).

thf(382,axiom,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_subset_1 ) )
             => ( ~ ( B @ ( C @ r2_hidden ) )
               => ( B @ ( A @ k3_subset_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).

thf(3350,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)],[382]) ).

thf(754,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( ( B @ ( D @ r2_hidden ) )
                        & ( B @ ( C @ r2_hidden ) ) )
                    <=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) )
           => ( A @ ( B @ m2_lattice4 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_filter_2) ).

thf(5227,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)],[754]) ).

thf(972,plain,
    sk1 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ),
    inference(cnfConj,[status(thm)],[969]) ).

thf(33325,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,972]) ).

thf(33326,plain,
    ( ( k1_xboole_0 @ u1_struct_0 @ ( sk2 @ m1_subset_1 ) )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[33325:[bind(A,$thf( sk1 ))]]) ).

thf(540,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ( ( A @ v1_finset_1 )
       => ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_finsub_1) ).

thf(4142,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)],[540]) ).

thf(33,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
         => ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_realset1) ).

thf(1127,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(646,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ! [C: $i] :
          ~ ( ~ ( B @ ( C @ r2_hidden ) )
            & ~ ( B @ ( C @ r2_tarski ) )
            & ( B @ ( C @ r1_tarski ) ) )
      & ! [C: $i] :
          ( ( B @ ( C @ r2_hidden ) )
         => ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
      & ! [C: $i,D: $i] :
          ( ( ( C @ ( D @ r1_tarski ) )
            & ( B @ ( C @ r2_hidden ) ) )
         => ( B @ ( D @ r2_hidden ) ) )
      & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).

thf(4713,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)],[646]) ).

thf(4714,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)],[4713]) ).

thf(4715,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ sk331 @ ( E @ r2_hidden ) )
        | ( A @ sk331 @ ( E @ r2_tarski ) )
        | ~ ( A @ sk331 @ ( E @ r1_tarski ) ) )
      & ( ( A @ sk331 @ ( D @ k1_zfmisc_1 @ r2_hidden ) )
        | ~ ( A @ sk331 @ ( D @ r2_hidden ) ) )
      & ( ( A @ sk331 @ ( C @ r2_hidden ) )
        | ~ ( B @ ( C @ r1_tarski ) )
        | ~ ( A @ sk331 @ ( B @ r2_hidden ) ) )
      & ( A @ sk331 @ ( A @ r2_hidden ) ) ),
    inference(cnf,[status(esa)],[4714]) ).

thf(4716,plain,
    ! [A: $i] : ( A @ sk331 @ ( A @ r2_hidden ) ),
    inference(cnfConj,[status(thm)],[4715]) ).

thf(17145,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk331 @ ( A @ r2_hidden ) )
       != ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4716,2961]) ).

thf(17146,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk331 @ ( A @ r2_hidden ) )
     != ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[17145]) ).

thf(17147,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk331 )
       != k1_xboole_0 )
      | ( A != B ) ),
    inference(simp,[status(thm)],[17146]) ).

thf(17154,plain,
    ! [A: $i] :
      ( ( A @ sk331 )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[17147]) ).

thf(30264,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ sk331 ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,17154]) ).

thf(30265,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ sk331 ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[30264]) ).

thf(30266,plain,
    ! [A: $i] : ( A @ sk331 @ sk18 @ v1_funct_1 ),
    inference(pattern_uni,[status(thm)],[30265:[bind(A,$thf( C @ sk331 )),bind(B,$thf( C ))]]) ).

thf(33463,plain,
    ! [A: $i] : ( A @ sk331 @ sk18 @ v1_funct_1 ),
    inference(simp,[status(thm)],[30266]) ).

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/sandbox/benchmark/theBenchmark.p',t129_zfmisc_1) ).

thf(2548,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(9402,plain,
    ( ( ( sk297 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4370,8209]) ).

thf(9403,plain,
    ( ( ( sk297 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9402]) ).

thf(9406,plain,
    ( ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9403]) ).

thf(12082,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,9406]) ).

thf(12083,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12082]) ).

thf(12141,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk207 )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12083]) ).

thf(413,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( B @ ( A @ k2_tarski ) ) )
    <=> ! [D: $i] :
          ( ( C @ ( D @ r2_hidden ) )
        <=> ( ( D = B )
            | ( D = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

thf(3502,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)],[413]) ).

thf(9797,plain,
    ( ( ( sk197 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3001,8691]) ).

thf(9798,plain,
    ( ( ( sk197 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9797]) ).

thf(9829,plain,
    ( ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9798]) ).

thf(16087,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( sk197 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,9829]) ).

thf(16088,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( sk197 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16087]) ).

thf(16238,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk295 != k1_xboole_0 )
      | ( sk197 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16088]) ).

thf(16304,plain,
    ( ( sk295 != k1_xboole_0 )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16238]) ).

thf(2985,plain,
    sk196 @ v15_lattices,
    inference(cnfConj,[status(thm)],[2983]) ).

thf(100,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
        | ( A @ ( C @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_zfmisc_1) ).

thf(1576,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(731,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k5_lattices )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_filter_0) ).

thf(5123,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)],[731]) ).

thf(524,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( D != k1_xboole_0 )
                       => ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ k4_lattices ) ) )
                          = ( E @ ( B @ ( A @ u1_lattices @ ( C @ ( A @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_lattice2) ).

thf(4079,plain,
    ! [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)],[524]) ).

thf(912,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m3_lattice4 ) )
                 => ( ( ( D @ ( C @ r2_hidden ) )
                      & ( D @ ( B @ r2_hidden ) ) )
                   => ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_lattice4) ).

thf(5938,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)],[912]) ).

thf(2886,plain,
    sk188 @ v3_filter_0,
    inference(cnfConj,[status(thm)],[2884]) ).

thf(9793,plain,
    ( ( ( sk297 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4370,8691]) ).

thf(9794,plain,
    ( ( ( sk297 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9793]) ).

thf(9825,plain,
    ( ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9794]) ).

thf(16116,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( sk297 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,9825]) ).

thf(16117,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( sk297 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16116]) ).

thf(16250,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk295 != k1_xboole_0 )
      | ( sk297 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16117]) ).

thf(16319,plain,
    ( ( sk295 != k1_xboole_0 )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16250]) ).

thf(4905,plain,
    ~ ? [A: $i] : ( A @ k1_tarski @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[4904]) ).

thf(4906,plain,
    ! [A: $i] :
      ~ ( A @ k1_tarski @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[4905]) ).

thf(7756,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3050,4906]) ).

thf(7757,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7756]) ).

thf(7769,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[7757]) ).

thf(32567,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ k1_tarski ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,7769]) ).

thf(32568,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ k1_tarski ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[32567]) ).

thf(32569,plain,
    ! [A: $i] : ( A @ k1_tarski @ sk18 @ v1_funct_1 ),
    inference(pattern_uni,[status(thm)],[32568:[bind(A,$thf( C @ k1_tarski )),bind(B,$thf( C ))]]) ).

thf(33775,plain,
    ! [A: $i] : ( A @ k1_tarski @ sk18 @ v1_funct_1 ),
    inference(simp,[status(thm)],[32569]) ).

thf(716,axiom,
    ! [A: $i] :
    ? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(5066,plain,
    ! [A: $i] :
    ? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(5067,plain,
    ! [A: $i] : ( A @ ( A @ sk366 @ m1_subset_1 ) ),
    inference(cnf,[status(esa)],[5066]) ).

thf(46857,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ sk366 @ m1_subset_1 ) )
       != ( sk14 @ ( B @ m1_subset_1 ) ) )
      | ~ ( B @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5067,1168]) ).

thf(46858,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ sk366 @ m1_subset_1 ) )
       != ( sk14 @ ( B @ m1_subset_1 ) ) )
      | ~ ( B @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[46857]) ).

thf(46859,plain,
    ~ ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[46858:[bind(A,$thf( sk14 )),bind(B,$thf( sk14 @ sk366 ))]]) ).

thf(47095,plain,
    ( ( ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2587,46859]) ).

thf(47096,plain,
    ( ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[47095]) ).

thf(47103,plain,
    ( ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk152 ),
    inference(simp,[status(thm)],[47096]) ).

thf(517,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r2_lattices ) ) )
              <=> ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
                    = ( A @ k5_lattices ) )
                  & ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                    = ( A @ k5_lattices ) )
                  & ( ( B @ ( C @ ( A @ k1_lattices ) ) )
                    = ( A @ k6_lattices ) )
                  & ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                    = ( A @ k6_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_lattices) ).

thf(4030,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)],[517]) ).

thf(538,axiom,
    ? [A: $i] : ( A @ l1_struct_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).

thf(4137,plain,
    ? [A: $i] : ( A @ l1_struct_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(3256,plain,
    sk218 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[3254]) ).

thf(50608,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk218 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3256,1179]) ).

thf(50609,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk218 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[50608]) ).

thf(50610,plain,
    ! [A: $i] : ( A @ ( sk218 @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[50609:[bind(A,$thf( A )),bind(B,$thf( sk218 ))]]) ).

thf(2400,plain,
    k13_nat_lat @ v7_lattices,
    inference(cnfConj,[status(thm)],[2398]) ).

thf(650,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
    <=> ! [C: $i] :
          ( ( A @ ( C @ r2_hidden ) )
         => ( B @ ( C @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

thf(4760,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)],[650]) ).

thf(161,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( A @ ( C @ v1_binop_1 ) )
               => ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
                <=> ( B @ ( C @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_binop_1) ).

thf(1967,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(293,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v1_lattice2 )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v3_filter_0 )
          & ( A @ v13_lattices )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattice2) ).

thf(2825,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)],[293]) ).

thf(485,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( B @ ( A @ k4_lattice4 ) @ ( C @ r2_hidden ) )
              <=> ? [D: $i] :
                    ( ? [E: $i] :
                        ( ( B @ ( E @ r2_hidden ) )
                        & ( B @ ( D @ r2_hidden ) )
                        & ( C
                          = ( E @ ( D @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) )
                        & ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_lattice4) ).

thf(3880,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)],[485]) ).

thf(15648,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
       != ( sk216 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3244,4338]) ).

thf(15649,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[15648]) ).

thf(15655,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) )
     != sk216 ),
    inference(simp,[status(thm)],[15649]) ).

thf(27641,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
       != ( C @ ( B @ k2_tarski ) ) )
      | ( ( A @ k1_tarski @ k1_zfmisc_1 )
       != sk216 ) ),
    inference(paramod_ordered,[status(thm)],[1994,15655]) ).

thf(27642,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk216 ),
    inference(pattern_uni,[status(thm)],[27641:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(27700,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk216 ),
    inference(simp,[status(thm)],[27642]) ).

thf(614,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v3_filter_0 )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( ( B @ ( A @ k10_filter_0 ) @ k3_relat_1 )
              = ( A @ u1_struct_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_filter_0) ).

thf(4511,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)],[614]) ).

thf(705,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_zfmisc_1) ).

thf(5024,plain,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(777,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v13_lattices )
       => ! [B: $i] :
            ( ( A @ ( B @ m1_filter_0 ) )
           => ~ ( ! [C: $i] :
                    ( ( A @ ( C @ m1_filter_0 ) )
                   => ~ ( ( A @ ( C @ v1_filter_0 ) )
                        & ( C @ ( B @ r1_tarski ) ) ) )
                & ( B
                 != ( A @ u1_struct_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_filter_0) ).

thf(5352,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)],[777]) ).

thf(775,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ v11_lattices ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_filter_0) ).

thf(5342,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)],[775]) ).

thf(266,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ v1_relat_1 )
     => ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_realset1) ).

thf(2603,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(768,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( A @ k1_lattice4 ) @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) )
                = ( C @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_lattice4) ).

thf(5306,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)],[768]) ).

thf(2667,plain,
    sk157 @ v7_lattices,
    inference(cnfConj,[status(thm)],[2661]) ).

thf(763,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m2_filter_2 ) )
        & ( A @ ( B @ m2_filter_2 ) )
        & ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( C @ ( B @ ( A @ k21_filter_2 ) ) @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k21_filter_2) ).

thf(5284,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)],[763]) ).

thf(3245,plain,
    sk216 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[3242]) ).

thf(8412,plain,
    ! [A: $i] :
      ( ( ( sk216 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3245,6622]) ).

thf(8413,plain,
    ! [A: $i] :
      ( ( ( sk216 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8412]) ).

thf(8414,plain,
    ( ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8413:[bind(A,$thf( sk216 ))]]) ).

thf(10660,plain,
    ( ( ( k6_nat_lat @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5390,8414]) ).

thf(10661,plain,
    ( ( ( k6_nat_lat @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[10660]) ).

thf(10674,plain,
    ( ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[10661]) ).

thf(16190,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( k6_nat_lat != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,10674]) ).

thf(16191,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( k6_nat_lat != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16190]) ).

thf(16222,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk216 != k1_xboole_0 )
      | ( k6_nat_lat != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16191]) ).

thf(16287,plain,
    ( ( sk216 != k1_xboole_0 )
    | ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16222]) ).

thf(1079,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
      | ~ ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ),
    inference(cnfConj,[status(thm)],[1078]) ).

thf(14316,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
       != ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
      | ( A @ ( C @ k1_relat_1 @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,1079]) ).

thf(14317,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
       != ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
      | ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14316]) ).

thf(14318,plain,
    f1_s4_funct_2 @ ( sk295 @ k1_relat_1 @ r1_tarski ),
    inference(pattern_uni,[status(thm)],[14317:[bind(A,$thf( f1_s4_funct_2 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( sk295 ))]]) ).

thf(14339,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( sk295 @ k1_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[14318,1030]) ).

thf(14340,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( sk295 @ k1_relat_1 @ r1_tarski ) )
       != ( B @ ( A @ r1_tarski ) ) )
      | ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[14339]) ).

thf(14341,plain,
    ! [A: $i] : ( f1_s4_funct_2 @ ( A @ ( sk295 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[14340:[bind(A,$thf( sk295 @ k1_relat_1 )),bind(B,$thf( f1_s4_funct_2 )),bind(C,$thf( C ))]]) ).

thf(14351,plain,
    ! [A: $i] : ( f1_s4_funct_2 @ ( A @ ( sk295 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[14341]) ).

thf(337,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
      & ( k1_xboole_0 @ v1_funct_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_partfun1) ).

thf(3084,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)],[337]) ).

thf(3085,plain,
    ( ! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
    & ( k1_xboole_0 @ v1_funct_1 ) ),
    inference(miniscope,[status(thm)],[3084]) ).

thf(3086,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
      & ( k1_xboole_0 @ v1_funct_1 ) ),
    inference(cnf,[status(esa)],[3085]) ).

thf(3087,plain,
    k1_xboole_0 @ v1_funct_1,
    inference(cnfConj,[status(thm)],[3086]) ).

thf(7792,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)],[3087,6617]) ).

thf(7793,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)],[7792]) ).

thf(7794,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)],[7793:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(16021,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[7794,2222]) ).

thf(16022,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16021]) ).

thf(748,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( ( E @ ( D @ ( A @ k1_lattice2 @ k3_lattices ) ) )
                          = ( E @ ( A @ k6_filter_2 ) @ ( D @ ( A @ k6_filter_2 ) @ ( A @ k4_lattices ) ) ) )
                        & ( ( E @ ( D @ ( A @ k1_lattice2 @ k4_lattices ) ) )
                          = ( E @ ( A @ k6_filter_2 ) @ ( D @ ( A @ k6_filter_2 ) @ ( A @ k3_lattices ) ) ) )
                        & ( ( C @ ( B @ ( A @ k3_lattices ) ) )
                          = ( C @ ( A @ k5_filter_2 ) @ ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k4_lattices ) ) ) )
                        & ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                          = ( C @ ( A @ k5_filter_2 ) @ ( B @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ k3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_filter_2) ).

thf(5188,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[748]) ).

thf(461,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k14_filter_2 ) )
        = ( B @ ( A @ k8_filter_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k14_filter_2) ).

thf(3776,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)],[461]) ).

thf(345,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ( ! [B: $i,C: $i] :
            ~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
       => ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).

thf(3125,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)],[345]) ).

thf(571,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( B @ ( B @ ( A @ r3_lattices ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).

thf(4275,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)],[571]) ).

thf(46967,plain,
    ( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1924,46818]) ).

thf(46968,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[46967]) ).

thf(47030,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk71 ),
    inference(simp,[status(thm)],[46968]) ).

thf(895,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ ( B @ v2_filter_0 ) )
          <=> ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
                    <=> ( ( B @ ( D @ r2_hidden ) )
                        | ( B @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_filter_0) ).

thf(5836,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)],[895]) ).

thf(474,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ l3_lattices )
        & ( B @ v17_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ! [C: $i] :
          ( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
            & ~ ( C @ v1_xboole_0 ) )
         => ( ( C @ ( B @ k4_lattice4 ) @ ( A @ r2_hidden ) )
          <=> ? [D: $i] :
                ( ? [E: $i] :
                    ( ( C @ ( E @ r2_hidden ) )
                    & ( C @ ( D @ r2_hidden ) )
                    & ( A
                      = ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
                    & ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) )
                & ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_lattice4) ).

thf(3820,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)],[474]) ).

thf(486,axiom,
    ? [A: $i] :
      ( ~ ( A @ v3_struct_0 )
      & ( A @ l1_struct_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).

thf(3891,plain,
    ? [A: $i] :
      ( ~ ( A @ v3_struct_0 )
      & ( A @ l1_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

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

thf(2654,plain,
    ( ( k1_xboole_0 @ k2_relat_1 )
    = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(359,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
                = ( C @ ( B @ ( A @ a_3_3_domain_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_domain_1) ).

thf(3204,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)],[359]) ).

thf(917,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k20_filter_2 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k20_filter_2) ).

thf(5953,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)],[917]) ).

thf(883,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) )
                      = ( D @ ( B @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
                      = ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_lattices) ).

thf(5765,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[883]) ).

thf(600,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
                = ( C @ ( B @ ( A @ k7_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_filter_0) ).

thf(4439,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)],[600]) ).

thf(61,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( ( A @ k1_relat_1 @ v1_relat_1 )
        & ( A @ k1_relat_1 @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).

thf(1287,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(499,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_lattice2 @ v3_lattices )
        & ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice2) ).

thf(3938,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)],[499]) ).

thf(357,axiom,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).

thf(3195,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(587,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ~ ( ! [E: $i] :
                          ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                         => ~ ( ( C @ ( E @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
                              & ( B @ ( E @ r2_hidden ) ) ) )
                      & ( B @ ( D @ ( A @ k2_filter_0 ) @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_lattice4) ).

thf(4348,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)],[587]) ).

thf(939,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ k1_lattice2 @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( ( C @ ( A @ k6_filter_2 ) @ ( A @ k5_filter_2 ) )
                  = C )
                & ( ( B @ ( A @ k5_filter_2 ) @ ( A @ k6_filter_2 ) )
                  = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_filter_2) ).

thf(6034,plain,
    ! [A: $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)],[939]) ).

thf(9821,plain,
    ( ( ( sk157 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2672,8691]) ).

thf(9822,plain,
    ( ( ( sk157 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9821]) ).

thf(9828,plain,
    ( ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9822]) ).

thf(7048,plain,
    ( ( ( sk157 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2672,6903]) ).

thf(7049,plain,
    ( ( ( sk157 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7048]) ).

thf(7051,plain,
    ( ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7049]) ).

thf(11993,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,7051]) ).

thf(11994,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[11993]) ).

thf(12122,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk138 )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[11994]) ).

thf(124,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ! [B: $i,C: $i] :
          ( ( C @ ( B @ ( A @ k1_binop_1 ) ) )
          = ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_binop_1) ).

thf(1760,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(347,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( ( A @ ( C @ r2_hidden ) )
          & ( D @ v2_funct_1 ) )
       => ( ( ( C @ ( D @ k1_funct_1 ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
            = C )
          | ( B = k1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_funct_2) ).

thf(3131,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)],[347]) ).

thf(582,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_domain_1) ).

thf(4334,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)],[582]) ).

thf(7758,plain,
    ( ( ( sk14 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3050,1167]) ).

thf(7759,plain,
    ( ( sk14 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7758]) ).

thf(7771,plain,
    sk14 != k1_xboole_0,
    inference(simp,[status(thm)],[7759]) ).

thf(850,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ~ ( B @ ( A @ k4_lattice4 ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice4) ).

thf(5640,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)],[850]) ).

thf(338,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ? [C: $i] :
          ( ! [D: $i] :
              ( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
             => ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
          & ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_realset1) ).

thf(3089,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)],[338]) ).

thf(931,axiom,
    ? [A: $i] :
      ( ( A @ v3_lattices )
      & ~ ( A @ v3_struct_0 )
      & ( A @ l3_lattices ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_lattices) ).

thf(6003,plain,
    ? [A: $i] :
      ( ( A @ v3_lattices )
      & ~ ( A @ v3_struct_0 )
      & ( A @ l3_lattices ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(6004,plain,
    ( ( sk445 @ v3_lattices )
    & ~ ( sk445 @ v3_struct_0 )
    & ( sk445 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[6003]) ).

thf(6006,plain,
    ~ ( sk445 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[6004]) ).

thf(6329,plain,
    ( ( ( sk341 @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2587,4839]) ).

thf(6330,plain,
    ( ( sk341 @ v1_xboole_0 )
   != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6329]) ).

thf(6332,plain,
    sk341 != sk152,
    inference(simp,[status(thm)],[6330]) ).

thf(865,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k5_lattices @ ( A @ k3_lattices ) ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_lattices) ).

thf(5706,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)],[865]) ).

thf(383,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( B != k1_xboole_0 )
       => ( ( C @ k2_relat_1 )
          = ( A @ ( C @ k1_funct_1 ) @ k1_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_2) ).

thf(3353,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)],[383]) ).

thf(3243,plain,
    sk216 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[3242]) ).

thf(8341,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk216 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3243,999]) ).

thf(8342,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk216 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[8341]) ).

thf(8343,plain,
    ! [A: $i] : ( sk216 @ k1_relat_1 @ ( sk216 @ k9_relat_1 ) @ ( A @ ( sk216 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[8342:[bind(A,$thf( A )),bind(B,$thf( sk216 ))]]) ).

thf(15477,plain,
    ! [A: $i] :
      ( ( ( sk216 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ~ $true
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[3243,1086]) ).

thf(15478,plain,
    ! [A: $i] :
      ( ( ( sk216 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[15477]) ).

thf(15479,plain,
    ( ( sk216 @ k1_relat_1 @ ( sk216 @ k9_relat_1 ) )
    = ( sk216 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15478:[bind(A,$thf( sk216 ))]]) ).

thf(27092,plain,
    ! [A: $i] : ( sk216 @ k2_relat_1 @ ( A @ ( sk216 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[8343,15479]) ).

thf(20,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_funct_1 )
        & ( B @ v1_relat_1 ) )
     => ( ( ( B @ k1_relat_1 )
          = k1_xboole_0 )
       => ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
          & ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
          & ( B @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_2) ).

thf(1059,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(34,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( C @ v2_funct_1 )
       => ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
          & ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_partfun1) ).

thf(1129,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(1130,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)],[1129]) ).

thf(1132,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)],[1130]) ).

thf(804,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
             => ( ( C @ ( B @ ( A @ r3_lattice4 ) ) )
              <=> ( ( A @ k5_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
                  = ( B @ k5_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice4) ).

thf(5461,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)],[804]) ).

thf(563,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( C @ ( A @ r1_tarski ) )
       => ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
          & ( D @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_partfun1) ).

thf(4243,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)],[563]) ).

thf(588,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
     => ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_finsub_1) ).

thf(4353,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)],[588]) ).

thf(637,axiom,
    ? [A: $i] :
      ( ( A @ v3_lattices )
      & ( A @ l3_lattices ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_lattices) ).

thf(4664,plain,
    ? [A: $i] :
      ( ( A @ v3_lattices )
      & ( A @ l3_lattices ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(8099,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk207 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3136,999]) ).

thf(8100,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk207 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[8099]) ).

thf(8101,plain,
    ! [A: $i] : ( sk207 @ k1_relat_1 @ ( sk207 @ k9_relat_1 ) @ ( A @ ( sk207 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[8100:[bind(A,$thf( A )),bind(B,$thf( sk207 ))]]) ).

thf(15498,plain,
    ! [A: $i] :
      ( ( ( sk207 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ~ $true
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[3136,1086]) ).

thf(15499,plain,
    ! [A: $i] :
      ( ( ( sk207 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[15498]) ).

thf(15500,plain,
    ( ( sk207 @ k1_relat_1 @ ( sk207 @ k9_relat_1 ) )
    = ( sk207 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15499:[bind(A,$thf( sk207 ))]]) ).

thf(26795,plain,
    ! [A: $i] : ( sk207 @ k2_relat_1 @ ( A @ ( sk207 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[8101,15500]) ).

thf(493,axiom,
    ! [A: $i] :
      ( ( A @ l1_lattices )
     => ( A @ l1_struct_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).

thf(3919,plain,
    ! [A: $i] :
      ( ( A @ l1_lattices )
     => ( A @ l1_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

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

thf(1013,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(173,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ( ( B @ ( A @ k3_subset_1 ) @ ( A @ k3_subset_1 ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).

thf(2024,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(569,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ( ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) )
      <=> ? [C: $i] :
            ( ( A = C )
            & ( B @ ( C @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).

thf(4265,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)],[569]) ).

thf(94,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
        = A )
    <=> ~ ( A @ ( B @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).

thf(1494,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(354,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
     => ( ( B @ ( D @ k2_relat_1 @ r1_tarski ) )
       => ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).

thf(3180,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)],[354]) ).

thf(660,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_lattice4 ) )
         => ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
               => ( ( B @ ( C @ r1_tarski ) )
                 => ( B @ ( C @ ( A @ k2_lattice4 ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_lattice4) ).

thf(4793,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)],[660]) ).

thf(1096,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)],[1095]) ).

thf(1097,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)],[1096]) ).

thf(1099,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)],[1097]) ).

thf(1100,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)],[1099]) ).

thf(628,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ( ( A @ ( B @ m2_lattice4 ) )
          <=> ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( ( B @ ( D @ r2_hidden ) )
                        & ( B @ ( C @ r2_hidden ) ) )
                     => ( ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
                        & ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_lattice4) ).

thf(4595,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)],[628]) ).

thf(33321,plain,
    ! [A: $i] :
      ( ( A != sk2 )
      | ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,972]) ).

thf(33322,plain,
    ( ( sk1 @ u1_struct_0 @ ( k1_xboole_0 @ m1_subset_1 ) )
    | ( sk2 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[33321:[bind(A,$thf( sk2 ))]]) ).

thf(341,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ( ( A != k1_xboole_0 )
       => ( A @ k1_zfmisc_1 @ ( B @ k1_tarski @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_subset_1) ).

thf(3099,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)],[341]) ).

thf(773,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ( ( D @ ( B @ r2_hidden ) )
                   => ( D @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_filter_0) ).

thf(5338,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)],[773]) ).

thf(387,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ! [C: $i] :
          ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
            & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ! [D: $i] :
              ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
                & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
                & ( D @ v1_funct_1 ) )
             => ! [E: $i] :
                  ( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
                 => ( ! [F: $i] :
                        ( ( A @ ( F @ m1_subset_1 ) )
                       => ( ( E @ ( F @ r2_hidden ) )
                         => ( ( F @ ( C @ k1_funct_1 ) )
                            = ( F @ ( D @ k1_funct_1 ) ) ) ) )
                   => ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
                      = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_lattice2) ).

thf(3374,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)],[387]) ).

thf(898,axiom,
    ( ( ! [A: $i] :
          ( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
         => ( ( f3_s4_subset_1 @ ( A @ r2_hidden ) )
          <=> ( A @ p1_s4_subset_1 ) ) )
      & ! [A: $i] :
          ( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
         => ( ( f2_s4_subset_1 @ ( A @ r2_hidden ) )
          <=> ( A @ p1_s4_subset_1 ) ) ) )
   => ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_subset_1) ).

thf(5852,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)],[898]) ).

thf(5853,plain,
    ( ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ ( f3_s4_subset_1 @ ( sk434 @ r2_hidden ) )
      | ~ ( sk434 @ p1_s4_subset_1 )
      | sk432 )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ( sk434 @ p1_s4_subset_1 )
      | ~ ( sk434 @ p1_s4_subset_1 )
      | sk432 )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ ( f3_s4_subset_1 @ ( sk434 @ r2_hidden ) )
      | ( f3_s4_subset_1 @ ( sk434 @ r2_hidden ) )
      | sk432 )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ( sk434 @ p1_s4_subset_1 )
      | ( f3_s4_subset_1 @ ( sk434 @ r2_hidden ) )
      | sk432 )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ( f1_s4_subset_1 @ ( sk434 @ m1_subset_1 ) )
      | sk432 )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ sk432
      | ~ ( f2_s4_subset_1 @ ( sk433 @ r2_hidden ) )
      | ~ ( sk433 @ p1_s4_subset_1 ) )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ sk432
      | ( sk433 @ p1_s4_subset_1 )
      | ~ ( sk433 @ p1_s4_subset_1 ) )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ sk432
      | ~ ( f2_s4_subset_1 @ ( sk433 @ r2_hidden ) )
      | ( f2_s4_subset_1 @ ( sk433 @ r2_hidden ) ) )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ sk432
      | ( sk433 @ p1_s4_subset_1 )
      | ( f2_s4_subset_1 @ ( sk433 @ r2_hidden ) ) )
    & ( ( f2_s4_subset_1 = f3_s4_subset_1 )
      | ~ sk432
      | ( f1_s4_subset_1 @ ( sk433 @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[5852]) ).

thf(5855,plain,
    ( ( f2_s4_subset_1 = f3_s4_subset_1 )
    | ( f1_s4_subset_1 @ ( sk434 @ m1_subset_1 ) )
    | sk432 ),
    inference(cnfConj,[status(thm)],[5853]) ).

thf(5868,plain,
    ( ( f1_s4_subset_1 @ ( sk434 @ m1_subset_1 ) )
    | sk432
    | ( f3_s4_subset_1 = f2_s4_subset_1 ) ),
    inference(lifteq,[status(thm)],[5855]) ).

thf(198,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ v1_relat_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_relat_1) ).

thf(2169,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ v1_relat_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(2403,plain,
    k13_nat_lat @ v3_lattices,
    inference(cnfConj,[status(thm)],[2398]) ).

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

thf(1087,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(816,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_nat_lat ) )
         => ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_nat_lat) ).

thf(5521,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)],[816]) ).

thf(6739,plain,
    ! [A: $i] :
      ( ( ( sk138 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2472,6617]) ).

thf(6740,plain,
    ! [A: $i] :
      ( ( ( sk138 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[6739]) ).

thf(6741,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[6740:[bind(A,$thf( sk138 ))]]) ).

thf(16082,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,6741]) ).

thf(16083,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16082]) ).

thf(16234,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk138 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[16083]) ).

thf(16300,plain,
    ( ( sk138 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[16234]) ).

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

thf(1147,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(552,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v14_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ! [F: $i] :
                            ( ( A @ ( F @ m1_subset_1 ) )
                           => ( ( B @ ( F @ r2_hidden ) )
                             => ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( E @ ( C @ r3_lattices ) ) ) ) )
                       => ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( E @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_lattice2) ).

thf(4194,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)],[552]) ).

thf(4358,plain,
    sk297 @ v11_lattices,
    inference(cnfConj,[status(thm)],[4356]) ).

thf(178,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ! [D: $i,E: $i] :
            ( ( E @ ( D @ k4_tarski ) )
           != A )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_zfmisc_1) ).

thf(2049,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(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/sandbox/benchmark/theBenchmark.p',t70_partfun1) ).

thf(2635,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(310,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ! [D: $i] :
              ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
                & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
                & ( D @ v1_funct_1 ) )
             => ! [E: $i] :
                  ( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
                    & ( B @ ( A @ ( E @ v1_funct_2 ) ) )
                    & ( E @ v1_funct_1 ) )
                 => ( ! [F: $i] :
                        ( ( A @ ( F @ m1_subset_1 ) )
                       => ( ( C @ ( F @ r2_hidden ) )
                         => ( ( F @ ( D @ k1_funct_1 ) )
                            = ( F @ ( E @ k1_funct_1 ) ) ) ) )
                   => ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( E @ k1_funct_4 ) )
                      = E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_lattice2) ).

thf(2929,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)],[310]) ).

thf(3503,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)],[3502]) ).

thf(3504,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( H
          = ( G @ ( F @ k2_tarski ) ) )
        | ~ ( H @ ( F @ ( G @ ( H @ sk236 ) ) @ r2_hidden ) )
        | ( H @ ( G @ ( F @ sk234 ) ) ) )
      & ( ( H
          = ( G @ ( F @ k2_tarski ) ) )
        | ( ( F @ ( G @ ( H @ sk236 ) ) )
          = G )
        | ( ( F @ ( G @ ( H @ sk236 ) ) )
          = F )
        | ( H @ ( G @ ( F @ sk234 ) ) ) )
      & ( ( H
          = ( G @ ( F @ k2_tarski ) ) )
        | ~ ( H @ ( G @ ( F @ sk234 ) ) )
        | ( ( F @ ( G @ ( H @ sk235 ) ) )
         != G ) )
      & ( ( H
          = ( G @ ( F @ k2_tarski ) ) )
        | ~ ( H @ ( G @ ( F @ sk234 ) ) )
        | ( ( F @ ( G @ ( H @ sk235 ) ) )
         != F ) )
      & ( ( H
          = ( G @ ( F @ k2_tarski ) ) )
        | ~ ( H @ ( G @ ( F @ sk234 ) ) )
        | ( H @ ( F @ ( G @ ( H @ sk235 ) ) @ r2_hidden ) ) )
      & ( ( C @ ( E @ r2_hidden ) )
        | ( E != B )
        | ( C
         != ( B @ ( A @ k2_tarski ) ) ) )
      & ( ( C @ ( E @ r2_hidden ) )
        | ( E != A )
        | ( C
         != ( B @ ( A @ k2_tarski ) ) ) )
      & ( ( D = B )
        | ( D = A )
        | ~ ( C @ ( D @ r2_hidden ) )
        | ( C
         != ( B @ ( A @ k2_tarski ) ) ) ) ),
    inference(cnf,[status(esa)],[3503]) ).

thf(3506,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ( D != B )
      | ( C
       != ( B @ ( A @ k2_tarski ) ) ) ),
    inference(cnfConj,[status(thm)],[3504]) ).

thf(3523,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ( D != B )
      | ( C
       != ( B @ ( A @ k2_tarski ) ) ) ),
    inference(lifteq,[status(thm)],[3506]) ).

thf(3524,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( B @ r2_hidden ) ),
    inference(simp,[status(thm)],[3523]) ).

thf(28864,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)],[1994,3524]) ).

thf(28865,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( A @ k1_tarski @ r2_hidden ) ),
    inference(pattern_uni,[status(thm)],[28864:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(28875,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( A @ k1_tarski @ r2_hidden ) ),
    inference(simp,[status(thm)],[28865]) ).

thf(617,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l2_lattices )
        & ( A @ v4_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k3_lattices ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_lattices) ).

thf(4551,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)],[617]) ).

thf(488,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( ( ! [E: $i] :
                  ( B
                 != ( E @ k1_tarski ) )
              & ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) )
           => ( C @ ( D @ r1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_funct_2) ).

thf(3902,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)],[488]) ).

thf(29942,plain,
    ! [A: $i] :
      ( ( A != k6_nat_lat )
      | ( k1_xboole_0 @ v7_lattices )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,3108]) ).

thf(29943,plain,
    ( ( k1_xboole_0 @ v7_lattices )
    | ( k6_nat_lat @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[29942:[bind(A,$thf( k6_nat_lat ))]]) ).

thf(98,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ( ( C @ ( B @ ( A @ r3_binop_1 ) ) )
          <=> ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
              & ( C @ ( B @ ( A @ r1_binop_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_binop_1) ).

thf(1568,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(4368,plain,
    sk297 @ v5_lattices,
    inference(cnfConj,[status(thm)],[4356]) ).

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/sandbox/benchmark/theBenchmark.p',t12_binop_1) ).

thf(2520,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(284,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ! [B: $i] :
          ( ( B @ ( A @ r3_relat_2 ) )
        <=> ! [C: $i,D: $i] :
              ( ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
                & ( B @ ( D @ r2_hidden ) )
                & ( B @ ( C @ r2_hidden ) ) )
             => ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_2) ).

thf(2730,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)],[284]) ).

thf(877,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( ( A @ v13_lattices )
           => ( B @ ( A @ k5_lattices @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_filter_2) ).

thf(5746,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)],[877]) ).

thf(8672,plain,
    ! [A: $i] :
      ( ( ( sk295 @ 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)],[4326,6617]) ).

thf(8673,plain,
    ! [A: $i] :
      ( ( ( sk295 @ 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)],[8672]) ).

thf(8674,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8673:[bind(A,$thf( sk295 ))]]) ).

thf(503,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ( B @ l3_lattices )
        & ( B @ v17_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ( ( C @ ( B @ a_2_0_lattice4 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i,E: $i] :
            ( ( C @ ( E @ r2_hidden ) )
            & ( C @ ( D @ r2_hidden ) )
            & ( A
              = ( E @ ( D @ ( B @ k4_filter_0 ) ) ) )
            & ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
            & ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice4) ).

thf(3951,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)],[503]) ).

thf(2158,plain,
    ~ ( sk94 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2154]) ).

thf(10670,plain,
    ( ( ( k6_nat_lat @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5390,8209]) ).

thf(10671,plain,
    ( ( ( k6_nat_lat @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[10670]) ).

thf(10675,plain,
    ( ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[10671]) ).

thf(16137,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( k6_nat_lat != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,10675]) ).

thf(16138,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( k6_nat_lat != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16137]) ).

thf(16247,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk207 != k1_xboole_0 )
      | ( k6_nat_lat != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16138]) ).

thf(16315,plain,
    ( ( sk207 != k1_xboole_0 )
    | ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16247]) ).

thf(575,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v14_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( B @ ( A @ k6_lattices @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_filter_0) ).

thf(4302,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)],[575]) ).

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/sandbox/benchmark/theBenchmark.p',fc2_lattice2) ).

thf(2388,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(482,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k1_lattice4 ) @ ( A @ k7_lattices ) )
            = ( A @ k5_lattice4 @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_lattice4) ).

thf(3866,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)],[482]) ).

thf(565,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( B @ ( A @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

thf(4253,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( B @ ( A @ m1_subset_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(371,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ ( k1_xboole_0 @ ( D @ m2_relset_1 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( C = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_partfun1) ).

thf(3268,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)],[371]) ).

thf(169,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v10_lattices )
          & ( A @ v6_group_1 )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v14_lattices )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_lattice2) ).

thf(2007,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(93,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
          <=> ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
              & ( C @ ( B @ ( A @ r4_binop_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_binop_1) ).

thf(1489,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(88,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_relat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ~ ( A @ k1_relat_1 @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).

thf(1465,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(902,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v16_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ? [C: $i] :
                ( ( B @ ( C @ ( A @ r2_lattices ) ) )
                & ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d19_lattices) ).

thf(5892,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)],[902]) ).

thf(174,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ( C @ ( B @ ( A @ r1_realset1 ) ) )
          <=> ! [D: $i] :
                ( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
               => ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_realset1) ).

thf(2027,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ( ! [D: $i] :
                  ( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
                 => ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
             => ( 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(5326,plain,
    ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk393 @ v1_funct_2 ) ) )
    | ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
    inference(cnfConj,[status(thm)],[5322]) ).

thf(5333,plain,
    ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk393 @ v1_funct_2 ) ) )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(lifteq,[status(thm)],[5326]) ).

thf(402,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v16_lattices )
        & ( A @ v15_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v17_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
             => ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
               => ( ( C @ ( A @ ( B @ r4_lattice4 ) ) )
                  & ( A @ v17_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_lattice4) ).

thf(3453,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)],[402]) ).

thf(508,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v17_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
              = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( C = D )
                     => ( ( C @ ( A @ k7_lattices ) )
                        = ( D @ ( B @ k7_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_filter_2) ).

thf(3983,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)],[508]) ).

thf(667,axiom,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
      & ( A @ k1_subset_1 @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_subset_1) ).

thf(4815,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)],[667]) ).

thf(309,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ! [E: $i,F: $i] :
            ( ( A @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
           => ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
        & ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
     => ( D @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_zfmisc_1) ).

thf(2925,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)],[309]) ).

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

thf(1051,plain,
    ! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(884,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ~ ( B @ ( A @ k8_filter_2 ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_filter_2) ).

thf(5787,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)],[884]) ).

thf(817,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ? [C: $i] : ( B @ ( A @ ( C @ m3_realset1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_realset1) ).

thf(5526,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)],[817]) ).

thf(12327,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,9829]) ).

thf(12328,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12327]) ).

thf(12351,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk295 )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12328]) ).

thf(12362,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12351]) ).

thf(838,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                   => ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) )
                      & ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_filter_0) ).

thf(5597,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[838]) ).

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

thf(2364,plain,
    ! [A: $i,B: $i] :
      ~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(2365,plain,
    ~ ? [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
    inference(miniscope,[status(thm)],[2364]) ).

thf(2366,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
    inference(cnf,[status(esa)],[2365]) ).

thf(14796,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( sk71 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1924,2366]) ).

thf(14797,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[14796]) ).

thf(14815,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != sk71 ),
    inference(simp,[status(thm)],[14797]) ).

thf(84,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ! [B: $i] :
          ( ( B @ v1_relat_1 )
         => ( B @ ( A @ k4_xboole_0 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_relat_1) ).

thf(1450,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(186,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_zfmisc_1) ).

thf(2090,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(677,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i,C: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
            & ~ ( C @ v1_xboole_0 ) )
         => ! [D: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
                & ~ ( D @ v1_xboole_0 ) )
             => ~ ( ! [E: $i] :
                      ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ~ ( ( D @ ( F @ r2_hidden ) )
                              & ( C @ ( E @ r2_hidden ) )
                              & ( B
                                = ( F @ ( E @ ( A @ k4_lattices ) ) ) ) ) ) )
                  & ( D @ ( C @ ( A @ k5_filter_0 ) ) @ ( B @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_filter_0) ).

thf(4857,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)],[677]) ).

thf(33896,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( sk197 @ sk18 @ v1_funct_1 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,29780]) ).

thf(33897,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( sk197 @ sk18 @ v1_funct_1 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[33896]) ).

thf(33898,plain,
    ( ( sk197 @ sk18 @ v1_funct_1 )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[33897:[bind(A,$thf( sk1 ))]]) ).

thf(567,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
      <=> ( C @ ( B @ ( A @ r1_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r3_lattices) ).

thf(4258,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)],[567]) ).

thf(2996,plain,
    sk196 @ v10_lattices,
    inference(cnfConj,[status(thm)],[2983]) ).

thf(1034,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)],[1032]) ).

thf(1040,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)],[1034]) ).

thf(7811,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3087,6622]) ).

thf(7812,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7811]) ).

thf(7813,plain,
    ( ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7812:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(10656,plain,
    ( ( ( k6_nat_lat @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5390,7813]) ).

thf(10657,plain,
    ( ( ( k6_nat_lat @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[10656]) ).

thf(10673,plain,
    ( ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[10657]) ).

thf(16017,plain,
    ( ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[10673,2222]) ).

thf(16018,plain,
    ( ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16017]) ).

thf(2893,plain,
    sk188 @ v8_lattices,
    inference(cnfConj,[status(thm)],[2884]) ).

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/sandbox/benchmark/theBenchmark.p',dt_k2_partfun1) ).

thf(2259,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(513,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ! [D: $i] :
              ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
             => ( ! [E: $i] :
                    ( ( A @ ( E @ m1_subset_1 ) )
                   => ( ( B @ ( E @ r2_hidden ) )
                    <=> ( ( D @ ( E @ r2_hidden ) )
                        | ( C @ ( E @ r2_hidden ) ) ) ) )
               => ( B
                  = ( D @ ( C @ ( A @ k4_subset_1 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_subset_1) ).

thf(4001,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)],[513]) ).

thf(2880,plain,
    sk187 @ v6_lattices,
    inference(cnfConj,[status(thm)],[2869]) ).

thf(8920,plain,
    ( ( ( sk157 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2672,8209]) ).

thf(8921,plain,
    ( ( ( sk157 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8920]) ).

thf(8929,plain,
    ( ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8921]) ).

thf(35,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( A
         != ( B @ k1_tarski ) )
        & ( A != k1_xboole_0 )
        & ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
          = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_zfmisc_1) ).

thf(1133,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(1134,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)],[1133]) ).

thf(1135,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)],[1134]) ).

thf(1136,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)],[1135]) ).

thf(47023,plain,
    ( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3244,46818]) ).

thf(47024,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[47023]) ).

thf(47026,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk216 ),
    inference(simp,[status(thm)],[47024]) ).

thf(47043,plain,
    ( ( ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1924,46859]) ).

thf(47044,plain,
    ( ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[47043]) ).

thf(47105,plain,
    ( ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk71 ),
    inference(simp,[status(thm)],[47044]) ).

thf(8118,plain,
    ( ( ( sk196 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2989,7813]) ).

thf(8119,plain,
    ( ( ( sk196 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8118]) ).

thf(8159,plain,
    ( ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8119]) ).

thf(16025,plain,
    ( ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[8159,2222]) ).

thf(16026,plain,
    ( ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16025]) ).

thf(31017,plain,
    ! [A: $i] :
      ( ( A != sk196 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,16026]) ).

thf(31018,plain,
    ! [A: $i] :
      ( ( A != sk196 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[31017]) ).

thf(31019,plain,
    ( ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ( sk196 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[31018:[bind(A,$thf( sk196 ))]]) ).

thf(824,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ m2_nat_lat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_nat_lat) ).

thf(5541,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)],[824]) ).

thf(975,plain,
    sk1 @ l3_lattices,
    inference(cnfConj,[status(thm)],[969]) ).

thf(6471,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)],[1003,975]) ).

thf(6472,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ ( A @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[6471:[bind(A,$thf( sk1 ))]]) ).

thf(6628,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)],[6472]) ).

thf(7680,plain,
    ! [A: $i] :
      ( ( ( sk71 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1922,6628]) ).

thf(7681,plain,
    ! [A: $i] :
      ( ( ( sk71 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7680]) ).

thf(7682,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7681:[bind(A,$thf( sk71 ))]]) ).

thf(16108,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,7682]) ).

thf(16109,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16108]) ).

thf(16227,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk71 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[16109]) ).

thf(16293,plain,
    ( ( sk71 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[16227]) ).

thf(1148,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)],[1147]) ).

thf(1151,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)],[1148]) ).

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

thf(1015,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(1016,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
        | ( ( A @ ( B @ ( C @ sk6 ) ) @ ( B @ ( C @ k1_binop_1 ) ) )
         != ( A @ ( B @ ( C @ sk6 ) ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( A @ ( B @ m1_subset_1 ) ) )
      & ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
        | ( A @ ( A @ ( B @ ( C @ sk6 ) ) @ m1_subset_1 ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( A @ ( B @ m1_subset_1 ) ) )
      & ( ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
          = D )
        | ~ ( A @ ( D @ m1_subset_1 ) )
        | ~ ( C @ ( B @ ( A @ r1_binop_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
        | ~ ( C @ v1_funct_1 )
        | ~ ( A @ ( B @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[1015]) ).

thf(1017,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)],[1016]) ).

thf(1020,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)],[1017]) ).

thf(116,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ! [B: $i] :
          ( ( ( B @ v1_funct_1 )
            & ( B @ v1_relat_1 ) )
         => ( ( ! [C: $i] :
                  ( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
                 => ( ( C @ ( A @ k1_funct_1 ) )
                    = ( C @ ( B @ k1_funct_1 ) ) ) )
              & ( ( A @ k1_relat_1 )
                = ( B @ k1_relat_1 ) ) )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).

thf(1677,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(888,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k2_filter_2 ) @ m1_filter_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_filter_2) ).

thf(5805,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)],[888]) ).

thf(176,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ( C @ ( B @ r1_tarski ) )
          <=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_subset_1) ).

thf(2034,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(926,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ k1_lattice2 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k6_filter_2 ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_filter_2) ).

thf(5985,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)],[926]) ).

thf(375,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = ( A @ ( B @ k2_zfmisc_1 ) ) )
     => ( ( A = B )
        | ( B = k1_xboole_0 )
        | ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_zfmisc_1) ).

thf(3300,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)],[375]) ).

thf(339,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_relat_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).

thf(3093,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)],[339]) ).

thf(803,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v13_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
             => ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
               => ( ( C @ ( A @ ( B @ r3_lattice4 ) ) )
                  & ( A @ v13_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_lattice4) ).

thf(5457,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)],[803]) ).

thf(656,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_zfmisc_1) ).

thf(4783,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)],[656]) ).

thf(30154,plain,
    ! [A: $i] :
      ( ( A != sk196 )
      | ( sk1 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,7168]) ).

thf(30155,plain,
    ( ( sk1 != k1_xboole_0 )
    | ( sk196 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[30154:[bind(A,$thf( sk196 ))]]) ).

thf(35768,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( sk196 @ sk18 @ v1_funct_1 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,30155]) ).

thf(35769,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( sk196 @ sk18 @ v1_funct_1 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[35768]) ).

thf(35770,plain,
    ( ( sk196 @ sk18 @ v1_funct_1 )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[35769:[bind(A,$thf( sk1 ))]]) ).

thf(778,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
                     => ( ( B @ ( A @ ( E @ v1_lattice4 ) ) )
                       => ( ( D @ ( C @ ( A @ r3_lattices ) ) )
                        <=> ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_lattice4) ).

thf(5360,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)],[778]) ).

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

thf(1180,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(1181,plain,
    ! [A: $i] :
      ( ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
        | ~ ( A @ v1_funct_1 )
        | ~ ( A @ v1_relat_1 ) )
      & ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ v1_funct_2 ) ) )
        | ~ ( A @ v1_funct_1 )
        | ~ ( A @ v1_relat_1 ) )
      & ( ( A @ v1_funct_1 )
        | ~ ( A @ v1_funct_1 )
        | ~ ( A @ v1_relat_1 ) ) ),
    inference(cnf,[status(esa)],[1180]) ).

thf(1183,plain,
    ! [A: $i] :
      ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ v1_funct_2 ) ) )
      | ~ ( A @ v1_funct_1 )
      | ~ ( A @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1181]) ).

thf(14808,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( sk216 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3244,2366]) ).

thf(14809,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[14808]) ).

thf(14812,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != sk216 ),
    inference(simp,[status(thm)],[14809]) ).

thf(788,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k4_lattice4 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattice4) ).

thf(5401,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)],[788]) ).

thf(751,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k2_filter_2 ) )
        = ( B @ ( A @ k2_filter_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_filter_2) ).

thf(5220,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)],[751]) ).

thf(395,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( C @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).

thf(3421,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)],[395]) ).

thf(27633,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
       != ( C @ ( B @ k2_tarski ) ) )
      | ( ( A @ k1_tarski @ k1_zfmisc_1 )
       != sk71 ) ),
    inference(paramod_ordered,[status(thm)],[1994,15651]) ).

thf(27634,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk71 ),
    inference(pattern_uni,[status(thm)],[27633:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(27697,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk71 ),
    inference(simp,[status(thm)],[27634]) ).

thf(8398,plain,
    ! [A: $i] :
      ( ( ( sk216 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3245,6628]) ).

thf(8399,plain,
    ! [A: $i] :
      ( ( ( sk216 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8398]) ).

thf(8400,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8399:[bind(A,$thf( sk216 ))]]) ).

thf(16201,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,8400]) ).

thf(16202,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16201]) ).

thf(16244,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk216 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[16202]) ).

thf(16312,plain,
    ( ( sk216 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[16244]) ).

thf(470,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( A @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( A @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_domain_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_domain_1) ).

thf(3808,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)],[470]) ).

thf(687,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k5_lattices @ ( A @ k7_lattices ) )
        = ( A @ k6_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_lattice4) ).

thf(4924,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)],[687]) ).

thf(7762,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3050,3815]) ).

thf(7763,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7762]) ).

thf(7770,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[7763]) ).

thf(31532,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ k1_zfmisc_1 ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,7770]) ).

thf(31533,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ k1_zfmisc_1 ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[31532]) ).

thf(31534,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ sk18 @ v1_funct_1 ),
    inference(pattern_uni,[status(thm)],[31533:[bind(A,$thf( C @ k1_zfmisc_1 )),bind(B,$thf( C ))]]) ).

thf(33623,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ sk18 @ v1_funct_1 ),
    inference(simp,[status(thm)],[31534]) ).

thf(8193,plain,
    ! [A: $i] :
      ( ( ( sk207 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3137,6628]) ).

thf(8194,plain,
    ! [A: $i] :
      ( ( ( sk207 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8193]) ).

thf(8195,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8194:[bind(A,$thf( sk207 ))]]) ).

thf(16125,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,8195]) ).

thf(16126,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16125]) ).

thf(16213,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk207 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[16126]) ).

thf(16276,plain,
    ( ( sk207 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[16213]) ).

thf(47048,plain,
    ( ( ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3050,46859]) ).

thf(47049,plain,
    ( ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[47048]) ).

thf(47104,plain,
    ( ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != k1_xboole_0 ),
    inference(simp,[status(thm)],[47049]) ).

thf(8918,plain,
    ( ( ( sk187 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2881,8209]) ).

thf(8919,plain,
    ( ( ( sk187 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8918]) ).

thf(8924,plain,
    ( ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8919]) ).

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

thf(976,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(977,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)],[976]) ).

thf(978,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)],[977]) ).

thf(980,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)],[978]) ).

thf(981,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)],[980]) ).

thf(317,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( B @ ( A @ k1_funct_2 ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t159_funct_2) ).

thf(2964,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)],[317]) ).

thf(713,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_lattice2) ).

thf(5059,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)],[713]) ).

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

thf(1169,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(230,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_relat_1) ).

thf(2367,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(152,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
     => ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_zfmisc_1) ).

thf(1928,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
     => ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(800,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( ( E @ ( D @ ( A @ r3_lattices ) ) )
                          & ( C @ ( B @ ( A @ r3_lattices ) ) ) )
                       => ( ( C @ ( E @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
                          & ( E @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_filter_0) ).

thf(5448,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[800]) ).

thf(689,axiom,
    ( ! [A: $i] :
        ( ( f1_s3_funct_2 @ ( A @ m1_subset_1 ) )
       => ? [B: $i] :
            ( ( B @ ( A @ p1_s3_funct_2 ) )
            & ( f2_s3_funct_2 @ ( B @ m1_subset_1 ) ) ) )
   => ? [A: $i] :
        ( ! [B: $i] :
            ( ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
           => ( B @ ( A @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) ) )
        & ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ m2_relset_1 ) ) )
        & ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ v1_funct_2 ) ) )
        & ( A @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_2) ).

thf(4930,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)],[689]) ).

thf(4931,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( sk354 @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) )
        | ~ ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
        | ~ sk352 )
      & ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk354 @ m2_relset_1 ) ) )
        | ~ sk352 )
      & ( ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( sk354 @ v1_funct_2 ) ) )
        | ~ sk352 )
      & ( ( sk354 @ v1_funct_1 )
        | ~ sk352 )
      & ( sk352
        | ~ ( A @ ( sk353 @ p1_s3_funct_2 ) )
        | ~ ( f2_s3_funct_2 @ ( A @ m1_subset_1 ) ) )
      & ( sk352
        | ( f1_s3_funct_2 @ ( sk353 @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[4930]) ).

thf(4935,plain,
    ( sk352
    | ( f1_s3_funct_2 @ ( sk353 @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[4931]) ).

thf(952,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( D @ ( C @ ( B @ ( A @ r1_filter_0 ) ) ) )
                  <=> ( B @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_filter_0) ).

thf(6110,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)],[952]) ).

thf(6727,plain,
    ( ( ( sk187 @ v13_lattices )
     != ( sk1 @ v13_lattices ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2881,970]) ).

thf(6728,plain,
    ( ( sk187 @ v13_lattices )
   != ( sk1 @ v13_lattices ) ),
    inference(simp,[status(thm)],[6727]) ).

thf(6731,plain,
    sk187 != sk1,
    inference(simp,[status(thm)],[6728]) ).

thf(30770,plain,
    ! [A: $i] :
      ( ( A != sk187 )
      | ( sk1 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,6731]) ).

thf(30771,plain,
    ( ( sk1 != k1_xboole_0 )
    | ( sk187 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[30770:[bind(A,$thf( sk187 ))]]) ).

thf(448,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ m1_subset_1 ) )
     => ( ( B @ ( A @ r2_hidden ) )
        | ( B @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

thf(3712,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)],[448]) ).

thf(15318,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( sk152 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2587,3056]) ).

thf(15319,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[15318]) ).

thf(15328,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != sk152 ),
    inference(simp,[status(thm)],[15319]) ).

thf(4364,plain,
    sk297 @ v10_lattices,
    inference(cnfConj,[status(thm)],[4356]) ).

thf(7189,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( sk152 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2587,3815]) ).

thf(7190,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7189]) ).

thf(7192,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != sk152 ),
    inference(simp,[status(thm)],[7190]) ).

thf(11412,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ( ( k1_xboole_0 @ k1_tarski )
       != sk152 ) ),
    inference(paramod_ordered,[status(thm)],[1902,7192]) ).

thf(11413,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != sk152 ),
    inference(pattern_uni,[status(thm)],[11412:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(78,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = ( A @ k1_tarski ) )
    <=> ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).

thf(1394,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(702,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( A @ ( C @ v1_binop_1 ) )
               => ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
                <=> ! [D: $i] :
                      ( ( A @ ( D @ m1_subset_1 ) )
                     => ! [E: $i] :
                          ( ( A @ ( E @ m1_subset_1 ) )
                         => ! [F: $i] :
                              ( ( A @ ( F @ m1_subset_1 ) )
                             => ( ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                                = ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_binop_1) ).

thf(4996,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)],[702]) ).

thf(765,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k3_filter_2 ) )
        = ( B @ ( A @ k3_filter_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_filter_2) ).

thf(5296,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)],[765]) ).

thf(759,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k5_lattices @ ( A @ k4_lattices ) ) )
            = ( A @ k5_lattices ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_lattices) ).

thf(5246,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)],[759]) ).

thf(577,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_subset_1) ).

thf(4307,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)],[577]) ).

thf(8148,plain,
    ( ( ( sk187 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2881,7813]) ).

thf(8149,plain,
    ( ( ( sk187 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8148]) ).

thf(8156,plain,
    ( ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8149]) ).

thf(16027,plain,
    ( ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[8156,2222]) ).

thf(16028,plain,
    ( ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16027]) ).

thf(988,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
      | ~ ( B @ ( A @ ( C @ sk3 ) ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( C @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[985]) ).

thf(216,axiom,
    ! [A: $i] :
      ( ( A @ v1_finset_1 )
     => ( ( A @ k5_finsub_1 )
        = ( A @ k1_zfmisc_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finsub_1) ).

thf(2286,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(12017,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,6955]) ).

thf(12018,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12017]) ).

thf(12133,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk71 )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12018]) ).

thf(847,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
             => ( ( C @ ( B @ ( A @ r4_lattice4 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( D @ ( A @ k7_lattices ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
                      = ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k7_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice4) ).

thf(5629,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( 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)],[847]) ).

thf(616,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ( ( C
                  = ( B @ ( A @ k8_filter_0 ) ) )
              <=> ? [D: $i] :
                    ( ? [E: $i] :
                        ( ( C
                          = ( E @ ( D @ ( B @ g3_lattices ) ) ) )
                        & ( E
                          = ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
                        & ( D
                          = ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
                        & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                        & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                    & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                    & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_filter_0) ).

thf(4519,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)],[616]) ).

thf(734,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v3_filter_0 )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r8_relat_2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_filter_0) ).

thf(5137,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)],[734]) ).

thf(50509,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk71 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1921,1179]) ).

thf(50510,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk71 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[50509]) ).

thf(50511,plain,
    ! [A: $i] : ( A @ ( sk71 @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[50510:[bind(A,$thf( A )),bind(B,$thf( sk71 ))]]) ).

thf(426,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( A @ ( B @ r1_tarski ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).

thf(3606,plain,
    ! [A: $i,B: $i] :
      ~ ( ( A @ ( B @ r1_tarski ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

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] :
              ( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
                & ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
               => ! [D: $i] :
                    ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ? [E: $i] :
                        ( ( D
                          = ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) ) )
                        & ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_lattice4) ).

thf(3906,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)],[489]) ).

thf(356,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
    <=> ( ( B = k1_xboole_0 )
        | ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).

thf(3184,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)],[356]) ).

thf(7158,plain,
    ( ( ( sk196 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2989,6900]) ).

thf(7159,plain,
    ( ( ( sk196 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7158]) ).

thf(7170,plain,
    ( ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7159]) ).

thf(523,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m3_lattice4 ) )
             => ( ( C
                  = ( B @ ( A @ k3_lattice4 ) ) )
              <=> ( ! [D: $i] :
                      ( ( A @ ( D @ m3_lattice4 ) )
                     => ( ( D @ ( B @ r1_tarski ) )
                       => ( D @ ( C @ r1_tarski ) ) ) )
                  & ( C @ ( B @ r1_tarski ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_lattice4) ).

thf(4065,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)],[523]) ).

thf(863,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ! [E: $i] :
                      ( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ( ( C = F )
                              & ( B = E ) )
                           => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                            <=> ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_filter_0) ).

thf(5695,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[863]) ).

thf(139,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ v1_funct_1 )
        & ( C @ v1_relat_1 ) )
     => ( ( ( C @ k1_relat_1 @ ( B @ r2_hidden ) )
          & ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
       => ( ( B @ ( A @ k2_tarski ) @ ( C @ k9_relat_1 ) )
          = ( B @ ( C @ k1_funct_1 ) @ ( A @ ( C @ k1_funct_1 ) @ k2_tarski ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_funct_1) ).

thf(1863,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(23,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
        & ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_2) ).

thf(1074,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(743,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v6_group_1 )
      <=> ( A @ k1_lattice2 @ v6_group_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_lattice2) ).

thf(5174,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)],[743]) ).

thf(9791,plain,
    ( ( ( sk196 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2989,8691]) ).

thf(9792,plain,
    ( ( ( sk196 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9791]) ).

thf(9826,plain,
    ( ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9792]) ).

thf(16160,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( sk196 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,9826]) ).

thf(16161,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( sk196 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16160]) ).

thf(16215,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk295 != k1_xboole_0 )
      | ( sk196 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16161]) ).

thf(16279,plain,
    ( ( sk295 != k1_xboole_0 )
    | ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16215]) ).

thf(704,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
      <=> ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).

thf(5017,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)],[704]) ).

thf(945,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v15_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v14_lattices )
          & ( A @ v13_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_lattices) ).

thf(6064,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)],[945]) ).

thf(921,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_filter_2 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k15_filter_2 ) )
        = ( B @ ( A @ k7_filter_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k15_filter_2) ).

thf(5968,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)],[921]) ).

thf(620,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( A @ ( B @ v2_filter_0 ) )
              & ( B
               != ( A @ k1_filter_0 ) ) )
          <=> ( A @ ( B @ v1_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_filter_0) ).

thf(4557,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)],[620]) ).

thf(8395,plain,
    ! [A: $i] :
      ( ( ( sk216 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3245,6617]) ).

thf(8396,plain,
    ! [A: $i] :
      ( ( ( sk216 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8395]) ).

thf(8397,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8396:[bind(A,$thf( sk216 ))]]) ).

thf(187,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
     => ( C @ v1_relat_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).

thf(2093,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(16045,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( sk197 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,8928]) ).

thf(16046,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( sk197 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16045]) ).

thf(16255,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk207 != k1_xboole_0 )
      | ( sk197 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16046]) ).

thf(16324,plain,
    ( ( sk207 != k1_xboole_0 )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16255]) ).

thf(644,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ m2_lattice4 ) )
        & ~ ( C @ v1_xboole_0 )
        & ( B @ l3_lattices )
        & ( B @ v17_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ( ( C @ ( B @ a_2_1_lattice4 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ( C @ ( B @ k4_lattice4 ) @ ( D @ r1_tarski ) )
            & ( A
              = ( D @ ( B @ k2_lattice4 ) ) )
            & ( B @ u1_struct_0 @ k5_finsub_1 @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_lattice4) ).

thf(4700,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)],[644]) ).

thf(3011,plain,
    sk197 @ v9_lattices,
    inference(cnfConj,[status(thm)],[2999]) ).

thf(629,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( ! [E: $i] :
                ( ( A @ ( E @ r2_hidden ) )
               => ( ( E @ ( C @ k1_funct_1 ) )
                  = ( E @ ( D @ k1_funct_1 ) ) ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_2) ).

thf(4604,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)],[629]) ).

thf(401,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( A @ ( C @ r2_hidden ) )
       => ( ( C @ ( D @ k1_funct_1 ) )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funct_2) ).

thf(3450,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)],[401]) ).

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 ) )
     => ( B @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_2) ).

thf(4199,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)],[553]) ).

thf(404,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                    & ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                        & ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( A @ ( F @ m1_subset_1 ) )
                           => ! [G: $i] :
                                ( ( B @ ( G @ m1_subset_1 ) )
                               => ( ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
                                  = ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
                       => ( D = E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_binop_1) ).

thf(3459,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)],[404]) ).

thf(557,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( B @ ( A @ k6_domain_1 ) )
        = ( B @ k1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).

thf(4216,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)],[557]) ).

thf(306,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_xboole_0 )
        & ( A @ v1_relat_1 ) )
     => ( ( A @ v2_funct_1 )
        & ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).

thf(2910,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)],[306]) ).

thf(204,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
     => ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
          & ( C @ ( B @ r1_tarski ) ) )
       => ( B = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_subset_1) ).

thf(2204,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)],[204]) ).

thf(376,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ! [B: $i] :
          ( ( B
            = ( A @ k2_relat_1 ) )
        <=> ! [C: $i] :
              ( ( B @ ( C @ r2_hidden ) )
            <=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).

thf(3303,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)],[376]) ).

thf(819,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_lattice4 ) )
         => ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_lattice4) ).

thf(5530,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)],[819]) ).

thf(934,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ? [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
          & ( A @ ( B @ m2_lattice4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_lattice4) ).

thf(6020,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)],[934]) ).

thf(2473,plain,
    sk138 @ v2_funct_1,
    inference(cnfConj,[status(thm)],[2470]) ).

thf(879,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v3_filter_0 )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r1_relat_2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_filter_0) ).

thf(5751,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)],[879]) ).

thf(6181,plain,
    ( ( ( sk71 @ v1_xboole_0 )
     != ( sk14 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1924,1167]) ).

thf(6182,plain,
    ( ( sk71 @ v1_xboole_0 )
   != ( sk14 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6181]) ).

thf(6183,plain,
    sk71 != sk14,
    inference(simp,[status(thm)],[6182]) ).

thf(625,axiom,
    k6_nat_lat @ ( k13_nat_lat @ m2_nat_lat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_nat_lat) ).

thf(4589,plain,
    k6_nat_lat @ ( k13_nat_lat @ m2_nat_lat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(8892,plain,
    ( ( ( sk196 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2989,8209]) ).

thf(8893,plain,
    ( ( ( sk196 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8892]) ).

thf(8927,plain,
    ( ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8893]) ).

thf(30657,plain,
    ! [A: $i] :
      ( ( A != sk187 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,16028]) ).

thf(30658,plain,
    ! [A: $i] :
      ( ( A != sk187 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[30657]) ).

thf(30659,plain,
    ( ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ( sk187 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[30658:[bind(A,$thf( sk187 ))]]) ).

thf(792,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u2_lattices @ ( A @ k5_lattices @ ( A @ u1_struct_0 @ r3_binop_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_lattice2) ).

thf(5411,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)],[792]) ).

thf(15644,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
       != ( sk152 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2587,4338]) ).

thf(15645,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[15644]) ).

thf(15653,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) )
     != sk152 ),
    inference(simp,[status(thm)],[15645]) ).

thf(27676,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
       != ( C @ ( B @ k2_tarski ) ) )
      | ( ( A @ k1_tarski @ k1_zfmisc_1 )
       != sk152 ) ),
    inference(paramod_ordered,[status(thm)],[1994,15653]) ).

thf(27677,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk152 ),
    inference(pattern_uni,[status(thm)],[27676:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(27695,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk152 ),
    inference(simp,[status(thm)],[27677]) ).

thf(431,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( A @ ( B @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).

thf(3635,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)],[431]) ).

thf(2164,plain,
    sk94 @ v3_lattices,
    inference(cnfConj,[status(thm)],[2154]) ).

thf(7354,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( sk152 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2587,4906]) ).

thf(7355,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7354]) ).

thf(7357,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != sk152 ),
    inference(simp,[status(thm)],[7355]) ).

thf(794,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_lattice4 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ k1_lattice2 @ ( B @ ( A @ k9_filter_2 ) @ m2_lattice4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_filter_2) ).

thf(5416,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)],[794]) ).

thf(623,axiom,
    ( ! [A: $i] :
        ( ( f1_s14_funct_2 @ ( A @ m1_subset_1 ) )
       => ? [B: $i] :
            ( ( B @ ( A @ p1_s14_funct_2 ) )
            & ( f2_s14_funct_2 @ ( B @ m1_subset_1 ) ) ) )
   => ? [A: $i] :
        ( ! [B: $i] :
            ( ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
           => ( B @ ( A @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) ) )
        & ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ m2_relset_1 ) ) )
        & ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ v1_funct_2 ) ) )
        & ( A @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s14_funct_2) ).

thf(4576,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)],[623]) ).

thf(684,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ~ ( C @ ( D @ r2_hidden ) )
            & ( A = D )
            & ( B @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_2_domain_1) ).

thf(4910,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)],[684]) ).

thf(16182,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( sk297 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,9406]) ).

thf(16183,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( sk297 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16182]) ).

thf(16231,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk207 != k1_xboole_0 )
      | ( sk297 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16183]) ).

thf(16297,plain,
    ( ( sk207 != k1_xboole_0 )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16231]) ).

thf(16076,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( sk187 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,8924]) ).

thf(16077,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( sk187 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16076]) ).

thf(16226,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk207 != k1_xboole_0 )
      | ( sk187 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16077]) ).

thf(16292,plain,
    ( ( sk207 != k1_xboole_0 )
    | ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16226]) ).

thf(11991,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,8691]) ).

thf(11992,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[11991]) ).

thf(12184,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk295 )
    | ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[11992]) ).

thf(12205,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12184]) ).

thf(1060,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)],[1059]) ).

thf(1063,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)],[1060]) ).

thf(1067,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)],[1063]) ).

thf(127,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funct_2) ).

thf(1768,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(19,axiom,
    ( ( ( k1_xboole_0 @ k2_relat_1 )
      = k1_xboole_0 )
    & ( ( k1_xboole_0 @ k1_relat_1 )
      = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).

thf(1053,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(1054,plain,
    ( ( ( k1_xboole_0 @ k2_relat_1 )
      = k1_xboole_0 )
    & ( ( k1_xboole_0 @ k1_relat_1 )
      = k1_xboole_0 ) ),
    inference(cnf,[status(esa)],[1053]) ).

thf(1055,plain,
    ( ( k1_xboole_0 @ k1_relat_1 )
    = k1_xboole_0 ),
    inference(cnfConj,[status(thm)],[1054]) ).

thf(1057,plain,
    ( ( k1_xboole_0 @ k1_relat_1 )
    = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1055]) ).

thf(2673,plain,
    sk157 @ v3_lattices,
    inference(cnfConj,[status(thm)],[2661]) ).

thf(1900,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
    inference(cnf,[status(esa)],[1899]) ).

thf(1019,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
      | ( ( A @ ( B @ ( C @ sk6 ) ) @ ( B @ ( C @ k1_binop_1 ) ) )
       != ( A @ ( B @ ( C @ sk6 ) ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( A @ ( B @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[1016]) ).

thf(1021,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( A @ ( B @ m1_subset_1 ) )
      | ( ( A @ ( B @ ( C @ sk6 ) ) @ ( B @ ( C @ k1_binop_1 ) ) )
       != ( A @ ( B @ ( C @ sk6 ) ) ) ) ),
    inference(lifteq,[status(thm)],[1019]) ).

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

thf(1042,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(938,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( ( C @ ( D @ ( A @ r3_lattices ) ) )
                      & ( C @ ( B @ ( A @ r3_lattices ) ) ) )
                   => ( C @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_filter_0) ).

thf(6032,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[938]) ).

thf(26839,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk207 @ k2_relat_1 @ ( A @ ( sk207 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[26795,1030]) ).

thf(26840,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk207 @ k2_relat_1 @ ( A @ ( sk207 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[26839]) ).

thf(26841,plain,
    ! [B: $i,A: $i] : ( sk207 @ k2_relat_1 @ ( A @ ( B @ ( sk207 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[26840:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk207 @ k9_relat_1 ) )),bind(C,$thf( sk207 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(26868,plain,
    ! [B: $i,A: $i] : ( sk207 @ k2_relat_1 @ ( A @ ( B @ ( sk207 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[26841]) ).

thf(510,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v11_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ! [F: $i] :
                          ( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ! [G: $i] :
                                ( ( A @ ( G @ m1_subset_1 ) )
                               => ( ( B @ ( G @ r2_hidden ) )
                                 => ( ( G @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) )
                                    = ( G @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( C @ k4_lattices ) ) ) ) ) )
                           => ( ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( F @ ( C @ k4_lattices ) ) )
                              = ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_lattice2) ).

thf(3989,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)],[510]) ).

thf(311,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
           => ( B @ ( A @ k3_subset_1 ) @ ( C @ r1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_subset_1) ).

thf(2937,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)],[311]) ).

thf(519,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( A @ ( B @ m3_lattice4 ) )
          <=> ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( ( B @ ( D @ r2_hidden ) )
                        & ( B @ ( C @ r2_hidden ) ) )
                     => ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
                        & ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_lattice4) ).

thf(4044,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)],[519]) ).

thf(710,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ ( C @ ( B @ ( A @ k22_filter_2 ) ) @ m2_lattice4 ) )
        & ~ ( C @ ( B @ ( A @ k22_filter_2 ) ) @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k22_filter_2) ).

thf(5049,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)],[710]) ).

thf(261,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k4_tarski ) )
      = ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

thf(2589,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(11971,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,8928]) ).

thf(11972,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[11971]) ).

thf(12110,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk207 )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[11972]) ).

thf(841,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k3_filter_0 ) @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_filter_0) ).

thf(5611,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)],[841]) ).

thf(873,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
                   => ( B @ ( C @ ( D @ ( A @ r1_filter_0 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_filter_0) ).

thf(5734,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( 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)],[873]) ).

thf(1088,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)],[1087]) ).

thf(1091,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)],[1088]) ).

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/sandbox/benchmark/theBenchmark.p',t31_relat_1) ).

thf(2601,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(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/sandbox/benchmark/theBenchmark.p',t59_partfun1) ).

thf(2428,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(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/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).

thf(2560,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(291,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( B @ ( D @ r2_hidden ) )
                <=> ~ ( C @ ( D @ r2_hidden ) ) ) )
           => ( B
              = ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_subset_1) ).

thf(2805,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)],[291]) ).

thf(506,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
                = ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_filter_0) ).

thf(3972,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)],[506]) ).

thf(8632,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( sk278 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4083,4906]) ).

thf(8633,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( sk278 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8632]) ).

thf(8645,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != sk278 ),
    inference(simp,[status(thm)],[8633]) ).

thf(53,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
     => ( ( B @ ( D @ k1_relat_1 @ r1_tarski ) )
       => ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_relset_1) ).

thf(1217,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(326,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ v1_relat_1 )
     => ! [C: $i] :
          ( ( C @ v1_relat_1 )
         => ( ( C @ ( B @ r1_tarski ) )
           => ( A @ ( C @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t157_relat_1) ).

thf(3022,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)],[326]) ).

thf(802,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( A @ ( B @ m2_lattice4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_lattice4) ).

thf(5455,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)],[802]) ).

thf(95,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ( A @ v2_funct_1 )
       => ! [B: $i] :
            ( ( ( B @ v1_funct_1 )
              & ( B @ v1_relat_1 ) )
           => ( ( B
                = ( A @ k2_funct_1 ) )
            <=> ( ! [C: $i,D: $i] :
                    ( ( ( ( C
                          = ( D @ ( A @ k1_funct_1 ) ) )
                        & ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
                     => ( ( D
                          = ( C @ ( B @ k1_funct_1 ) ) )
                        & ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
                    & ( ( ( D
                          = ( C @ ( B @ k1_funct_1 ) ) )
                        & ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
                     => ( ( C
                          = ( D @ ( A @ k1_funct_1 ) ) )
                        & ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
                & ( ( B @ k1_relat_1 )
                  = ( A @ k2_relat_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).

thf(1502,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(890,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k4_filter_0 ) ) )
                = ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_filter_0) ).

thf(5815,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)],[890]) ).

thf(657,axiom,
    ? [A: $i] : ( A @ l2_lattices ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).

thf(4785,plain,
    ? [A: $i] : ( A @ l2_lattices ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

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/sandbox/benchmark/theBenchmark.p',t7_funct_2) ).

thf(2606,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(9390,plain,
    ( ( ( sk297 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4370,7813]) ).

thf(9391,plain,
    ( ( ( sk297 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9390]) ).

thf(9405,plain,
    ( ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9391]) ).

thf(16015,plain,
    ( ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[9405,2222]) ).

thf(16016,plain,
    ( ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16015]) ).

thf(132,axiom,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).

thf(1822,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(1823,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(cnf,[status(esa)],[1822]) ).

thf(1824,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1823]) ).

thf(880,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v13_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_filter_0) ).

thf(5754,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)],[880]) ).

thf(473,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( A @ k1_lattice2 @ l3_lattices )
        & ( A @ k1_lattice2 @ v3_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice2) ).

thf(3816,plain,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( A @ k1_lattice2 @ l3_lattices )
        & ( A @ k1_lattice2 @ v3_lattices ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(175,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( D @ r2_hidden ) )
        & ( A @ ( C @ r2_hidden ) ) )
     => ( B @ ( A @ ( D @ ( C @ k4_tarski ) @ k1_tarski @ m2_relset_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_relset_1) ).

thf(2032,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(815,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v11_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
      <=> ( ( A @ k1_lattice2 @ l3_lattices )
          & ( A @ k1_lattice2 @ v11_lattices )
          & ( A @ k1_lattice2 @ v10_lattices )
          & ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_lattice2) ).

thf(5507,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)],[815]) ).

thf(668,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( C @ ( B @ ( A @ r7_binop_1 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ ( D @ m1_subset_1 ) )
                   => ! [E: $i] :
                        ( ( A @ ( E @ m1_subset_1 ) )
                       => ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) )
                          = ( E @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d20_binop_1) ).

thf(4821,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)],[668]) ).

thf(2986,plain,
    ~ ( sk196 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2983]) ).

thf(30477,plain,
    ! [A: $i] :
      ( ( A != k6_nat_lat )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,16018]) ).

thf(30478,plain,
    ! [A: $i] :
      ( ( A != k6_nat_lat )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[30477]) ).

thf(30479,plain,
    ( ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ( k6_nat_lat @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[30478:[bind(A,$thf( k6_nat_lat ))]]) ).

thf(11997,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
    | ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,8924]) ).

thf(11998,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
    | ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[11997]) ).

thf(12115,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk207 )
    | ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[11998]) ).

thf(2890,plain,
    ~ ( sk188 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2884]) ).

thf(837,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ k1_setwiseo @ ( A @ k2_lattice4 ) )
        = ( A @ k6_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_lattice4) ).

thf(5594,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)],[837]) ).

thf(545,axiom,
    ! [A: $i,B: $i] :
      ~ ( ! [C: $i] :
            ~ ( ! [D: $i] :
                  ~ ( ( C @ ( D @ r2_hidden ) )
                    & ( B @ ( D @ r2_hidden ) ) )
              & ( B @ ( C @ r2_hidden ) ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).

thf(4160,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)],[545]) ).

thf(636,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A @ ( D @ r2_hidden ) )
        & ( D @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_ordinal1) ).

thf(4661,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)],[636]) ).

thf(360,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
    <=> ! [B: $i] :
          ~ ( ! [C: $i,D: $i] :
                ( B
               != ( D @ ( C @ k4_tarski ) ) )
            & ( A @ ( B @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).

thf(3207,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)],[360]) ).

thf(16055,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( sk157 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,9828]) ).

thf(16056,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( sk157 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16055]) ).

thf(16240,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk295 != k1_xboole_0 )
      | ( sk157 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16056]) ).

thf(16307,plain,
    ( ( sk295 != k1_xboole_0 )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16240]) ).

thf(3509,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ( D != A )
      | ( C
       != ( B @ ( A @ k2_tarski ) ) ) ),
    inference(cnfConj,[status(thm)],[3504]) ).

thf(3513,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ r2_hidden ) )
      | ( D != A )
      | ( C
       != ( B @ ( A @ k2_tarski ) ) ) ),
    inference(lifteq,[status(thm)],[3509]) ).

thf(3514,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ r2_hidden ) ),
    inference(simp,[status(thm)],[3513]) ).

thf(502,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
                = ( C @ ( B @ ( A @ a_3_2_domain_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_domain_1) ).

thf(3948,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)],[502]) ).

thf(372,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v11_lattices )
          & ( A @ v10_lattices )
          & ( A @ v6_group_1 )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v1_lattice2 )
          & ( A @ v3_filter_0 )
          & ( A @ v13_lattices )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_lattice2) ).

thf(3271,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)],[372]) ).

thf(428,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ! [D: $i] :
              ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
                & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
                & ( D @ v1_funct_1 ) )
             => ! [E: $i] :
                  ( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
                    & ( B @ ( A @ ( E @ v1_funct_2 ) ) )
                    & ( E @ v1_funct_1 ) )
                 => ( ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
                      = ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
                  <=> ! [F: $i] :
                        ( ( A @ ( F @ m1_subset_1 ) )
                       => ( ( C @ ( F @ r2_hidden ) )
                         => ( ( F @ ( E @ k1_funct_1 ) )
                            = ( F @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_lattice2) ).

thf(3618,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)],[428]) ).

thf(12286,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,9828]) ).

thf(12287,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12286]) ).

thf(12311,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk295 )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12287]) ).

thf(12321,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12311]) ).

thf(2872,plain,
    sk187 @ v7_lattices,
    inference(cnfConj,[status(thm)],[2869]) ).

thf(618,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
     => ( ( B @ ( A @ r1_tarski ) )
       => ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_relset_1) ).

thf(4553,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)],[618]) ).

thf(118,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( B @ ( A @ k1_funct_2 ) ) )
    <=> ! [D: $i] :
          ( ( C @ ( D @ r2_hidden ) )
        <=> ? [E: $i] :
              ( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
              & ( ( E @ k1_relat_1 )
                = A )
              & ( D = E )
              & ( E @ v1_funct_1 )
              & ( E @ v1_relat_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funct_2) ).

thf(1687,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(52,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( B @ ( D @ ( C @ k1_binop_1 ) ) )
                  = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_binop_1) ).

thf(1210,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(871,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k2_struct_0 ) ) )
        = ( B @ ( C @ ( A @ k2_struct_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_struct_0) ).

thf(5729,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)],[871]) ).

thf(605,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
              & ( A @ l3_lattices )
              & ( A @ v13_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( ( ( B @ ( A @ k3_filter_0 ) )
                = ( A @ u1_struct_0 ) )
              & ( ( B @ ( A @ k3_filter_0 ) )
                = ( A @ k1_filter_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_filter_0) ).

thf(4461,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)],[605]) ).

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/sandbox/benchmark/theBenchmark.p',t13_lattice2) ).

thf(2464,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(156,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ! [D: $i] :
            ~ ( ! [E: $i] :
                  ~ ( ( D
                      = ( E @ ( C @ k1_funct_1 ) ) )
                    & ( A @ ( E @ r2_hidden ) ) )
              & ( B @ ( D @ r2_hidden ) ) )
       => ( ( ( C @ k2_relat_1 )
            = B )
          | ( B = k1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_2) ).

thf(1938,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(10662,plain,
    ( ( ( sk1 @ v13_lattices )
     != ( k6_nat_lat @ v13_lattices ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5390,970]) ).

thf(10663,plain,
    ( ( sk1 @ v13_lattices )
   != ( k6_nat_lat @ v13_lattices ) ),
    inference(simp,[status(thm)],[10662]) ).

thf(10677,plain,
    sk1 != k6_nat_lat,
    inference(simp,[status(thm)],[10663]) ).

thf(31867,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k6_nat_lat != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,10677]) ).

thf(31868,plain,
    ( ( k6_nat_lat != k1_xboole_0 )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[31867:[bind(A,$thf( sk1 ))]]) ).

thf(5391,plain,
    k6_nat_lat @ l3_lattices,
    inference(cnfConj,[status(thm)],[5387]) ).

thf(2873,plain,
    sk187 @ v5_lattices,
    inference(cnfConj,[status(thm)],[2869]) ).

thf(30244,plain,
    ! [A: $i] :
      ( ( A != sk14 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,7771]) ).

thf(30245,plain,
    ! [A: $i] :
      ( ( A != sk14 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[30244]) ).

thf(30246,plain,
    sk14 @ sk18 @ v1_funct_1,
    inference(pattern_uni,[status(thm)],[30245:[bind(A,$thf( sk14 ))]]) ).

thf(925,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_lattice4 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k23_filter_2 ) @ m2_nat_lat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k23_filter_2) ).

thf(5983,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)],[925]) ).

thf(8358,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( sk216 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3244,4906]) ).

thf(8359,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8358]) ).

thf(8371,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != sk216 ),
    inference(simp,[status(thm)],[8359]) ).

thf(2670,plain,
    sk157 @ v10_lattices,
    inference(cnfConj,[status(thm)],[2661]) ).

thf(471,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ( ( A @ k2_subset_1 @ ( B @ ( A @ k4_subset_1 ) ) )
        = ( A @ k2_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_subset_1) ).

thf(3810,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)],[471]) ).

thf(520,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_filter_0 ) )
        & ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k4_filter_2 ) ) )
        = ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_filter_2) ).

thf(4053,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)],[520]) ).

thf(624,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( C @ ( B @ r1_tarski ) )
       => ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
          & ( D @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_partfun1) ).

thf(4585,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)],[624]) ).

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/sandbox/benchmark/theBenchmark.p',t38_funct_2) ).

thf(2477,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(2663,plain,
    sk157 @ v4_lattices,
    inference(cnfConj,[status(thm)],[2661]) ).

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

thf(2332,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(941,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ~ ( ! [D: $i] :
                      ( ( A @ ( D @ m1_filter_0 ) )
                     => ~ ( ( ( ( D @ ( C @ r2_hidden ) )
                              & ~ ( D @ ( B @ r2_hidden ) ) )
                            | ( ~ ( D @ ( C @ r2_hidden ) )
                              & ( D @ ( B @ r2_hidden ) ) ) )
                          & ( A @ ( D @ v1_filter_0 ) ) ) )
                  & ( B != C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_filter_0) ).

thf(6043,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)],[941]) ).

thf(544,axiom,
    ! [A: $i] :
      ( ( A @ l1_lattices )
     => ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ m2_relset_1 ) ) )
        & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
        & ( A @ u1_lattices @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).

thf(4155,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)],[544]) ).

thf(701,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_domain_1) ).

thf(4994,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)],[701]) ).

thf(692,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ v11_lattices )
           => ( B @ ( A @ k8_filter_0 ) @ v11_lattices ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_filter_0) ).

thf(4947,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)],[692]) ).

thf(412,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
              & ( B @ ( A @ k5_lattices @ r2_hidden ) ) )
           => ( ( B @ ( A @ a_2_1_lattice4 ) )
              = ( B @ ( A @ k3_lattice4 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_lattice4) ).

thf(3499,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)],[412]) ).

thf(927,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) )
            = ( A @ k5_lattices ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_lattices) ).

thf(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 ) )
         => ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) )
            = ( A @ k5_lattices ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).

thf(3892,plain,
    ( ~ ( sk265 @ v3_struct_0 )
    & ( sk265 @ l1_struct_0 ) ),
    inference(cnf,[status(esa)],[3891]) ).

thf(3894,plain,
    ~ ( sk265 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[3892]) ).

thf(4327,plain,
    f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ v1_funct_2 ) ),
    inference(cnfConj,[status(thm)],[4325]) ).

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 ) )
     => ( ( C @ ( B @ ( A @ g3_lattices ) ) @ l3_lattices )
        & ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g3_lattices) ).

thf(2200,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)],[203]) ).

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

thf(2609,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(594,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ! [B: $i] :
          ( ( B @ l3_lattices )
         => ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
              = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
           => ( ( A @ k1_lattice2 )
              = ( B @ k1_lattice2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_filter_2) ).

thf(4402,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)],[594]) ).

thf(135,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ v1_relat_1 )
     => ( ( C
          = ( B @ ( A @ k4_tarski ) @ k1_tarski ) )
       => ( ( ( C @ k2_relat_1 )
            = ( B @ k1_tarski ) )
          & ( ( C @ k1_relat_1 )
            = ( A @ k1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relat_1) ).

thf(1836,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(130,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k4_xboole_0 ) )
        = k1_xboole_0 )
    <=> ( B @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).

thf(1787,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(832,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ ( B @ v1_filter_0 ) )
          <=> ( ! [C: $i] :
                  ( ( A @ ( C @ m1_filter_0 ) )
                 => ( ( C @ ( B @ r1_tarski ) )
                   => ( ( B = C )
                      | ( C
                        = ( A @ u1_struct_0 ) ) ) ) )
              & ( B
               != ( A @ u1_struct_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_filter_0) ).

thf(5566,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)],[832]) ).

thf(943,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( B @ ( A @ k6_filter_2 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_filter_2) ).

thf(6060,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)],[943]) ).

thf(206,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = ( D @ ( C @ k2_zfmisc_1 ) ) )
     => ( ( ( B = D )
          & ( A = C ) )
        | ( B = k1_xboole_0 )
        | ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).

thf(2213,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)],[206]) ).

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

thf(1025,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(1026,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)],[1025]) ).

thf(1027,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)],[1026]) ).

thf(16146,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( sk187 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,9830]) ).

thf(16147,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( sk187 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16146]) ).

thf(16211,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk295 != k1_xboole_0 )
      | ( sk187 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16147]) ).

thf(16274,plain,
    ( ( sk295 != k1_xboole_0 )
    | ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16211]) ).

thf(597,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v14_lattices )
       => ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ( ( B
                = ( A @ k6_lattices ) )
            <=> ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ( ( ( B @ ( C @ ( A @ k1_lattices ) ) )
                      = B )
                    & ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                      = B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_lattices) ).

thf(4417,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)],[597]) ).

thf(2345,plain,
    sk118 @ v8_lattices,
    inference(cnfConj,[status(thm)],[2342]) ).

thf(2344,plain,
    sk118 @ l3_lattices,
    inference(cnfConj,[status(thm)],[2342]) ).

thf(1128,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)],[1127]) ).

thf(432,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_2 ) )
         => ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_filter_2) ).

thf(3647,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)],[432]) ).

thf(193,axiom,
    ! [A: $i] :
      ( ( ! [B: $i,C: $i,D: $i] :
            ( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
              & ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
           => ( C = D ) )
        & ! [B: $i] :
            ~ ( ! [C: $i,D: $i] :
                  ( ( D @ ( C @ k4_tarski ) )
                 != B )
              & ( A @ ( B @ r2_hidden ) ) ) )
     => ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funct_1) ).

thf(2112,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(62,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ v1_relat_1 )
     => ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) @ ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t155_relat_1) ).

thf(1291,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(120,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ( A @ v2_funct_1 )
       => ( A @ k2_funct_1 @ v2_funct_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).

thf(1740,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(47097,plain,
    ( ( ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk278 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4083,46859]) ).

thf(47098,plain,
    ( ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk278 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[47097]) ).

thf(47108,plain,
    ( ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk278 ),
    inference(simp,[status(thm)],[47098]) ).

thf(9113,plain,
    ( ( ( sk197 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3001,8414]) ).

thf(9114,plain,
    ( ( ( sk197 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9113]) ).

thf(9144,plain,
    ( ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9114]) ).

thf(16121,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( sk197 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,9144]) ).

thf(16122,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( sk197 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16121]) ).

thf(16235,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk216 != k1_xboole_0 )
      | ( sk197 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16122]) ).

thf(16301,plain,
    ( ( sk216 != k1_xboole_0 )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16235]) ).

thf(99,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ! [B: $i] :
          ( ( ( B @ v1_funct_1 )
            & ( B @ v1_relat_1 ) )
         => ( ( A @ ( B @ r1_tarski ) )
           => ( ( B @ ( A @ k1_funct_4 ) )
              = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_lattice2) ).

thf(1573,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(5328,plain,
    ( ( ( f3_s11_funct_2 @ ( sk393 @ ( 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)],[5322]) ).

thf(5330,plain,
    ( ( ( f3_s11_funct_2 @ ( sk393 @ ( 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)],[5328]) ).

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

thf(1011,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(1012,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)],[1011]) ).

thf(522,axiom,
    ! [A: $i] :
      ( ( A @ l2_lattices )
     => ( A @ l1_struct_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).

thf(4063,plain,
    ! [A: $i] :
      ( ( A @ l2_lattices )
     => ( A @ l1_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(30,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
       => ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
          & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
          & ( C @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_funct_2) ).

thf(1103,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(1104,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)],[1103]) ).

thf(1106,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)],[1104]) ).

thf(453,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A @ v1_funct_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).

thf(3731,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A @ v1_funct_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(165,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
     => ~ ( ! [E: $i,F: $i] :
              ~ ( ( B @ ( F @ r2_hidden ) )
                & ( A @ ( E @ r2_hidden ) )
                & ( C
                  = ( F @ ( E @ k4_tarski ) ) ) )
          & ( D @ ( C @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relset_1) ).

thf(1983,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(711,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ( ( C @ ( B @ ( D @ ( A @ r1_filter_0 ) ) ) )
                  <=> ( D @ ( A @ k10_filter_0 ) @ ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_filter_0) ).

thf(5053,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[711]) ).

thf(962,axiom,
    ? [A: $i] : ( A @ l3_lattices ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_lattices) ).

thf(6153,plain,
    ? [A: $i] : ( A @ l3_lattices ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).

thf(696,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( C @ ( B @ r2_hidden ) )
               => ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k2_filter_0 ) @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_filter_0) ).

thf(4974,plain,
    ! [A: $i] :
      ( ( ( A @ l3_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)],[696]) ).

thf(843,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( ( ( C @ ( B @ ( A @ k3_lattices ) ) )
                        = ( D @ ( B @ ( A @ k3_lattices ) ) ) )
                      & ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                        = ( D @ ( B @ ( A @ k4_lattices ) ) ) ) )
                   => ( C = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_lattices) ).

thf(5615,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)],[843]) ).

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

thf(1108,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(1109,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)],[1108]) ).

thf(1111,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)],[1109]) ).

thf(598,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
     => ( ( B @ ( A @ r1_tarski ) )
       => ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_relset_1) ).

thf(4429,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)],[598]) ).

thf(82,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_subset_1 ) )
         => ( ( A @ ( B @ v1_binop_1 ) )
           => ( ( B @ ( C @ ( A @ r1_binop_1 ) ) )
            <=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_binop_1) ).

thf(1425,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(504,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v16_lattices )
          & ( A @ v15_lattices )
          & ( A @ v11_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v17_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_lattices) ).

thf(3963,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)],[504]) ).

thf(16195,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,6903]) ).

thf(16196,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16195]) ).

thf(16220,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk138 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16196]) ).

thf(16284,plain,
    ( ( sk138 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16220]) ).

thf(14494,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk393 @ 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)],[5329,1079]) ).

thf(14495,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk393 @ 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)],[14494]) ).

thf(14496,plain,
    ( ( f1_s11_funct_2 @ ( sk393 @ k1_relat_1 @ r1_tarski ) )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(pattern_uni,[status(thm)],[14495:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk393 ))]]) ).

thf(15717,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s11_funct_2 @ ( sk393 @ 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)],[14496,1030]) ).

thf(15718,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s11_funct_2 @ ( sk393 @ 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)],[15717]) ).

thf(15719,plain,
    ! [A: $i] :
      ( ( f1_s11_funct_2 @ ( A @ ( sk393 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(pattern_uni,[status(thm)],[15718:[bind(A,$thf( sk393 @ k1_relat_1 )),bind(B,$thf( f1_s11_funct_2 )),bind(C,$thf( C ))]]) ).

thf(15729,plain,
    ! [A: $i] :
      ( ( f1_s11_funct_2 @ ( A @ ( sk393 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(simp,[status(thm)],[15719]) ).

thf(666,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( ? [C: $i] :
            ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
            & ( A @ ( C @ m1_subset_1 ) ) )
       => ! [C: $i] :
            ( ( A @ ( C @ m1_subset_1 ) )
           => ( ( C
                = ( B @ ( A @ k3_binop_1 ) ) )
            <=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_binop_1) ).

thf(4808,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)],[666]) ).

thf(155,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ( A @ v5_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( A @ u2_lattices @ v2_binop_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_lattice2) ).

thf(1936,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(3105,plain,
    k6_nat_lat @ v10_lattices,
    inference(cnfConj,[status(thm)],[3103]) ).

thf(405,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ u1_lattices )
          = ( A @ k1_lattice2 @ u2_lattices ) )
        & ( ( A @ u2_lattices )
          = ( A @ k1_lattice2 @ u1_lattices ) )
        & ( ( A @ u1_struct_0 )
          = ( A @ k1_lattice2 @ u1_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_lattice2) ).

thf(3467,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)],[405]) ).

thf(28595,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)],[3514,2961]) ).

thf(28596,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ ( A @ r2_hidden ) )
     != ( k1_xboole_0 @ ( C @ r2_hidden ) ) ),
    inference(simp,[status(thm)],[28595]) ).

thf(28599,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) )
       != k1_xboole_0 )
      | ( A != C ) ),
    inference(simp,[status(thm)],[28596]) ).

thf(28611,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k2_tarski ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[28599]) ).

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/sandbox/benchmark/theBenchmark.p',t77_funct_2) ).

thf(2300,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(905,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ? [C: $i] : ( B @ ( A @ ( C @ m1_lattice4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_lattice4) ).

thf(5904,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)],[905]) ).

thf(1089,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)],[1088]) ).

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/sandbox/benchmark/theBenchmark.p',t11_funct_2) ).

thf(2498,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(475,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v6_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                  = ( B @ ( C @ ( A @ k2_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_lattices) ).

thf(3831,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)],[475]) ).

thf(2157,plain,
    sk94 @ l3_lattices,
    inference(cnfConj,[status(thm)],[2154]) ).

thf(295,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ( C @ ( B @ ( A @ k6_subset_1 ) ) @ ( A @ k3_subset_1 ) )
            = ( C @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_subset_1) ).

thf(2840,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)],[295]) ).

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

thf(1140,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( ( ! [C: $i] :
              ( ( 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(1141,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ v3_binop_1 ) )
        | ( ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk12 ) @ ( B @ k1_binop_1 ) ) )
         != ( A @ ( B @ sk12 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        | ~ ( B @ v1_funct_1 ) )
      & ( ( A @ ( B @ v3_binop_1 ) )
        | ( A @ ( A @ ( B @ sk12 ) @ m1_subset_1 ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        | ~ ( B @ v1_funct_1 ) )
      & ( ( ( C @ ( C @ ( B @ k1_binop_1 ) ) )
          = C )
        | ~ ( A @ ( C @ m1_subset_1 ) )
        | ~ ( A @ ( B @ v3_binop_1 ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        | ~ ( B @ v1_funct_1 ) ) ),
    inference(cnf,[status(esa)],[1140]) ).

thf(1143,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ v3_binop_1 ) )
      | ( A @ ( A @ ( B @ sk12 ) @ m1_subset_1 ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
      | ~ ( B @ v1_funct_1 ) ),
    inference(cnfConj,[status(thm)],[1141]) ).

thf(840,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k18_filter_2 ) @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k18_filter_2) ).

thf(5609,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)],[840]) ).

thf(8675,plain,
    ! [A: $i] :
      ( ( ( sk295 @ 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)],[4326,6628]) ).

thf(8676,plain,
    ! [A: $i] :
      ( ( ( sk295 @ 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)],[8675]) ).

thf(8677,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[8676:[bind(A,$thf( sk295 ))]]) ).

thf(315,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
    <=> ( ( D @ ( B @ r2_hidden ) )
        & ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).

thf(2946,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)],[315]) ).

thf(2990,plain,
    sk196 @ v9_lattices,
    inference(cnfConj,[status(thm)],[2983]) ).

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

thf(1851,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(9137,plain,
    ( ( ( sk157 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2672,8414]) ).

thf(9138,plain,
    ( ( ( sk157 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9137]) ).

thf(9145,plain,
    ( ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9138]) ).

thf(638,axiom,
    ( ! [A: $i] :
        ( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
       => ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) )
   => ? [A: $i] :
        ( ! [B: $i] :
            ( ( f1_s13_funct_2 @ ( B @ m1_subset_1 ) )
           => ( ( B @ ( A @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
              = ( B @ f3_s13_funct_2 ) ) )
        & ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ m2_relset_1 ) ) )
        & ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ v1_funct_2 ) ) )
        & ( A @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s13_funct_2) ).

thf(4668,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)],[638]) ).

thf(290,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ v1_relat_1 )
     => ( ( C
          = ( B @ ( A @ k4_tarski ) @ k1_tarski ) )
       => ( ( C @ k3_relat_1 )
          = ( B @ ( A @ k2_tarski ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_relat_1) ).

thf(2801,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)],[290]) ).

thf(32934,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( B @ k2_tarski ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,15652]) ).

thf(32935,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( B @ k2_tarski ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[32934]) ).

thf(32936,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ sk18 @ v1_funct_1 ),
    inference(pattern_uni,[status(thm)],[32935:[bind(A,$thf( E @ ( D @ k2_tarski ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).

thf(33342,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k2_tarski ) @ sk18 @ v1_funct_1 ),
    inference(simp,[status(thm)],[32936]) ).

thf(2895,plain,
    sk188 @ l3_lattices,
    inference(cnfConj,[status(thm)],[2884]) ).

thf(74,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
         => ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
              & ( C @ v1_funct_1 ) )
           => ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
              & ( B @ ( A @ ( C @ v1_partfun1 ) ) )
              & ( C @ v1_funct_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_funct_2) ).

thf(1375,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(32,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ! [B: $i] :
          ( ( ( B @ v1_funct_1 )
            & ( B @ v1_relat_1 ) )
         => ( ( ! [C: $i,D: $i] :
                  ( ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
                    & ( A @ k1_relat_1 @ ( C @ r2_hidden ) ) )
                 => ( ( ( C @ ( A @ k1_funct_1 ) )
                      = D )
                  <=> ( ( D @ ( B @ k1_funct_1 ) )
                      = C ) ) )
              & ( ( A @ k2_relat_1 )
                = ( B @ k1_relat_1 ) )
              & ( ( A @ k1_relat_1 )
                = ( B @ k2_relat_1 ) )
              & ( A @ v2_funct_1 ) )
           => ( B
              = ( A @ k2_funct_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funct_1) ).

thf(1113,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(1114,plain,
    ! [B: $i,A: $i] :
      ( ( ( B
          = ( A @ k2_funct_1 ) )
        | ( ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) )
         != ( A @ ( B @ sk11 ) ) )
        | ( ( A @ ( B @ sk11 ) @ ( B @ k1_funct_1 ) )
         != ( A @ ( B @ sk10 ) ) )
        | ( ( A @ k2_relat_1 )
         != ( B @ k1_relat_1 ) )
        | ( ( A @ k1_relat_1 )
         != ( B @ k2_relat_1 ) )
        | ~ ( A @ v2_funct_1 )
        | ~ ( B @ v1_funct_1 )
        | ~ ( B @ v1_relat_1 )
        | ~ ( A @ v1_funct_1 )
        | ~ ( A @ v1_relat_1 ) )
      & ( ( B
          = ( A @ k2_funct_1 ) )
        | ( ( A @ ( B @ sk11 ) @ ( B @ k1_funct_1 ) )
          = ( A @ ( B @ sk10 ) ) )
        | ( ( A @ ( B @ sk11 ) @ ( B @ k1_funct_1 ) )
         != ( A @ ( B @ sk10 ) ) )
        | ( ( A @ k2_relat_1 )
         != ( B @ k1_relat_1 ) )
        | ( ( A @ k1_relat_1 )
         != ( B @ k2_relat_1 ) )
        | ~ ( A @ v2_funct_1 )
        | ~ ( B @ v1_funct_1 )
        | ~ ( B @ v1_relat_1 )
        | ~ ( A @ v1_funct_1 )
        | ~ ( A @ v1_relat_1 ) )
      & ( ( B
          = ( A @ k2_funct_1 ) )
        | ( ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) )
         != ( A @ ( B @ sk11 ) ) )
        | ( ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) )
          = ( A @ ( B @ sk11 ) ) )
        | ( ( A @ k2_relat_1 )
         != ( B @ k1_relat_1 ) )
        | ( ( A @ k1_relat_1 )
         != ( B @ k2_relat_1 ) )
        | ~ ( A @ v2_funct_1 )
        | ~ ( B @ v1_funct_1 )
        | ~ ( B @ v1_relat_1 )
        | ~ ( A @ v1_funct_1 )
        | ~ ( A @ v1_relat_1 ) )
      & ( ( B
          = ( A @ k2_funct_1 ) )
        | ( ( A @ ( B @ sk11 ) @ ( B @ k1_funct_1 ) )
          = ( A @ ( B @ sk10 ) ) )
        | ( ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) )
          = ( A @ ( B @ sk11 ) ) )
        | ( ( A @ k2_relat_1 )
         != ( B @ k1_relat_1 ) )
        | ( ( A @ k1_relat_1 )
         != ( B @ k2_relat_1 ) )
        | ~ ( A @ v2_funct_1 )
        | ~ ( B @ v1_funct_1 )
        | ~ ( B @ v1_relat_1 )
        | ~ ( A @ v1_funct_1 )
        | ~ ( A @ v1_relat_1 ) )
      & ( ( B
          = ( A @ k2_funct_1 ) )
        | ( B @ k1_relat_1 @ ( A @ ( B @ sk11 ) @ r2_hidden ) )
        | ( ( A @ k2_relat_1 )
         != ( B @ k1_relat_1 ) )
        | ( ( A @ k1_relat_1 )
         != ( B @ k2_relat_1 ) )
        | ~ ( A @ v2_funct_1 )
        | ~ ( B @ v1_funct_1 )
        | ~ ( B @ v1_relat_1 )
        | ~ ( A @ v1_funct_1 )
        | ~ ( A @ v1_relat_1 ) )
      & ( ( B
          = ( A @ k2_funct_1 ) )
        | ( A @ k1_relat_1 @ ( A @ ( B @ sk10 ) @ r2_hidden ) )
        | ( ( A @ k2_relat_1 )
         != ( B @ k1_relat_1 ) )
        | ( ( A @ k1_relat_1 )
         != ( B @ k2_relat_1 ) )
        | ~ ( A @ v2_funct_1 )
        | ~ ( B @ v1_funct_1 )
        | ~ ( B @ v1_relat_1 )
        | ~ ( A @ v1_funct_1 )
        | ~ ( A @ v1_relat_1 ) ) ),
    inference(cnf,[status(esa)],[1113]) ).

thf(1115,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ k2_funct_1 ) )
      | ( B @ k1_relat_1 @ ( A @ ( B @ sk11 ) @ r2_hidden ) )
      | ( ( A @ k2_relat_1 )
       != ( B @ k1_relat_1 ) )
      | ( ( A @ k1_relat_1 )
       != ( B @ k2_relat_1 ) )
      | ~ ( A @ v2_funct_1 )
      | ~ ( B @ v1_funct_1 )
      | ~ ( B @ v1_relat_1 )
      | ~ ( A @ v1_funct_1 )
      | ~ ( A @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1114]) ).

thf(1121,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_relat_1 @ ( A @ ( B @ sk11 ) @ r2_hidden ) )
      | ~ ( A @ v2_funct_1 )
      | ~ ( B @ v1_funct_1 )
      | ~ ( B @ v1_relat_1 )
      | ~ ( A @ v1_funct_1 )
      | ~ ( A @ v1_relat_1 )
      | ( B
        = ( A @ k2_funct_1 ) )
      | ( ( A @ k2_relat_1 )
       != ( B @ k1_relat_1 ) )
      | ( ( A @ k1_relat_1 )
       != ( B @ k2_relat_1 ) ) ),
    inference(lifteq,[status(thm)],[1115]) ).

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/sandbox/benchmark/theBenchmark.p',t118_funct_2) ).

thf(2577,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(1043,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)],[1042]) ).

thf(1044,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)],[1043]) ).

thf(14330,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( sk295 @ 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)],[14318,1044]) ).

thf(14331,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( sk295 @ 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)],[14330]) ).

thf(14332,plain,
    ! [A: $i] : ( sk295 @ k1_relat_1 @ ( A @ k4_xboole_0 ) @ ( f1_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[14331:[bind(A,$thf( sk295 @ k1_relat_1 )),bind(B,$thf( f1_s4_funct_2 )),bind(C,$thf( C ))]]) ).

thf(14353,plain,
    ! [A: $i] : ( sk295 @ k1_relat_1 @ ( A @ k4_xboole_0 ) @ ( f1_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[14332]) ).

thf(50595,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk152 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2588,1179]) ).

thf(50596,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk152 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[50595]) ).

thf(50597,plain,
    ! [A: $i] : ( A @ ( sk152 @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[50596:[bind(A,$thf( A )),bind(B,$thf( sk152 ))]]) ).

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

thf(1587,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(12945,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( B @ k1_zfmisc_1 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3676,3815]) ).

thf(12946,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( B @ k1_zfmisc_1 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[12945]) ).

thf(12950,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk249 )
     != ( B @ k1_zfmisc_1 ) ),
    inference(simp,[status(thm)],[12946]) ).

thf(3675,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ sk249 @ m1_subset_1 ) ),
    inference(cnfConj,[status(thm)],[3674]) ).

thf(23836,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ( k1_xboole_0 @ k1_tarski @ ( A @ sk249 @ m1_subset_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[1902,3675]) ).

thf(23837,plain,
    k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ sk249 @ m1_subset_1 ),
    inference(pattern_uni,[status(thm)],[23836:[bind(A,$thf( k1_xboole_0 ))]]) ).

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 @ u1_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_setwiseo ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_lattice4) ).

thf(5889,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)],[901]) ).

thf(530,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                  = ( A @ k5_lattices ) )
              <=> ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_lattices) ).

thf(4095,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)],[530]) ).

thf(782,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v15_lattices )
      <=> ( ( A @ v14_lattices )
          & ( A @ v13_lattices ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_lattices) ).

thf(5373,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)],[782]) ).

thf(673,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k11_filter_2 ) )
        = ( B @ ( A @ k8_filter_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k11_filter_2) ).

thf(4840,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)],[673]) ).

thf(11979,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,9410]) ).

thf(11980,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[11979]) ).

thf(12142,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk71 )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[11980]) ).

thf(10658,plain,
    ( ( ( k6_nat_lat @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5390,8691]) ).

thf(10659,plain,
    ( ( ( k6_nat_lat @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[10658]) ).

thf(10678,plain,
    ( ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[10659]) ).

thf(558,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( A @ ( B @ m1_filter_0 ) )
          <=> ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( ( B @ ( D @ r2_hidden ) )
                        & ( B @ ( C @ r2_hidden ) ) )
                    <=> ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_filter_0) ).

thf(4219,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)],[558]) ).

thf(7760,plain,
    ( ( ( sk218 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3050,3255]) ).

thf(7761,plain,
    ( ( sk218 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7760]) ).

thf(7768,plain,
    sk218 != k1_xboole_0,
    inference(simp,[status(thm)],[7761]) ).

thf(32082,plain,
    ! [A: $i] :
      ( ( A != sk218 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,7768]) ).

thf(32083,plain,
    ! [A: $i] :
      ( ( A != sk218 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[32082]) ).

thf(32084,plain,
    sk218 @ sk18 @ v1_funct_1,
    inference(pattern_uni,[status(thm)],[32083:[bind(A,$thf( sk218 ))]]) ).

thf(894,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ k3_lattices ) ) )
                  = C ) )
           => ( B
              = ( A @ k5_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_lattice2) ).

thf(5830,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( 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)],[894]) ).

thf(2877,plain,
    sk187 @ v8_lattices,
    inference(cnfConj,[status(thm)],[2869]) ).

thf(350,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v10_lattices )
          & ( A @ v6_group_1 )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v15_lattices )
          & ( A @ v14_lattices )
          & ( A @ v13_lattices )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_lattice2) ).

thf(3143,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)],[350]) ).

thf(72,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
        = ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
      & ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
        = ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_zfmisc_1) ).

thf(1361,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(891,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_filter_0 ) )
        & ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( C @ ( B @ ( A @ k6_filter_0 ) ) @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_filter_0) ).

thf(5818,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)],[891]) ).

thf(3000,plain,
    ~ ( sk197 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2999]) ).

thf(449,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ! [F: $i] :
                            ( ( A @ ( F @ m1_subset_1 ) )
                           => ( ( B @ ( F @ r2_hidden ) )
                             => ( E @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
                       => ( E @ ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_lattice2) ).

thf(3714,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)],[449]) ).

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 ) )
         => ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k2_lattice4 ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_lattice4) ).

thf(5743,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)],[876]) ).

thf(3010,plain,
    sk197 @ v6_lattices,
    inference(cnfConj,[status(thm)],[2999]) ).

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

thf(1152,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(1153,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( B @ ( A @ k4_xboole_0 ) )
       != ( A @ ( B @ k4_xboole_0 ) ) ) ),
    inference(cnf,[status(esa)],[1152]) ).

thf(1154,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( B @ ( A @ k4_xboole_0 ) )
       != ( A @ ( B @ k4_xboole_0 ) ) ) ),
    inference(lifteq,[status(thm)],[1153]) ).

thf(1155,plain,
    ? [A: $i > $i > $i] :
    ! [B: $i,C: $i] :
      ( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
      = B ),
    inference(detectInverse,[status(thm)],[1154]) ).

thf(1156,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk13 ) )
      = A ),
    inference(cnf,[status(esa)],[1155]) ).

thf(41985,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk13 ) )
      = A ),
    inference(lifteq,[status(thm)],[1156]) ).

thf(41986,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
       != ( C @ ( B @ k4_xboole_0 ) ) )
      | ( ( k1_xboole_0 @ ( C @ sk13 ) )
        = B ) ),
    inference(paramod_ordered,[status(thm)],[1824,41985]) ).

thf(41987,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ sk13 ) )
      = k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[41986:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).

thf(2666,plain,
    sk157 @ v8_lattices,
    inference(cnfConj,[status(thm)],[2661]) ).

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/sandbox/benchmark/theBenchmark.p',t14_binop_1) ).

thf(2460,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(117,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_xboole_1) ).

thf(1683,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(46969,plain,
    ! [A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3676,46818]) ).

thf(46970,plain,
    ! [A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[46969]) ).

thf(47029,plain,
    ! [A: $i] :
      ( ( A @ sk249 )
     != ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) ),
    inference(simp,[status(thm)],[46970]) ).

thf(720,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_filter_0 ) )
        & ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( C @ ( B @ ( A @ k7_filter_0 ) ) @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_filter_0) ).

thf(5080,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)],[720]) ).

thf(811,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) )
            = ( A @ k6_lattices ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_lattices) ).

thf(5496,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)],[811]) ).

thf(393,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
        & ( C @ ( B @ ( E @ v1_funct_2 ) ) )
        & ( E @ v1_funct_1 )
        & ( B @ ( A @ ( D @ m1_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ m2_relset_1 ) ) )
        & ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_2 ) ) )
        & ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funct_2) ).

thf(3407,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)],[393]) ).

thf(954,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( D @ m1_filter_0 ) )
        & ( B @ ( C @ m1_filter_0 ) )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_1_filter_0 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ? [F: $i] :
                ( ? [G: $i] :
                    ( ( D @ ( G @ r2_hidden ) )
                    & ( C @ ( F @ r2_hidden ) )
                    & ( E @ ( G @ ( F @ ( B @ k4_lattices ) ) @ ( B @ r3_lattices ) ) )
                    & ( B @ u1_struct_0 @ ( G @ m1_subset_1 ) ) )
                & ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) ) )
            & ( A = E )
            & ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_filter_0) ).

thf(6116,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)],[954]) ).

thf(7185,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( sk71 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1924,3815]) ).

thf(7186,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7185]) ).

thf(7191,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != sk71 ),
    inference(simp,[status(thm)],[7186]) ).

thf(11402,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ( ( k1_xboole_0 @ k1_tarski )
       != sk71 ) ),
    inference(paramod_ordered,[status(thm)],[1902,7191]) ).

thf(11403,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != sk71 ),
    inference(pattern_uni,[status(thm)],[11402:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(14800,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3050,2366]) ).

thf(14801,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[14800]) ).

thf(14810,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[14801]) ).

thf(32341,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( B @ k4_tarski ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,14810]) ).

thf(32342,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( C @ ( B @ k4_tarski ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[32341]) ).

thf(32343,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ sk18 @ v1_funct_1 ),
    inference(pattern_uni,[status(thm)],[32342:[bind(A,$thf( E @ ( D @ k4_tarski ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).

thf(33740,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ sk18 @ v1_funct_1 ),
    inference(simp,[status(thm)],[32343]) ).

thf(86,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_funct_1 )
        & ( B @ v1_relat_1 ) )
     => ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
       => ( B @ k2_relat_1 @ ( A @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_1) ).

thf(1461,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(179,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

thf(2053,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(202,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_lattices )
        & ~ ( C @ ( B @ ( A @ g3_lattices ) ) @ v3_struct_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattices) ).

thf(2196,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)],[202]) ).

thf(826,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_struct_0 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_struct_0) ).

thf(5547,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)],[826]) ).

thf(966,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ k17_filter_2 @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_filter_2) ).

thf(6164,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)],[966]) ).

thf(5862,plain,
    ( ( f2_s4_subset_1 = f3_s4_subset_1 )
    | ( sk434 @ p1_s4_subset_1 )
    | ( f3_s4_subset_1 @ ( sk434 @ r2_hidden ) )
    | sk432 ),
    inference(cnfConj,[status(thm)],[5853]) ).

thf(5865,plain,
    ( ( sk434 @ p1_s4_subset_1 )
    | ( f3_s4_subset_1 @ ( sk434 @ r2_hidden ) )
    | sk432
    | ( f3_s4_subset_1 = f2_s4_subset_1 ) ),
    inference(lifteq,[status(thm)],[5862]) ).

thf(3185,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)],[3184]) ).

thf(3186,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)],[3185]) ).

thf(3189,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[3186]) ).

thf(3193,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[3189]) ).

thf(3194,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[3193]) ).

thf(2349,plain,
    sk118 @ v10_lattices,
    inference(cnfConj,[status(thm)],[2342]) ).

thf(177,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v10_lattices )
          & ( A @ v6_group_1 )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v13_lattices )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_lattice2) ).

thf(2038,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(51,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_2) ).

thf(1207,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(435,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_lattice4 ) )
         => ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
               => ( ( B @ ( C @ r1_tarski ) )
                 => ( B @ ( C @ ( A @ k1_lattice4 ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_lattice4) ).

thf(3671,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)],[435]) ).

thf(185,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ k2_zfmisc_1 ) )
        = ( B @ ( B @ k2_zfmisc_1 ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).

thf(2085,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(1035,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)],[1032]) ).

thf(1039,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)],[1035]) ).

thf(163,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
          <=> ! [D: $i] :
                ( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
               => ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_realset1) ).

thf(1974,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(955,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_setwiseo ) )
       => ( ( A @ k6_lattices )
          = ( A @ u1_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_lattice2) ).

thf(6129,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)],[955]) ).

thf(17,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ v1_funct_1 )
        & ( D @ v1_relat_1 ) )
     => ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
          & ( B @ ( A @ r2_hidden ) )
          & ( ( D @ k1_relat_1 )
            = ( A @ k1_tarski ) ) )
       => ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
          & ( D @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_partfun1) ).

thf(1045,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(1046,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)],[1045]) ).

thf(1048,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)],[1046]) ).

thf(1050,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)],[1048]) ).

thf(333,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( ( A != k1_xboole_0 )
       => ( ( B @ ( k1_xboole_0 @ ( A @ k5_partfun1 ) ) )
          = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t172_partfun1) ).

thf(3064,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)],[333]) ).

thf(527,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v3_filter_0 )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( B @ ( A @ k8_filter_0 ) @ v3_filter_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_filter_0) ).

thf(4086,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)],[527]) ).

thf(352,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ~ ( ( B @ ( D @ r2_hidden ) )
                  <=> ( C @ ( D @ r2_hidden ) ) ) )
           => ( B
              = ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_subset_1) ).

thf(3162,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)],[352]) ).

thf(445,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
                & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ( ( D @ ( B @ ( C @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_setwiseo ) ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
                    = ( D @ ( C @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funct_2 ) ) ) ) @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_lattice4) ).

thf(3703,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)],[445]) ).

thf(133,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ v1_relat_1 )
     => ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
       => ( ( C @ k2_relat_1 @ ( B @ r2_hidden ) )
          & ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).

thf(1825,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(715,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m2_filter_2 ) )
        & ( A @ ( B @ m2_filter_2 ) )
        & ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k21_filter_2 ) ) )
        = ( C @ ( B @ ( A @ k20_filter_2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k21_filter_2) ).

thf(5063,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)],[715]) ).

thf(675,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( C @ ( B @ ( A @ r1_lattice2 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ ( D @ m1_subset_1 ) )
                   => ! [E: $i] :
                        ( ( A @ ( E @ m1_subset_1 ) )
                       => ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                          = D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattice2) ).

thf(4846,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)],[675]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
        = ( B @ k2_relat_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funct_2) ).

thf(995,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(996,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)],[995]) ).

thf(997,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)],[996]) ).

thf(897,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_struct_0 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_struct_0) ).

thf(5850,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)],[897]) ).

thf(1150,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)],[1148]) ).

thf(870,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k1_lattice4 ) )
            = ( A @ k7_grcat_1 @ ( B @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_setwiseo ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_lattice4) ).

thf(5726,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)],[870]) ).

thf(64,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
        & ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k3_funct_2 ) ) ) )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funct_2) ).

thf(1297,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(29761,plain,
    ! [A: $i] :
      ( ( A != sk94 )
      | ( k1_xboole_0 @ v4_lattices )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,2163]) ).

thf(29762,plain,
    ( ( k1_xboole_0 @ v4_lattices )
    | ( sk94 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[29761:[bind(A,$thf( sk94 ))]]) ).

thf(416,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( ( C @ ( D @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) )
                          = ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) ) )
                       => ( ( ( D @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) )
                            = ( E @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) ) )
                          | ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_lattice2) ).

thf(3541,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)],[416]) ).

thf(464,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_tarski )
        = ( C @ ( B @ k2_tarski ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).

thf(3787,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_tarski )
        = ( C @ ( B @ k2_tarski ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(76,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_funct_1 )
        & ( B @ v1_relat_1 ) )
     => ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
       => ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
          & ( B @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_partfun1) ).

thf(1382,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(248,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ r1_tarski ) )
    <=> ( ( A
          = ( B @ k1_tarski ) )
        | ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).

thf(2487,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(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/sandbox/benchmark/theBenchmark.p',t9_lattice2) ).

thf(2598,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(6327,plain,
    ( ( ( sk341 @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1924,4839]) ).

thf(6328,plain,
    ( ( sk341 @ v1_xboole_0 )
   != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6327]) ).

thf(6331,plain,
    sk341 != sk71,
    inference(simp,[status(thm)],[6328]) ).

thf(56,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ v1_relat_1 )
     => ( ( B @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ( B @ ( D @ r2_hidden ) )
            & ( C @ ( A @ ( D @ k4_tarski ) @ r2_hidden ) )
            & ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).

thf(1231,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(1131,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)],[1130]) ).

thf(457,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r1_tarski ) )
     => ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finsub_1) ).

thf(3743,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)],[457]) ).

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/sandbox/benchmark/theBenchmark.p',d19_binop_1) ).

thf(2355,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(154,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_subset_1 ) )
         => ( ( A @ ( B @ v1_binop_1 ) )
           => ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
            <=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_binop_1) ).

thf(1932,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(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/sandbox/benchmark/theBenchmark.p',rc1_nat_lat) ).

thf(2505,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(561,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) )
        = ( D @ ( C @ k4_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).

thf(4237,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)],[561]) ).

thf(669,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( B @ ( A @ r1_filter_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_filter_2) ).

thf(4829,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)],[669]) ).

thf(158,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [D: $i,E: $i,F: $i] :
          ( ( ( C @ ( B @ ( A @ g3_lattices ) ) )
            = ( F @ ( E @ ( D @ g3_lattices ) ) ) )
         => ( ( C = F )
            & ( B = E )
            & ( A = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).

thf(1947,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(859,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k6_lattices @ ( A @ k3_lattices ) ) )
            = ( A @ k6_lattices ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_lattices) ).

thf(5683,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)],[859]) ).

thf(559,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v14_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
              = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
           => ( ( A @ k6_lattices )
              = ( B @ k6_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_filter_2) ).

thf(4231,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)],[559]) ).

thf(429,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).

thf(3628,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)],[429]) ).

thf(6005,plain,
    sk445 @ l3_lattices,
    inference(cnfConj,[status(thm)],[6004]) ).

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

thf(1429,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(505,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
         => ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_realset1) ).

thf(3967,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)],[505]) ).

thf(299,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( B @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
        & ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
        = ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).

thf(2862,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)],[299]) ).

thf(537,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_domain_1 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_domain_1) ).

thf(4135,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)],[537]) ).

thf(886,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_filter_0) ).

thf(5801,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)],[886]) ).

thf(381,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
    <=> ~ ( ( A
           != ( C @ ( B @ k2_tarski ) ) )
          & ( A
           != ( C @ k1_tarski ) )
          & ( A
           != ( B @ k1_tarski ) )
          & ( A != k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_zfmisc_1) ).

thf(3333,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)],[381]) ).

thf(694,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r1_lattices ) ) )
              <=> ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                  = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_lattices) ).

thf(4953,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)],[694]) ).

thf(3109,plain,
    k6_nat_lat @ v3_lattices,
    inference(cnfConj,[status(thm)],[3103]) ).

thf(164,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ v1_relat_1 )
     => ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
       => ( ( C @ k3_relat_1 @ ( B @ r2_hidden ) )
          & ( C @ k3_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).

thf(1979,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(641,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v16_lattices )
        & ( A @ v15_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v3_filter_0 )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
             => ! [D: $i] :
                  ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_lattice4) ).

thf(4689,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)],[641]) ).

thf(3005,plain,
    sk197 @ v3_filter_0,
    inference(cnfConj,[status(thm)],[2999]) ).

thf(28593,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)],[1994,3514]) ).

thf(28594,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ r2_hidden ) ),
    inference(pattern_uni,[status(thm)],[28593:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(28608,plain,
    ! [A: $i] : ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ r2_hidden ) ),
    inference(simp,[status(thm)],[28594]) ).

thf(4361,plain,
    ~ ( sk297 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[4356]) ).

thf(7046,plain,
    ( ( ( sk187 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2881,6903]) ).

thf(7047,plain,
    ( ( ( sk187 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7046]) ).

thf(7050,plain,
    ( ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7047]) ).

thf(12100,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
    | ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,7050]) ).

thf(12101,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
    | ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12100]) ).

thf(12138,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk138 )
    | ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12101]) ).

thf(1324,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ sk25 ) @ v1_funct_1 )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1319]) ).

thf(1332,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ sk25 ) @ v1_funct_1 )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1324]) ).

thf(1333,plain,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ sk25 ) @ v1_funct_1 ),
    inference(simp,[status(thm)],[1332]) ).

thf(867,axiom,
    ! [A: $i] :
      ( ( a_0_2_domain_1 @ ( A @ r2_hidden ) )
    <=> ? [B: $i,C: $i] :
          ( ( C @ ( B @ p1_s9_domain_1 ) )
          & ( A
            = ( C @ ( B @ f4_s9_domain_1 ) ) )
          & ( f2_s9_domain_1 @ ( C @ m1_subset_1 ) )
          & ( f1_s9_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_2_domain_1) ).

thf(5711,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)],[867]) ).

thf(48800,plain,
    ! [A: $i] :
      ( ( A
       != ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,47104]) ).

thf(48801,plain,
    ! [A: $i] :
      ( ( A
       != ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[48800]) ).

thf(48802,plain,
    sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ sk18 @ v1_funct_1,
    inference(pattern_uni,[status(thm)],[48801:[bind(A,$thf( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ))]]) ).

thf(680,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( A @ k1_tarski ) )
    <=> ! [C: $i] :
          ( ( B @ ( C @ r2_hidden ) )
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

thf(4873,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)],[680]) ).

thf(4874,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)],[4873]) ).

thf(4875,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( F
          = ( E @ k1_tarski ) )
        | ~ ( F @ ( E @ ( F @ sk348 ) @ r2_hidden ) )
        | ( ( E @ ( F @ sk347 ) )
         != E ) )
      & ( ( F
          = ( E @ k1_tarski ) )
        | ( ( E @ ( F @ sk348 ) )
          = E )
        | ( ( E @ ( F @ sk347 ) )
         != E ) )
      & ( ( F
          = ( E @ k1_tarski ) )
        | ~ ( F @ ( E @ ( F @ sk348 ) @ r2_hidden ) )
        | ( F @ ( E @ ( F @ sk347 ) @ r2_hidden ) ) )
      & ( ( F
          = ( E @ k1_tarski ) )
        | ( ( E @ ( F @ sk348 ) )
          = E )
        | ( F @ ( E @ ( F @ sk347 ) @ 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)],[4874]) ).

thf(4881,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ r2_hidden ) )
      | ( C != A )
      | ( B
       != ( A @ k1_tarski ) ) ),
    inference(cnfConj,[status(thm)],[4875]) ).

thf(4888,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ r2_hidden ) )
      | ( C != A )
      | ( B
       != ( A @ k1_tarski ) ) ),
    inference(lifteq,[status(thm)],[4881]) ).

thf(4889,plain,
    ! [A: $i] : ( A @ k1_tarski @ ( A @ r2_hidden ) ),
    inference(simp,[status(thm)],[4888]) ).

thf(7685,plain,
    ! [A: $i] :
      ( ( ( sk138 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2472,6628]) ).

thf(7686,plain,
    ! [A: $i] :
      ( ( ( sk138 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7685]) ).

thf(7687,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[7686:[bind(A,$thf( sk138 ))]]) ).

thf(424,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
                    & ~ ( D @ v1_xboole_0 ) )
                 => ( ( C @ ( A @ u1_struct_0 @ k6_domain_1 ) @ ( D @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r2_hidden ) )
                   => ( D @ ( A @ k3_filter_0 ) @ ( B @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_filter_0) ).

thf(3592,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)],[424]) ).

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/sandbox/benchmark/theBenchmark.p',t112_zfmisc_1) ).

thf(2408,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(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/sandbox/benchmark/theBenchmark.p',t49_domain_1) ).

thf(2529,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(119,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = k1_xboole_0 )
    <=> ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).

thf(1732,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(30106,plain,
    ! [A: $i] :
      ( ( A != sk118 )
      | ( k1_xboole_0 @ v4_lattices )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,2348]) ).

thf(30107,plain,
    ( ( k1_xboole_0 @ v4_lattices )
    | ( sk118 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[30106:[bind(A,$thf( sk118 ))]]) ).

thf(728,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v14_lattices )
      <=> ( A @ k1_lattice2 @ v13_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_lattice2) ).

thf(5112,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)],[728]) ).

thf(829,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( A @ ( E @ m1_filter_0 ) )
                     => ( ( ( E @ ( D @ ( C @ ( A @ k9_filter_0 ) ) @ r2_hidden ) )
                          & ( E @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) )
                       => ( E @ ( D @ ( B @ ( A @ k9_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_filter_0) ).

thf(5557,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)],[829]) ).

thf(549,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( A @ k1_zfmisc_1 @ ( A @ a_1_2_domain_1 @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_domain_1) ).

thf(4184,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)],[549]) ).

thf(11981,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,8674]) ).

thf(11982,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[11981]) ).

thf(12179,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk295 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[11982]) ).

thf(12201,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[12179]) ).

thf(288,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_lattices) ).

thf(2788,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)],[288]) ).

thf(7370,plain,
    ( ( ( sk197 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3001,6903]) ).

thf(7371,plain,
    ( ( ( sk197 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7370]) ).

thf(7374,plain,
    ( ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7371]) ).

thf(16180,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( sk197 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,7374]) ).

thf(16181,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( sk197 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16180]) ).

thf(16212,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk138 != k1_xboole_0 )
      | ( sk197 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16181]) ).

thf(16275,plain,
    ( ( sk138 != k1_xboole_0 )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16212]) ).

thf(739,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( B @ ( A @ k5_lattices @ ( A @ r3_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_lattices) ).

thf(5153,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)],[739]) ).

thf(632,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_3_domain_1 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ~ ( D @ ( E @ r2_hidden ) )
            & ( C @ ( E @ r2_hidden ) )
            & ( A = E )
            & ( B @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_3_domain_1) ).

thf(4625,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)],[632]) ).

thf(964,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( A @ k5_lattices @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattices) ).

thf(6160,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)],[964]) ).

thf(724,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
                = ( C @ ( B @ ( A @ a_3_0_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_filter_0) ).

thf(5090,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)],[724]) ).

thf(512,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ( A @ v6_lattices )
        & ( A @ v5_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( C @ ( B @ ( A @ k1_lattices ) ) @ ( B @ ( A @ r1_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_lattices) ).

thf(3999,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)],[512]) ).

thf(47099,plain,
    ( ( ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3244,46859]) ).

thf(47100,plain,
    ( ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[47099]) ).

thf(47101,plain,
    ( ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk216 ),
    inference(simp,[status(thm)],[47100]) ).

thf(2368,plain,
    ! [B: $i,A: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
    inference(cnf,[status(esa)],[2367]) ).

thf(2402,plain,
    k13_nat_lat @ v10_lattices,
    inference(cnfConj,[status(thm)],[2398]) ).

thf(307,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_binop_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_lattice2) ).

thf(2915,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)],[307]) ).

thf(9109,plain,
    ( ( ( sk196 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2989,8414]) ).

thf(9110,plain,
    ( ( ( sk196 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9109]) ).

thf(9146,plain,
    ( ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9110]) ).

thf(16139,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( sk196 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,9146]) ).

thf(16140,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( sk196 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16139]) ).

thf(16230,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk216 != k1_xboole_0 )
      | ( sk196 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16140]) ).

thf(16296,plain,
    ( ( sk216 != k1_xboole_0 )
    | ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16230]) ).

thf(749,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ k1_filter_0 @ v2_filter_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_lattice4) ).

thf(5198,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)],[749]) ).

thf(2995,plain,
    sk196 @ v6_lattices,
    inference(cnfConj,[status(thm)],[2983]) ).

thf(907,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v13_lattices )
       => ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ( ( B
                = ( A @ k5_lattices ) )
            <=> ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
                      = B )
                    & ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                      = B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_lattices) ).

thf(5909,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)],[907]) ).

thf(477,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k4_lattices ) ) )
        = ( C @ ( B @ ( A @ k2_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_lattices) ).

thf(3841,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)],[477]) ).

thf(760,axiom,
    f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s9_domain_1) ).

thf(5249,plain,
    f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(732,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k9_filter_0 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_filter_0) ).

thf(5126,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)],[732]) ).

thf(2662,plain,
    sk157 @ v6_lattices,
    inference(cnfConj,[status(thm)],[2661]) ).

thf(47,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ v1_funct_1 )
        & ( C @ v1_relat_1 ) )
     => ( ( ( C @ v2_funct_1 )
          & ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
          & ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) )
       => ( B @ ( A @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t157_funct_1) ).

thf(1185,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(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/sandbox/benchmark/theBenchmark.p',t57_partfun1) ).

thf(2338,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(12943,plain,
    ! [A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( sk218 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3676,3255]) ).

thf(12944,plain,
    ! [A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( sk218 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[12943]) ).

thf(12953,plain,
    ! [A: $i] :
      ( ( A @ sk249 )
     != sk218 ),
    inference(simp,[status(thm)],[12944]) ).

thf(686,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( B @ v1_xboole_0 )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

thf(4921,plain,
    ! [A: $i,B: $i] :
      ~ ( ( B @ v1_xboole_0 )
        & ( B @ ( A @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(685,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( B @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_subset_1) ).

thf(4919,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)],[685]) ).

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 ) )
         => ( ( A @ ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) )
           => ( A @ v14_lattices ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_filter_0) ).

thf(5722,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)],[868]) ).

thf(936,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( ( E @ ( D @ ( A @ r3_lattices ) ) )
                          & ( C @ ( B @ ( A @ r3_lattices ) ) ) )
                       => ( ( C @ ( E @ ( A @ k4_lattices ) ) @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
                          & ( E @ ( C @ ( A @ k4_lattices ) ) @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_filter_0) ).

thf(6026,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[936]) ).

thf(37931,plain,
    ( ( ( sk197 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[3001,31369]) ).

thf(37932,plain,
    ( ( ( sk197 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[37931]) ).

thf(38087,plain,
    ( ( sk197 != k1_xboole_0 )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[37932]) ).

thf(313,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
     => ~ ( ( C @ ( B @ r2_hidden ) )
          & ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).

thf(2941,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)],[313]) ).

thf(12039,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,9404]) ).

thf(12040,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12039]) ).

thf(12119,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk138 )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12040]) ).

thf(16041,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( k6_nat_lat != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,10679]) ).

thf(16042,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( k6_nat_lat != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16041]) ).

thf(16243,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk138 != k1_xboole_0 )
      | ( k6_nat_lat != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16042]) ).

thf(16311,plain,
    ( ( sk138 != k1_xboole_0 )
    | ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16243]) ).

thf(662,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ( A @ v4_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( ( B @ ( C @ ( A @ r1_lattices ) ) )
                  & ( C @ ( B @ ( A @ r1_lattices ) ) ) )
               => ( B = C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_lattices) ).

thf(4797,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)],[662]) ).

thf(911,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v17_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ l3_lattices )
              & ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v17_lattices )
              & ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v10_lattices )
              & ~ ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_filter_0) ).

thf(5928,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)],[911]) ).

thf(609,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( B @ ( A @ k10_filter_0 ) @ v1_relat_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_filter_0) ).

thf(4489,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)],[609]) ).

thf(604,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v4_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                  = ( B @ ( C @ ( A @ k1_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lattices) ).

thf(4453,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)],[604]) ).

thf(1144,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ v3_binop_1 ) )
      | ( ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk12 ) @ ( B @ k1_binop_1 ) ) )
       != ( A @ ( B @ sk12 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
      | ~ ( B @ v1_funct_1 ) ),
    inference(cnfConj,[status(thm)],[1141]) ).

thf(1146,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ v3_binop_1 ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
      | ~ ( B @ v1_funct_1 )
      | ( ( A @ ( B @ sk12 ) @ ( A @ ( B @ sk12 ) @ ( B @ k1_binop_1 ) ) )
       != ( A @ ( B @ sk12 ) ) ) ),
    inference(lifteq,[status(thm)],[1144]) ).

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/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).

thf(2289,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(2290,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ sk110 ) @ v1_funct_1 )
      & ( A @ ( B @ sk110 ) @ v1_relat_1 )
      & ( B @ ( A @ ( A @ ( B @ sk110 ) @ m1_relset_1 ) ) ) ),
    inference(cnf,[status(esa)],[2289]) ).

thf(2292,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ sk110 ) @ v1_relat_1 ),
    inference(cnfConj,[status(thm)],[2290]) ).

thf(385,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
          <=> ! [D: $i] :
                ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
               => ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_realset1) ).

thf(3358,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)],[385]) ).

thf(882,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k5_lattices )
        = ( A @ k1_lattice2 @ k6_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_lattice2) ).

thf(5762,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)],[882]) ).

thf(1069,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
      = A ),
    inference(cnf,[status(esa)],[1068]) ).

thf(1070,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
      = A ),
    inference(lifteq,[status(thm)],[1069]) ).

thf(42008,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
       != ( C @ ( B @ k4_xboole_0 ) ) )
      | ( ( A @ ( C @ sk13 ) )
        = B ) ),
    inference(paramod_ordered,[status(thm)],[1070,41985]) ).

thf(42009,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ sk13 ) )
      = A ),
    inference(pattern_uni,[status(thm)],[42008:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).

thf(369,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ( ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
      <=> ( B
          = ( A @ k1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_subset_1) ).

thf(3257,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)],[369]) ).

thf(54,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
        = k1_xboole_0 )
    <=> ( ( C @ ( B @ r2_hidden ) )
        & ( C @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).

thf(1219,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(476,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) )
          & ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) )
          & ( A @ u1_struct_0 @ ( A @ u1_lattices @ v2_binop_1 ) )
          & ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_binop_1 ) )
          & ( A @ u1_struct_0 @ ( A @ u2_lattices @ v2_binop_1 ) )
          & ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_binop_1 ) ) )
       => ( A @ v10_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_lattice2) ).

thf(3839,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)],[476]) ).

thf(4359,plain,
    sk297 @ v17_lattices,
    inference(cnfConj,[status(thm)],[4356]) ).

thf(923,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u2_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lattice2) ).

thf(5979,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)],[923]) ).

thf(3111,plain,
    k6_nat_lat @ v6_lattices,
    inference(cnfConj,[status(thm)],[3103]) ).

thf(440,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( B @ ( A @ k8_filter_0 ) @ u1_lattices )
              = ( B @ ( A @ u1_lattices @ k1_realset1 ) ) )
            & ( ( B @ ( A @ k8_filter_0 ) @ u2_lattices )
              = ( B @ ( A @ u2_lattices @ k1_realset1 ) ) )
            & ( ( B @ ( A @ k8_filter_0 ) @ u1_struct_0 )
              = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_filter_0) ).

thf(3686,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)],[440]) ).

thf(515,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( B @ ( D @ r2_hidden ) )
                 => ( C @ ( D @ r2_hidden ) ) ) )
           => ( C @ ( B @ r1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_subset_1) ).

thf(4017,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)],[515]) ).

thf(2894,plain,
    sk188 @ v5_lattices,
    inference(cnfConj,[status(thm)],[2884]) ).

thf(4365,plain,
    sk297 @ v9_lattices,
    inference(cnfConj,[status(thm)],[4356]) ).

thf(459,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( ( B @ ( A @ k6_lattices @ r2_hidden ) )
              & ( B @ ( A @ k5_lattices @ r2_hidden ) ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
               => ~ ( ! [D: $i] :
                        ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                       => ~ ( ( ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
                              = ( D @ ( A @ k2_lattice4 ) ) )
                            & ( B @ ( A @ k4_lattice4 ) @ ( D @ r1_tarski ) ) ) )
                    & ( B @ ( A @ k4_lattice4 ) @ ( C @ r1_tarski ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_lattice4) ).

thf(3768,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)],[459]) ).

thf(1116,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ k2_funct_1 ) )
      | ( ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) )
       != ( A @ ( B @ sk11 ) ) )
      | ( ( A @ ( B @ sk11 ) @ ( B @ k1_funct_1 ) )
       != ( A @ ( B @ sk10 ) ) )
      | ( ( A @ k2_relat_1 )
       != ( B @ k1_relat_1 ) )
      | ( ( A @ k1_relat_1 )
       != ( B @ k2_relat_1 ) )
      | ~ ( A @ v2_funct_1 )
      | ~ ( B @ v1_funct_1 )
      | ~ ( B @ v1_relat_1 )
      | ~ ( A @ v1_funct_1 )
      | ~ ( A @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1114]) ).

thf(1125,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ v2_funct_1 )
      | ~ ( B @ v1_funct_1 )
      | ~ ( B @ v1_relat_1 )
      | ~ ( A @ v1_funct_1 )
      | ~ ( A @ v1_relat_1 )
      | ( B
        = ( A @ k2_funct_1 ) )
      | ( ( A @ ( B @ sk11 ) )
       != ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) ) )
      | ( ( A @ ( B @ sk11 ) @ ( B @ k1_funct_1 ) )
       != ( A @ ( B @ sk10 ) ) )
      | ( ( A @ k2_relat_1 )
       != ( B @ k1_relat_1 ) )
      | ( ( A @ k1_relat_1 )
       != ( B @ k2_relat_1 ) ) ),
    inference(lifteq,[status(thm)],[1116]) ).

thf(534,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( A @ ( H @ m1_subset_1 ) )
        & ( A @ ( G @ m1_subset_1 ) )
        & ( A @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( A @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k12_domain_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_domain_1) ).

thf(4122,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)],[534]) ).

thf(919,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( C
                  = ( B @ ( A @ u1_struct_0 @ k6_domain_1 ) ) )
               => ( ( C @ ( A @ k3_filter_0 ) )
                  = ( B @ ( A @ k2_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_filter_0) ).

thf(5962,plain,
    ! [A: $i] :
      ( ( ( A @ l3_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)],[919]) ).

thf(645,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( A @ l2_lattices )
        & ( A @ l1_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).

thf(4709,plain,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( A @ l2_lattices )
        & ( A @ l1_lattices ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(26217,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)],[1902,5028]) ).

thf(26218,plain,
    k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k5_finsub_1 @ r1_tarski ),
    inference(pattern_uni,[status(thm)],[26217:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(244,axiom,
    ( ( k1_xboole_0 @ k5_finsub_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finsub_1) ).

thf(2467,plain,
    ( ( k1_xboole_0 @ k5_finsub_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(2468,plain,
    ( ( k1_xboole_0 @ k5_finsub_1 )
    = ( k1_xboole_0 @ k1_tarski ) ),
    inference(lifteq,[status(thm)],[2467]) ).

thf(26238,plain,
    k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ r1_tarski ),
    inference(rewrite,[status(thm)],[26218,2468]) ).

thf(958,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( B @ ( A @ k2_lattice4 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattice4) ).

thf(6140,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)],[958]) ).

thf(4786,plain,
    sk338 @ l2_lattices,
    inference(cnf,[status(esa)],[4785]) ).

thf(541,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) )
       => ( A @ v11_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_lattice2) ).

thf(4144,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)],[541]) ).

thf(50514,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk216 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3243,1179]) ).

thf(50515,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk216 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[50514]) ).

thf(50516,plain,
    ! [A: $i] : ( A @ ( sk216 @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[50515:[bind(A,$thf( A )),bind(B,$thf( sk216 ))]]) ).

thf(319,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ v1_funct_1 )
        & ( C @ v1_relat_1 ) )
     => ! [D: $i] :
          ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( ( D @ ( C @ r1_tarski ) )
           => ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
              & ( C @ v1_funct_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_partfun1) ).

thf(2970,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)],[319]) ).

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

thf(1004,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(1005,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)],[1004]) ).

thf(1006,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E
          = ( A @ ( B @ ( C @ ( D @ ( E @ sk5 ) ) ) ) @ ( D @ k1_funct_1 ) ) )
        | ~ ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) )
        | ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        | ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        | ~ ( D @ v1_funct_1 ) )
      & ( ( C @ ( A @ ( B @ ( C @ ( D @ ( E @ sk5 ) ) ) ) @ r2_hidden ) )
        | ~ ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) )
        | ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        | ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        | ~ ( D @ v1_funct_1 ) )
      & ( ( A @ ( A @ ( B @ ( C @ ( D @ ( E @ sk5 ) ) ) ) @ m1_subset_1 ) )
        | ~ ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) )
        | ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        | ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        | ~ ( D @ v1_funct_1 ) ) ),
    inference(cnf,[status(esa)],[1005]) ).

thf(1007,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ ( D @ ( E @ sk5 ) ) ) ) @ m1_subset_1 ) )
      | ~ ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) )
      | ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
      | ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
      | ~ ( D @ v1_funct_1 ) ),
    inference(cnfConj,[status(thm)],[1006]) ).

thf(33323,plain,
    ! [A: $i] :
      ( ( A
       != ( sk1 @ u1_struct_0 ) )
      | ( k1_xboole_0 @ ( sk2 @ m1_subset_1 ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,972]) ).

thf(33324,plain,
    ( ( k1_xboole_0 @ ( sk2 @ m1_subset_1 ) )
    | ( sk1 @ u1_struct_0 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[33323:[bind(A,$thf( sk1 @ u1_struct_0 ))]]) ).

thf(12937,plain,
    ! [A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( sk341 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3676,4839]) ).

thf(12938,plain,
    ! [A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( sk341 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[12937]) ).

thf(12951,plain,
    ! [A: $i] :
      ( ( A @ sk249 )
     != sk341 ),
    inference(simp,[status(thm)],[12938]) ).

thf(9135,plain,
    ( ( ( sk187 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2881,8414]) ).

thf(9136,plain,
    ( ( ( sk187 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9135]) ).

thf(9142,plain,
    ( ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9136]) ).

thf(574,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_6_domain_1 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ( ( C @ ( E @ r2_hidden ) )
            <=> ~ ( D @ ( E @ r2_hidden ) ) )
            & ( A = E )
            & ( B @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_6_domain_1) ).

thf(4283,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)],[574]) ).

thf(808,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( C @ ( B @ ( A @ k5_filter_0 ) ) )
                = ( B @ ( C @ ( A @ k5_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_filter_0) ).

thf(5488,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)],[808]) ).

thf(611,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( C @ ( B @ ( A @ k7_domain_1 ) ) )
        = ( C @ ( B @ k2_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_domain_1) ).

thf(4494,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)],[611]) ).

thf(786,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v14_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v15_lattices ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_filter_0) ).

thf(5395,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)],[786]) ).

thf(951,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_filter_2 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k16_filter_2 ) @ m1_filter_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_filter_2) ).

thf(6108,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)],[951]) ).

thf(7795,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)],[3087,6628]) ).

thf(7796,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)],[7795]) ).

thf(7797,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)],[7796:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(16029,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[7797,2222]) ).

thf(16030,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16029]) ).

thf(427,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( A @ ( C @ v1_binop_1 ) )
               => ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
                <=> ! [D: $i] :
                      ( ( A @ ( D @ m1_subset_1 ) )
                     => ! [E: $i] :
                          ( ( A @ ( E @ m1_subset_1 ) )
                         => ! [F: $i] :
                              ( ( A @ ( F @ m1_subset_1 ) )
                             => ( ( F @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                                = ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_binop_1) ).

thf(3609,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)],[427]) ).

thf(16074,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( sk196 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,7170]) ).

thf(16075,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( sk196 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16074]) ).

thf(16236,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk71 != k1_xboole_0 )
      | ( sk196 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16075]) ).

thf(16302,plain,
    ( ( sk71 != k1_xboole_0 )
    | ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16236]) ).

thf(578,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ ( B @ v1_filter_0 ) )
          <=> ( ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ( ( B @ ( C @ ( A @ k7_lattices ) @ r2_hidden ) )
                    | ( B @ ( C @ r2_hidden ) ) ) )
              & ( B
               != ( A @ u1_struct_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_filter_0) ).

thf(4309,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)],[578]) ).

thf(909,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( A @ k1_lattice4 ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_lattice4) ).

thf(5923,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)],[909]) ).

thf(12094,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,8209]) ).

thf(12095,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
    | ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12094]) ).

thf(12143,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk207 )
    | ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12095]) ).

thf(455,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ? [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
          & ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).

thf(3736,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)],[455]) ).

thf(336,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( B @ ( C @ k9_relat_1 ) )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_partfun1) ).

thf(3081,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)],[336]) ).

thf(913,axiom,
    ( ( k13_nat_lat @ l3_lattices )
    & ( k13_nat_lat @ v10_lattices )
    & ~ ( k13_nat_lat @ v3_struct_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_nat_lat) ).

thf(5940,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)],[913]) ).

thf(16065,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( sk157 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,8929]) ).

thf(16066,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( sk157 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16065]) ).

thf(16254,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk207 != k1_xboole_0 )
      | ( sk157 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16066]) ).

thf(16323,plain,
    ( ( sk207 != k1_xboole_0 )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16254]) ).

thf(639,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_1_domain_1 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ( D @ ( E @ r2_hidden ) )
            & ( C @ ( E @ r2_hidden ) )
            & ( A = E )
            & ( B @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_domain_1) ).

thf(4677,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)],[639]) ).

thf(2674,plain,
    sk157 @ l3_lattices,
    inference(cnfConj,[status(thm)],[2661]) ).

thf(97,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ! [B: $i,C: $i] :
          ( ( C
            = ( B @ ( A @ k9_relat_1 ) ) )
        <=> ! [D: $i] :
              ( ( C @ ( D @ r2_hidden ) )
            <=> ? [E: $i] :
                  ( ( D
                    = ( E @ ( A @ k1_funct_1 ) ) )
                  & ( B @ ( E @ r2_hidden ) )
                  & ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).

thf(1535,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(6736,plain,
    ! [A: $i] :
      ( ( ( sk71 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1922,6617]) ).

thf(6737,plain,
    ! [A: $i] :
      ( ( ( sk71 @ v1_funct_1 )
       != ( A @ v1_funct_1 ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ v1_partfun1 ) ) )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( A @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[6736]) ).

thf(6738,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(pattern_uni,[status(thm)],[6737:[bind(A,$thf( sk71 ))]]) ).

thf(16152,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,6738]) ).

thf(16153,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16152]) ).

thf(16214,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk71 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[16153]) ).

thf(16278,plain,
    ( ( sk71 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[16214]) ).

thf(2991,plain,
    sk196 @ v3_lattices,
    inference(cnfConj,[status(thm)],[2983]) ).

thf(10654,plain,
    ( ( ( k6_nat_lat @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5390,6900]) ).

thf(10655,plain,
    ( ( ( k6_nat_lat @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[10654]) ).

thf(10672,plain,
    ( ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[10655]) ).

thf(16165,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( k6_nat_lat != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,10672]) ).

thf(16166,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( k6_nat_lat != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16165]) ).

thf(16245,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk71 != k1_xboole_0 )
      | ( k6_nat_lat != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16166]) ).

thf(16313,plain,
    ( ( sk71 != k1_xboole_0 )
    | ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16245]) ).

thf(30126,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ~ ( k1_xboole_0 @ v3_struct_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,973]) ).

thf(30127,plain,
    ( ~ ( k1_xboole_0 @ v3_struct_0 )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[30126:[bind(A,$thf( sk1 ))]]) ).

thf(79,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ v1_relat_1 )
     => ~ ( ! [C: $i] :
              ~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
          & ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_relat_1) ).

thf(1403,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(726,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 ) )
     => ( ( C @ ( B @ a_2_0_filter_0 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ( D @ ( C @ ( B @ r3_lattices ) ) )
            & ( A = D )
            & ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_filter_0) ).

thf(5097,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)],[726]) ).

thf(131,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( B @ ( A @ k4_xboole_0 ) ) )
    <=> ! [D: $i] :
          ( ( C @ ( D @ r2_hidden ) )
        <=> ( ~ ( B @ ( D @ r2_hidden ) )
            & ( A @ ( D @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).

thf(1795,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(626,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k2_lattice4 ) @ ( A @ k7_lattices ) )
            = ( A @ k5_lattice4 @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_lattice4) ).

thf(4590,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)],[626]) ).

thf(292,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
        & ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ! [E: $i] :
          ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
            & ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
            & ( E @ v1_funct_1 ) )
         => ( ! [F: $i] :
                ( ( A @ ( F @ m1_subset_1 ) )
               => ! [G: $i] :
                    ( ( B @ ( G @ m1_subset_1 ) )
                   => ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
                      = ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) ) )
           => ( D = E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_funct_2) ).

thf(2817,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)],[292]) ).

thf(1117,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ k2_funct_1 ) )
      | ( A @ k1_relat_1 @ ( A @ ( B @ sk10 ) @ r2_hidden ) )
      | ( ( A @ k2_relat_1 )
       != ( B @ k1_relat_1 ) )
      | ( ( A @ k1_relat_1 )
       != ( B @ k2_relat_1 ) )
      | ~ ( A @ v2_funct_1 )
      | ~ ( B @ v1_funct_1 )
      | ~ ( B @ v1_relat_1 )
      | ~ ( A @ v1_funct_1 )
      | ~ ( A @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1114]) ).

thf(1124,plain,
    ! [B: $i,A: $i] :
      ( ( A @ k1_relat_1 @ ( A @ ( B @ sk10 ) @ r2_hidden ) )
      | ~ ( A @ v2_funct_1 )
      | ~ ( B @ v1_funct_1 )
      | ~ ( B @ v1_relat_1 )
      | ~ ( A @ v1_funct_1 )
      | ~ ( A @ v1_relat_1 )
      | ( B
        = ( A @ k2_funct_1 ) )
      | ( ( A @ k2_relat_1 )
       != ( B @ k1_relat_1 ) )
      | ( ( A @ k1_relat_1 )
       != ( B @ k2_relat_1 ) ) ),
    inference(lifteq,[status(thm)],[1117]) ).

thf(813,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_lattice2) ).

thf(5503,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)],[813]) ).

thf(37891,plain,
    ( ( ( sk196 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[2989,31369]) ).

thf(37892,plain,
    ( ( ( sk196 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[37891]) ).

thf(38089,plain,
    ( ( sk196 != k1_xboole_0 )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[37892]) ).

thf(822,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_setwiseo ) )
       => ( ( A @ k5_lattices )
          = ( A @ u2_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_lattice2) ).

thf(5535,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)],[822]) ).

thf(2161,plain,
    sk94 @ v9_lattices,
    inference(cnfConj,[status(thm)],[2154]) ).

thf(698,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ? [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
          & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).

thf(4978,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)],[698]) ).

thf(536,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( C @ ( F @ m1_subset_1 ) )
                           => ( ( D @ ( F @ r2_hidden ) )
                             => ( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) )
                                = B ) ) )
                       => ( ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) )
                            = B )
                          | ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_lattice2) ).

thf(4127,plain,
    ! [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)],[536]) ).

thf(16098,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( k6_nat_lat != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,10678]) ).

thf(16099,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( k6_nat_lat != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16098]) ).

thf(16225,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk295 != k1_xboole_0 )
      | ( k6_nat_lat != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16099]) ).

thf(16291,plain,
    ( ( sk295 != k1_xboole_0 )
    | ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16225]) ).

thf(3002,plain,
    sk197 @ l3_lattices,
    inference(cnfConj,[status(thm)],[2999]) ).

thf(1056,plain,
    ( ( k1_xboole_0 @ k2_relat_1 )
    = k1_xboole_0 ),
    inference(cnfConj,[status(thm)],[1054]) ).

thf(1058,plain,
    ( ( k1_xboole_0 @ k2_relat_1 )
    = k1_xboole_0 ),
    inference(lifteq,[status(thm)],[1056]) ).

thf(737,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v14_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( A @ ( A @ k6_lattices @ ( A @ u1_struct_0 @ k6_domain_1 ) @ m1_filter_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_filter_0) ).

thf(5148,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)],[737]) ).

thf(15314,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( k1_xboole_0 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3050,3056]) ).

thf(15315,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[15314]) ).

thf(15329,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != k1_xboole_0 ),
    inference(simp,[status(thm)],[15315]) ).

thf(930,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
             => ( ( C @ ( B @ ( A @ r2_lattice4 ) ) )
              <=> ( ( A @ k6_lattices @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
                  = ( B @ k6_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_lattice4) ).

thf(5997,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)],[930]) ).

thf(419,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k12_filter_2 ) )
        = ( B @ ( A @ k8_filter_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k12_filter_2) ).

thf(3568,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)],[419]) ).

thf(353,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
       => ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( C @ ( A @ ( D @ v1_funct_2 ) ) )
            & ( D @ v1_funct_1 ) )
          | ( ( A != k1_xboole_0 )
            & ( B = k1_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_2) ).

thf(3170,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)],[353]) ).

thf(1138,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)],[1137]) ).

thf(1139,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)],[1138]) ).

thf(467,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ~ ( A @ ( B @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(3796,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ r2_hidden ) )
     => ~ ( A @ ( B @ r2_hidden ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(747,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k2_struct_0 ) ) )
        = ( C @ ( B @ k2_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_struct_0) ).

thf(5185,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)],[747]) ).

thf(550,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
                = ( C @ ( B @ ( A @ k6_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_filter_0) ).

thf(4186,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)],[550]) ).

thf(730,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( B @ ( A @ k2_filter_0 ) @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
                & ( B @ ( A @ k2_filter_0 ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) )
                & ( B @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_filter_0) ).

thf(5118,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( 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)],[730]) ).

thf(2293,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ sk110 ) @ v1_funct_1 ),
    inference(cnfConj,[status(thm)],[2290]) ).

thf(2891,plain,
    sk188 @ v6_lattices,
    inference(cnfConj,[status(thm)],[2884]) ).

thf(433,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( C @ ( B @ a_2_3_domain_1 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i,E: $i] :
            ( ( E @ ( D @ p1_s2_domain_1 ) )
            & ( A
              = ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
            & ( C @ ( E @ m1_subset_1 ) )
            & ( B @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_3_domain_1) ).

thf(3651,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)],[433]) ).

thf(442,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v11_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_lattice2) ).

thf(3695,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)],[442]) ).

thf(543,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
    <=> ( B @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

thf(4149,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)],[543]) ).

thf(5327,plain,
    ( ( ( f4_s11_funct_2 @ ( sk393 @ ( 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)],[5322]) ).

thf(5331,plain,
    ( ( ( f4_s11_funct_2 @ ( sk393 @ ( 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)],[5327]) ).

thf(425,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( B @ ( D @ r2_hidden ) )
                <=> ( C @ ( D @ r2_hidden ) ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_subset_1) ).

thf(3594,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)],[425]) ).

thf(722,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( A @ u2_lattices @ v1_setwiseo ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_lattice2) ).

thf(5086,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)],[722]) ).

thf(463,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v16_lattices )
        & ( A @ v15_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v16_lattices )
            & ( B @ v15_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
              = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ! [E: $i] :
                        ( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                       => ! [F: $i] :
                            ( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                           => ( ( ( D @ ( C @ ( A @ r2_lattices ) ) )
                                & ( D = F )
                                & ( C = E ) )
                             => ( F @ ( E @ ( B @ r2_lattices ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_filter_2) ).

thf(3783,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)],[463]) ).

thf(28,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_funct_1 )
        & ( B @ v1_relat_1 ) )
     => ! [C: $i] :
          ( ( ( C @ v1_funct_1 )
            & ( C @ v1_relat_1 ) )
         => ( ( ( ( C @ k2_relat_1 )
                = ( A @ k1_tarski ) )
              & ( ( B @ k2_relat_1 )
                = ( A @ k1_tarski ) )
              & ( ( B @ k1_relat_1 )
                = ( C @ k1_relat_1 ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_1) ).

thf(1092,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(444,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( A @ v3_lattices )
       => ( A
          = ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).

thf(3700,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)],[444]) ).

thf(864,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k13_filter_2 ) )
        = ( B @ ( A @ k7_filter_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k13_filter_2) ).

thf(5703,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)],[864]) ).

thf(421,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_lattice4 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_lattice2 @ ( B @ ( A @ k10_filter_2 ) @ m2_lattice4 ) )
        & ~ ( B @ ( A @ k10_filter_2 ) @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_filter_2) ).

thf(3579,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)],[421]) ).

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

thf(1765,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(1090,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)],[1088]) ).

thf(676,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( ( B @ ( D @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) )
                          = ( B @ ( E @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) ) )
                       => ( ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) )
                          = ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_lattice2) ).

thf(4854,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)],[676]) ).

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

thf(1897,plain,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
           => ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(635,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( A @ k1_zfmisc_1 ) )
    <=> ! [C: $i] :
          ( ( B @ ( C @ r2_hidden ) )
        <=> ( A @ ( C @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).

thf(4640,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)],[635]) ).

thf(570,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ( B @ ( A @ r2_hidden ) ) )
     => ( C @ ( A @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).

thf(4273,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)],[570]) ).

thf(741,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v3_filter_0 )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( C @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ! [G: $i] :
                              ( ( C @ ( G @ m1_filter_0 ) )
                             => ! [H: $i] :
                                  ( ( A @ u1_struct_0 @ ( H @ m1_subset_1 ) )
                                 => ! [I: $i] :
                                      ( ( A @ u1_struct_0 @ ( I @ m1_subset_1 ) )
                                     => ! [J: $i] :
                                          ( ( A @ u1_struct_0 @ ( J @ m1_subset_1 ) )
                                         => ( ( ( ( J @ ( I @ ( B @ ( A @ r1_filter_0 ) ) ) )
                                                & ( I @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
                                             => ( J @ ( H @ ( B @ ( A @ r1_filter_0 ) ) ) ) )
                                            & ( ( ( F @ ( E @ ( G @ ( C @ r1_filter_0 ) ) ) )
                                                & ( E @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) )
                                             => ( F @ ( D @ ( G @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_filter_0) ).

thf(5158,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)],[741]) ).

thf(450,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ? [F: $i] :
                            ( ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) )
                            & ( D @ ( F @ r2_hidden ) )
                            & ( C @ ( F @ m1_subset_1 ) ) )
                       => ( B @ ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_lattice2) ).

thf(3719,plain,
    ! [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)],[450]) ).

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/sandbox/benchmark/theBenchmark.p',t65_partfun1) ).

thf(2319,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(659,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k3_lattices ) ) )
                = ( B @ ( C @ ( A @ k7_grcat_1 @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funcop_1 ) ) ) ) @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_setwiseo ) ) ) @ ( A @ k2_lattice4 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_lattice4) ).

thf(4790,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)],[659]) ).

thf(283,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v10_lattices )
      <=> ( ( A @ v9_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v8_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_lattices) ).

thf(2721,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)],[283]) ).

thf(8447,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk218 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3256,999]) ).

thf(8448,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk218 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[8447]) ).

thf(8449,plain,
    ! [A: $i] : ( sk218 @ k1_relat_1 @ ( sk218 @ k9_relat_1 ) @ ( A @ ( sk218 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[8448:[bind(A,$thf( A )),bind(B,$thf( sk218 ))]]) ).

thf(15495,plain,
    ! [A: $i] :
      ( ( ( sk218 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ~ $true
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[3256,1086]) ).

thf(15496,plain,
    ! [A: $i] :
      ( ( ( sk218 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[15495]) ).

thf(15497,plain,
    ( ( sk218 @ k1_relat_1 @ ( sk218 @ k9_relat_1 ) )
    = ( sk218 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15496:[bind(A,$thf( sk218 ))]]) ).

thf(27172,plain,
    ! [A: $i] : ( sk218 @ k2_relat_1 @ ( A @ ( sk218 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[8449,15497]) ).

thf(430,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
        & ( E @ v1_funct_1 ) )
     => ( ( ( D @ ( B @ r1_tarski ) )
          & ( C @ ( A @ r1_tarski ) ) )
       => ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
          & ( E @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_partfun1) ).

thf(3631,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)],[430]) ).

thf(4369,plain,
    sk297 @ v6_lattices,
    inference(cnfConj,[status(thm)],[4356]) ).

thf(462,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != D )
        & ( A != C )
        & ( ( B @ ( A @ k2_tarski ) )
          = ( D @ ( C @ k2_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).

thf(3779,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)],[462]) ).

thf(16197,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,8209]) ).

thf(16198,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16197]) ).

thf(16248,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk207 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16198]) ).

thf(16317,plain,
    ( ( sk207 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16248]) ).

thf(104,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
     => ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
          & ( C @ v1_funct_1 ) )
       => ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
          & ( C @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_2) ).

thf(1589,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(1119,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ k2_funct_1 ) )
      | ( ( A @ ( B @ sk11 ) @ ( B @ k1_funct_1 ) )
        = ( A @ ( B @ sk10 ) ) )
      | ( ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) )
        = ( A @ ( B @ sk11 ) ) )
      | ( ( A @ k2_relat_1 )
       != ( B @ k1_relat_1 ) )
      | ( ( A @ k1_relat_1 )
       != ( B @ k2_relat_1 ) )
      | ~ ( A @ v2_funct_1 )
      | ~ ( B @ v1_funct_1 )
      | ~ ( B @ v1_relat_1 )
      | ~ ( A @ v1_funct_1 )
      | ~ ( A @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1114]) ).

thf(1122,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ v2_funct_1 )
      | ~ ( B @ v1_funct_1 )
      | ~ ( B @ v1_relat_1 )
      | ~ ( A @ v1_funct_1 )
      | ~ ( A @ v1_relat_1 )
      | ( B
        = ( A @ k2_funct_1 ) )
      | ( ( A @ ( B @ sk11 ) @ ( B @ k1_funct_1 ) )
        = ( A @ ( B @ sk10 ) ) )
      | ( ( A @ ( B @ sk11 ) )
        = ( A @ ( B @ sk10 ) @ ( A @ k1_funct_1 ) ) )
      | ( ( A @ k2_relat_1 )
       != ( B @ k1_relat_1 ) )
      | ( ( A @ k1_relat_1 )
       != ( B @ k2_relat_1 ) ) ),
    inference(lifteq,[status(thm)],[1119]) ).

thf(1191,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != C )
      | ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) ),
    inference(cnfConj,[status(thm)],[1189]) ).

thf(1193,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
      | ( A != C ) ),
    inference(lifteq,[status(thm)],[1191]) ).

thf(1194,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ r2_hidden ) ),
    inference(simp,[status(thm)],[1193]) ).

thf(30104,plain,
    ! [A: $i] :
      ( ( A != sk95 )
      | ( k1_xboole_0 @ v2_struct_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,2168]) ).

thf(30105,plain,
    ( ( k1_xboole_0 @ v2_struct_0 )
    | ( sk95 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[30104:[bind(A,$thf( sk95 ))]]) ).

thf(960,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
                  = C ) )
           => ( B
              = ( A @ k5_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_lattice2) ).

thf(6144,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( 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)],[960]) ).

thf(2346,plain,
    sk118 @ v5_lattices,
    inference(cnfConj,[status(thm)],[2342]) ).

thf(29792,plain,
    ! [A: $i] :
      ( ( A != sk188 )
      | ( k1_xboole_0 @ v3_lattices )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,2889]) ).

thf(29793,plain,
    ( ( k1_xboole_0 @ v3_lattices )
    | ( sk188 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[29792:[bind(A,$thf( sk188 ))]]) ).

thf(935,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ~ ( B @ ( A @ k7_filter_2 ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_filter_2) ).

thf(6024,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)],[935]) ).

thf(365,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( A @ ( D @ m1_subset_1 ) )
        & ( B @ ( A @ ( C @ m1_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
        = ( D @ ( C @ k1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).

thf(3238,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)],[365]) ).

thf(758,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ u1_struct_0 @ m2_lattice4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_lattice4) ).

thf(5244,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)],[758]) ).

thf(12062,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,9826]) ).

thf(12063,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12062]) ).

thf(12146,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk295 )
    | ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12063]) ).

thf(12227,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12146]) ).

thf(2987,plain,
    sk196 @ v16_lattices,
    inference(cnfConj,[status(thm)],[2983]) ).

thf(275,axiom,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
     => ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_2) ).

thf(2637,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(576,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ? [C: $i] : ( B @ ( A @ ( C @ m1_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_struct_0) ).

thf(4305,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)],[576]) ).

thf(896,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( A @ u1_struct_0 @ ( B @ ( A @ k10_filter_0 ) @ r3_relat_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_filter_0) ).

thf(5848,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)],[896]) ).

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 ) )
         => ( ( A @ v14_lattices )
           => ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ k6_lattices )
              = ( A @ k6_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_filter_0) ).

thf(5491,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)],[809]) ).

thf(3106,plain,
    k6_nat_lat @ v4_lattices,
    inference(cnfConj,[status(thm)],[3103]) ).

thf(29206,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
       != ( D @ ( C @ k2_tarski ) ) )
      | ( ( A @ k1_tarski @ k1_zfmisc_1 )
       != ( B @ sk249 ) ) ),
    inference(paramod_ordered,[status(thm)],[1994,15650]) ).

thf(29207,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_tarski @ k1_zfmisc_1 )
     != ( A @ sk249 ) ),
    inference(pattern_uni,[status(thm)],[29206:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( k1_xboole_0 )),bind(D,$thf( E @ k1_tarski ))]]) ).

thf(29216,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k1_tarski @ k1_zfmisc_1 )
     != ( A @ sk249 ) ),
    inference(simp,[status(thm)],[29207]) ).

thf(2669,plain,
    ~ ( sk157 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2661]) ).

thf(539,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( C @ ( A @ r1_tarski ) )
       => ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
          = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_2) ).

thf(4139,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)],[539]) ).

thf(314,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ! [C: $i] :
          ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
            & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ! [D: $i] :
              ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
                & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
                & ( D @ v1_funct_1 ) )
             => ! [E: $i] :
                  ( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
                 => ( ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) )
                      = ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
                   => ( ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
                      = ( E @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_lattice2) ).

thf(2943,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)],[314]) ).

thf(790,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ~ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_filter_0) ).

thf(5407,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)],[790]) ).

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 @ k2_lattice2 ) ) ) @ ( B @ ( A @ k3_lattices ) ) )
                          = ( E @ ( B @ ( A @ u2_lattices @ ( C @ ( A @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_lattice2) ).

thf(4213,plain,
    ! [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)],[556]) ).

thf(358,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ( A @ v5_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_partfun1 ) ) )
        & ( A @ u1_struct_0 @ ( A @ u2_lattices @ v2_binop_1 ) )
        & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
        & ( A @ u2_lattices @ v1_funct_1 )
        & ( A @ u2_lattices @ v1_relat_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattice2) ).

thf(3197,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)],[358]) ).

thf(725,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v14_lattices )
          & ( A @ v13_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v15_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_lattices) ).

thf(5093,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)],[725]) ).

thf(4665,plain,
    ( ( sk325 @ v3_lattices )
    & ( sk325 @ l3_lattices ) ),
    inference(cnf,[status(esa)],[4664]) ).

thf(4667,plain,
    sk325 @ v3_lattices,
    inference(cnfConj,[status(thm)],[4665]) ).

thf(6154,plain,
    sk458 @ l3_lattices,
    inference(cnf,[status(esa)],[6153]) ).

thf(349,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
          <=> ! [D: $i] :
                ( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
               => ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_realset1) ).

thf(3138,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)],[349]) ).

thf(355,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
     => ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_subset_1 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).

thf(3182,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)],[355]) ).

thf(303,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ( ( k1_xboole_0 @ ( A @ k9_relat_1 ) )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_relat_1) ).

thf(2896,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)],[303]) ).

thf(389,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ v1_funct_1 )
        & ( C @ v1_relat_1 ) )
     => ( ( ( C @ k2_relat_1 )
          = k1_xboole_0 )
       => ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
          & ( C @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_partfun1) ).

thf(3384,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)],[389]) ).

thf(653,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v17_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ! [D: $i] :
                      ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                     => ( ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
                       => ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( D @ ( A @ r3_lattices ) ) ) ) )
                  & ( C @ ( C @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_filter_0) ).

thf(4773,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)],[653]) ).

thf(15646,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
       != ( sk278 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4083,4338]) ).

thf(15647,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) @ v1_xboole_0 )
     != ( sk278 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[15646]) ).

thf(15654,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k2_tarski ) )
     != sk278 ),
    inference(simp,[status(thm)],[15647]) ).

thf(2871,plain,
    ~ ( sk187 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2869]) ).

thf(613,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( A @ ( E @ m1_subset_1 ) )
        & ( A @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_domain_1) ).

thf(4509,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)],[613]) ).

thf(532,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_nat_lat ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_lattice2 @ ( B @ ( A @ k24_filter_2 ) @ m2_nat_lat ) )
        & ( B @ ( A @ k24_filter_2 ) @ v3_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k24_filter_2) ).

thf(4107,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)],[532]) ).

thf(67,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( B @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_funct_2) ).

thf(1307,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(182,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).

thf(2065,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(29824,plain,
    ! [A: $i] :
      ( ( A != sk187 )
      | ( k1_xboole_0 @ v14_lattices )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,2876]) ).

thf(29825,plain,
    ( ( k1_xboole_0 @ v14_lattices )
    | ( sk187 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[29824:[bind(A,$thf( sk187 ))]]) ).

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

thf(1172,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(1173,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_funct_1 )
        & ( B @ v1_relat_1 ) )
     => ( ~ ? [C: $i] :
              ( ~ ? [D: $i] :
                    ( ( C
                      = ( D @ ( B @ k1_funct_1 ) ) )
                    & ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
              & ( A @ ( C @ r2_hidden ) ) )
       => ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
    inference(miniscope,[status(thm)],[1172]) ).

thf(1174,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
        | ( ( A @ ( B @ sk15 ) )
         != ( C @ ( B @ k1_funct_1 ) ) )
        | ~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
        | ~ ( B @ v1_funct_1 )
        | ~ ( B @ v1_relat_1 ) )
      & ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
        | ( A @ ( A @ ( B @ sk15 ) @ r2_hidden ) )
        | ~ ( B @ v1_funct_1 )
        | ~ ( B @ v1_relat_1 ) ) ),
    inference(cnf,[status(esa)],[1173]) ).

thf(1175,plain,
    ! [B: $i,A: $i] :
      ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
      | ( A @ ( A @ ( B @ sk15 ) @ r2_hidden ) )
      | ~ ( B @ v1_funct_1 )
      | ~ ( B @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1174]) ).

thf(285,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ k4_tarski ) )
        = ( D @ ( C @ k4_tarski ) ) )
     => ( ( B = D )
        & ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).

thf(2742,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)],[285]) ).

thf(602,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( ! [E: $i] :
                ( ( A @ ( E @ m1_subset_1 ) )
               => ( ( E @ ( C @ k1_funct_1 ) )
                  = ( E @ ( D @ k1_funct_1 ) ) ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_funct_2) ).

thf(4445,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)],[602]) ).

thf(12013,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,9145]) ).

thf(12014,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12013]) ).

thf(12111,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk216 )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12014]) ).

thf(3188,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[3186]) ).

thf(3191,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k2_zfmisc_1 ) )
        = k1_xboole_0 )
      | ( A != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[3188]) ).

thf(3192,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[3191]) ).

thf(785,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k1_struct_0 ) )
        = ( B @ k1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_struct_0) ).

thf(5392,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)],[785]) ).

thf(47021,plain,
    ( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk278 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4083,46818]) ).

thf(47022,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk278 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[47021]) ).

thf(47028,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk278 ),
    inference(simp,[status(thm)],[47022]) ).

thf(422,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v17_lattices )
      <=> ( ( A @ v11_lattices )
          & ( A @ v16_lattices )
          & ( A @ v15_lattices ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d20_lattices) ).

thf(3583,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)],[422]) ).

thf(63,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
        = ( D @ ( C @ k9_relat_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).

thf(1293,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(1176,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
      | ( ( A @ ( B @ sk15 ) )
       != ( C @ ( B @ k1_funct_1 ) ) )
      | ~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
      | ~ ( B @ v1_funct_1 )
      | ~ ( B @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1174]) ).

thf(1177,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
      | ~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
      | ~ ( B @ v1_funct_1 )
      | ~ ( B @ v1_relat_1 )
      | ( ( A @ ( B @ sk15 ) )
       != ( C @ ( B @ k1_funct_1 ) ) ) ),
    inference(lifteq,[status(thm)],[1176]) ).

thf(320,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
        = ( C @ ( B @ k4_tarski ) @ ( C @ ( A @ k4_tarski ) @ k2_tarski ) ) )
      & ( ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
        = ( C @ ( A @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_zfmisc_1) ).

thf(2974,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)],[320]) ).

thf(6951,plain,
    ( ( ( sk187 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2881,6900]) ).

thf(6952,plain,
    ( ( ( sk187 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[6951]) ).

thf(6956,plain,
    ( ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[6952]) ).

thf(3893,plain,
    sk265 @ l1_struct_0,
    inference(cnfConj,[status(thm)],[3892]) ).

thf(1110,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)],[1109]) ).

thf(1112,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)],[1110]) ).

thf(9392,plain,
    ( ( ( sk297 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4370,8414]) ).

thf(9393,plain,
    ( ( ( sk297 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9392]) ).

thf(9407,plain,
    ( ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[9393]) ).

thf(114,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( A @ ( C @ r1_tarski ) )
       => ( ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( C @ r1_tarski ) )
          | ( ( A != k1_xboole_0 )
            & ( B = k1_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_funct_2) ).

thf(1667,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(200,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ( A @ v7_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_partfun1 ) ) )
        & ( A @ u1_struct_0 @ ( A @ u1_lattices @ v2_binop_1 ) )
        & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
        & ( A @ u1_lattices @ v1_funct_1 )
        & ( A @ u1_lattices @ v1_relat_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_lattice2) ).

thf(2180,plain,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ( A @ v7_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_partfun1 ) ) )
        & ( A @ u1_struct_0 @ ( A @ u1_lattices @ v2_binop_1 ) )
        & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
        & ( A @ u1_lattices @ v1_funct_1 )
        & ( A @ u1_lattices @ v1_relat_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(633,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( C @ v1_xboole_0 )
        & ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

thf(4635,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)],[633]) ).

thf(780,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                   => ( ( C @ ( B @ ( D @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
                      & ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_filter_0) ).

thf(5367,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[780]) ).

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 ) )
             => ( ( ( A @ l3_lattices )
                  & ( A @ v3_filter_0 )
                  & ( A @ v10_lattices )
                  & ~ ( A @ v3_struct_0 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( D
                        = ( C @ ( B @ ( A @ k4_filter_0 ) ) ) )
                    <=> ( ! [E: $i] :
                            ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                           => ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
                             => ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
                        & ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_filter_0) ).

thf(6087,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( 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)],[949]) ).

thf(834,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
              = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
           => ! [C: $i] :
                ( ( A @ ( C @ m2_filter_2 ) )
               => ( B @ ( C @ m2_filter_2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_filter_2) ).

thf(5584,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)],[834]) ).

thf(142,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_funct_1 )
        & ( B @ v1_relat_1 ) )
     => ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
       => ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
          & ( A @ ( B @ k1_relat_1 @ ( B @ v1_funct_2 ) ) )
          & ( B @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_2) ).

thf(1877,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(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/sandbox/benchmark/theBenchmark.p',t25_subset_1) ).

thf(2632,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(12001,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,8397]) ).

thf(12002,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ v10_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12001]) ).

thf(12114,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk216 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[12002]) ).

thf(2343,plain,
    sk118 @ v9_lattices,
    inference(cnfConj,[status(thm)],[2342]) ).

thf(16019,plain,
    ( ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[7813,2222]) ).

thf(16020,plain,
    ( ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16019]) ).

thf(721,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v3_filter_0 )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( C @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( C @ ( E @ m1_filter_0 ) )
                     => ! [F: $i] :
                          ( ( A @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ( F @ ( F @ ( B @ ( A @ r1_filter_0 ) ) ) )
                            & ( D @ ( D @ ( E @ ( C @ r1_filter_0 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_filter_0) ).

thf(5082,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)],[721]) ).

thf(929,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k7_filter_2 ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_filter_2) ).

thf(5994,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)],[929]) ).

thf(335,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ( ( C @ ( B @ ( A @ r7_binop_1 ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ! [E: $i] :
                    ( ( A @ ( E @ m1_subset_1 ) )
                   => ( ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_funct_1 ) )
                      = ( E @ ( B @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_binop_1) ).

thf(3073,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)],[335]) ).

thf(47045,plain,
    ! [A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3676,46859]) ).

thf(47046,plain,
    ! [A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[47045]) ).

thf(47107,plain,
    ! [A: $i] :
      ( ( A @ sk249 )
     != ( sk14 @ sk366 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) ) ),
    inference(simp,[status(thm)],[47046]) ).

thf(772,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_lattice4 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k9_filter_2 ) )
        = ( B @ ( A @ k7_filter_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_filter_2) ).

thf(5335,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)],[772]) ).

thf(797,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k6_lattices )
        = ( A @ u1_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_lattice2) ).

thf(5439,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)],[797]) ).

thf(469,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( C @ ( F @ m1_subset_1 ) )
                           => ( ( D @ ( F @ r2_hidden ) )
                             => ( B @ ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
                       => ( ( B @ ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
                          | ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_lattice2) ).

thf(3800,plain,
    ! [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)],[469]) ).

thf(497,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != C )
        & ( A != B )
        & ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_zfmisc_1) ).

thf(3932,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)],[497]) ).

thf(40,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
      <=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
          = ( C @ k1_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_partfun1) ).

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

thf(1160,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)],[1158]) ).

thf(1162,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)],[1160]) ).

thf(700,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ ( D @ m1_subset_1 ) )
                   => ( ( B @ ( D @ r2_hidden ) )
                    <=> ( C @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_filter_2) ).

thf(4985,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)],[700]) ).

thf(764,axiom,
    ! [A: $i] :
      ( ( a_0_0_domain_1 @ ( A @ r2_hidden ) )
    <=> ? [B: $i] :
          ( ( B @ p1_s7_domain_1 )
          & ( A = B )
          & ( f1_s7_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_0_domain_1) ).

thf(5286,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)],[764]) ).

thf(287,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
      = ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_zfmisc_1) ).

thf(2785,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)],[287]) ).

thf(3006,plain,
    sk197 @ v7_lattices,
    inference(cnfConj,[status(thm)],[2999]) ).

thf(1149,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)],[1148]) ).

thf(2471,plain,
    sk138 @ v1_relat_1,
    inference(cnfConj,[status(thm)],[2470]) ).

thf(15485,plain,
    ! [A: $i] :
      ( ( ( sk138 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ~ $true
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(paramod_ordered,[status(thm)],[2471,1086]) ).

thf(15486,plain,
    ! [A: $i] :
      ( ( ( sk138 @ v1_relat_1 )
       != ( A @ v1_relat_1 ) )
      | ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
        = ( A @ k2_relat_1 ) ) ),
    inference(simp,[status(thm)],[15485]) ).

thf(15487,plain,
    ( ( sk138 @ k1_relat_1 @ ( sk138 @ k9_relat_1 ) )
    = ( sk138 @ k2_relat_1 ) ),
    inference(pattern_uni,[status(thm)],[15486:[bind(A,$thf( sk138 ))]]) ).

thf(8362,plain,
    ( ( ( sk218 @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3244,3255]) ).

thf(8363,plain,
    ( ( sk218 @ v1_xboole_0 )
   != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8362]) ).

thf(8372,plain,
    sk218 != sk216,
    inference(simp,[status(thm)],[8363]) ).

thf(2874,plain,
    sk187 @ l3_lattices,
    inference(cnfConj,[status(thm)],[2869]) ).

thf(745,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v13_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
              = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
           => ( ( A @ k5_lattices )
              = ( B @ k5_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_filter_2) ).

thf(5180,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)],[745]) ).

thf(648,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
     => ( ( B @ ( B @ ( A @ k4_subset_1 ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).

thf(4726,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)],[648]) ).

thf(2664,plain,
    sk157 @ v11_lattices,
    inference(cnfConj,[status(thm)],[2661]) ).

thf(480,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( A @ ( E @ r2_hidden ) )
        & ( E @ ( D @ r2_hidden ) )
        & ( D @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_ordinal1) ).

thf(3861,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)],[480]) ).

thf(762,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( A @ ( B @ m2_filter_2 ) )
          <=> ( ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ! [D: $i] :
                      ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                     => ( ( ( C @ ( D @ ( A @ r3_lattices ) ) )
                          & ( B @ ( C @ r2_hidden ) ) )
                       => ( B @ ( D @ r2_hidden ) ) ) ) )
              & ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ! [D: $i] :
                      ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                     => ( ( ( B @ ( D @ r2_hidden ) )
                          & ( B @ ( C @ r2_hidden ) ) )
                       => ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_filter_2) ).

thf(5254,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)],[762]) ).

thf(2350,plain,
    ~ ( sk118 @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2342]) ).

thf(2401,plain,
    ~ ( k13_nat_lat @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[2398]) ).

thf(492,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) )
       => ( A @ v11_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_lattice2) ).

thf(3917,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)],[492]) ).

thf(766,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( B @ ( A @ r1_filter_1 ) )
          <=> ? [C: $i] :
                ( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
                & ( B @ ( A @ ( C @ m1_lattice4 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_lattice4) ).

thf(5299,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)],[766]) ).

thf(2156,plain,
    sk94 @ v8_lattices,
    inference(cnfConj,[status(thm)],[2154]) ).

thf(205,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ~ ( ! [C: $i] :
              ( ( A @ ( C @ m1_subset_1 ) )
             => ~ ( B @ ( C @ r2_hidden ) ) )
          & ( B != k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_subset_1) ).

thf(2207,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)],[205]) ).

thf(7350,plain,
    ! [A: $i] :
      ( ( ( A @ k1_tarski @ v1_xboole_0 )
       != ( sk71 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1924,4906]) ).

thf(7351,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7350]) ).

thf(7356,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski )
     != sk71 ),
    inference(simp,[status(thm)],[7351]) ).

thf(526,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m1_struct_0 ) ) )
         => ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_struct_0) ).

thf(4084,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)],[526]) ).

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/sandbox/benchmark/theBenchmark.p',dt_g2_struct_0) ).

thf(3480,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(1170,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
        = C )
      | ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
      | ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
      | ~ ( D @ v1_funct_1 )
      | ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
      | ( B @ v1_xboole_0 ) ),
    inference(cnf,[status(esa)],[1169]) ).

thf(1171,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
      | ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
      | ~ ( D @ v1_funct_1 )
      | ~ ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
      | ( B @ v1_xboole_0 )
      | ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
        = C ) ),
    inference(lifteq,[status(thm)],[1170]) ).

thf(979,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)],[977]) ).

thf(982,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)],[979]) ).

thf(983,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)],[982]) ).

thf(670,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k6_lattices @ ( A @ k7_lattices ) )
        = ( A @ k5_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_lattice4) ).

thf(4832,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)],[670]) ).

thf(774,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ? [B: $i] : ( A @ ( B @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_filter_2) ).

thf(5340,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)],[774]) ).

thf(712,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k19_filter_2 ) @ m2_filter_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k19_filter_2) ).

thf(5057,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)],[712]) ).

thf(798,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( B @ ( A @ k3_filter_0 ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_filter_0) ).

thf(5442,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)],[798]) ).

thf(199,axiom,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
           => ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
        & ! [C: $i] :
            ~ ( ! [D: $i,E: $i] :
                  ( C
                 != ( E @ ( D @ k4_tarski ) ) )
              & ( A @ ( C @ r2_hidden ) ) ) )
     => ( B @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_zfmisc_1) ).

thf(2171,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i,D: $i] :
            ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
           => ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
        & ! [C: $i] :
            ~ ( ! [D: $i,E: $i] :
                  ( C
                 != ( E @ ( D @ k4_tarski ) ) )
              & ( A @ ( C @ r2_hidden ) ) ) )
     => ( B @ ( A @ r1_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(396,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_subset_1 ) )
         => ! [D: $i] :
              ( ( A @ ( D @ m1_subset_1 ) )
             => ( ( ( B @ ( D @ ( A @ r3_binop_1 ) ) )
                  & ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
               => ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_binop_1) ).

thf(3423,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)],[396]) ).

thf(1062,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)],[1060]) ).

thf(1066,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)],[1062]) ).

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/sandbox/benchmark/theBenchmark.p',t7_lattice2) ).

thf(2620,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(6339,plain,
    ( ( ( sk157 @ v13_lattices )
     != ( sk1 @ v13_lattices ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2672,970]) ).

thf(6340,plain,
    ( ( sk157 @ v13_lattices )
   != ( sk1 @ v13_lattices ) ),
    inference(simp,[status(thm)],[6339]) ).

thf(6341,plain,
    sk157 != sk1,
    inference(simp,[status(thm)],[6340]) ).

thf(32845,plain,
    ! [A: $i] :
      ( ( A != sk157 )
      | ( sk1 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,6341]) ).

thf(32846,plain,
    ( ( sk1 != k1_xboole_0 )
    | ( sk157 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[32845:[bind(A,$thf( sk157 ))]]) ).

thf(3110,plain,
    ~ ( k6_nat_lat @ v3_struct_0 ),
    inference(cnfConj,[status(thm)],[3103]) ).

thf(15312,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( B @ ( B @ k1_funct_2 ) @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3676,3056]) ).

thf(15313,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( B @ ( B @ k1_funct_2 ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[15312]) ).

thf(15326,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk249 )
     != ( B @ ( B @ k1_funct_2 ) ) ),
    inference(simp,[status(thm)],[15313]) ).

thf(590,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ~ ( ( A @ ( F @ r2_hidden ) )
        & ( F @ ( E @ r2_hidden ) )
        & ( E @ ( D @ r2_hidden ) )
        & ( D @ ( C @ r2_hidden ) )
        & ( C @ ( B @ r2_hidden ) )
        & ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_ordinal1) ).

thf(4373,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)],[590]) ).

thf(110,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ! [B: $i] :
          ( ( B @ v1_relat_1 )
         => ( ( B @ ( A @ r1_tarski ) )
           => ( ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
              & ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).

thf(1643,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(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/sandbox/benchmark/theBenchmark.p',fc2_realset1) ).

thf(2369,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(4362,plain,
    sk297 @ v14_lattices,
    inference(cnfConj,[status(thm)],[4356]) ).

thf(289,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( A @ ( C @ v1_binop_1 ) )
               => ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
                <=> ( B @ ( C @ ( A @ r5_binop_1 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_binop_1) ).

thf(2797,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)],[289]) ).

thf(286,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( B @ ( A @ k2_zfmisc_1 ) ) )
    <=> ! [D: $i] :
          ( ( C @ ( D @ r2_hidden ) )
        <=> ? [E: $i,F: $i] :
              ( ( D
                = ( F @ ( E @ k4_tarski ) ) )
              & ( B @ ( F @ r2_hidden ) )
              & ( A @ ( E @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).

thf(2752,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)],[286]) ).

thf(128,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
           => ( B @ ( A @ ( D @ v1_partfun1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t169_partfun1) ).

thf(1775,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(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/sandbox/benchmark/theBenchmark.p',t12_lattice2) ).

thf(2592,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(172,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( ( C @ ( D @ r1_tarski ) )
           => ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t165_funct_2) ).

thf(2022,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(386,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v3_filter_0 )
          & ( A @ v13_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v1_lattice2 )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_lattice2) ).

thf(3363,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)],[386]) ).

thf(446,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v14_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( ( B @ ( D @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) )
                          = ( B @ ( E @ ( C @ u1_struct_0 @ ( A @ k2_partfun1 ) ) ) ) )
                       => ( ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) )
                          = ( E @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_lattice2) ).

thf(3706,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)],[446]) ).

thf(378,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( B != k1_xboole_0 )
       => ( B @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_2) ).

thf(3325,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)],[378]) ).

thf(1098,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)],[1096]) ).

thf(1101,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)],[1098]) ).

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

thf(789,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ? [C: $i] :
              ( ( B @ ( C @ r2_hidden ) )
              & ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_filter_2) ).

thf(5403,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)],[789]) ).

thf(612,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_2_domain_1 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ( ( D @ ( E @ r2_hidden ) )
              | ( C @ ( E @ r2_hidden ) ) )
            & ( A = E )
            & ( B @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_2_domain_1) ).

thf(4497,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)],[612]) ).

thf(555,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
                    & ~ ( D @ v1_xboole_0 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
                        & ~ ( E @ v1_xboole_0 ) )
                     => ( ( ( E @ ( C @ r2_hidden ) )
                          & ( D @ ( B @ r2_hidden ) ) )
                       => ( ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
                          & ( E @ ( D @ ( A @ k5_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_filter_0) ).

thf(4209,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[555]) ).

thf(2984,plain,
    sk196 @ v14_lattices,
    inference(cnfConj,[status(thm)],[2983]) ).

thf(16106,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,8414]) ).

thf(16107,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16106]) ).

thf(16239,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk216 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16107]) ).

thf(16305,plain,
    ( ( sk216 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16239]) ).

thf(1075,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)],[1074]) ).

thf(1076,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)],[1075]) ).

thf(7166,plain,
    ( ( ( sk196 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2989,6903]) ).

thf(7167,plain,
    ( ( ( sk196 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7166]) ).

thf(7171,plain,
    ( ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[7167]) ).

thf(12096,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
    | ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,7171]) ).

thf(12097,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
    | ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12096]) ).

thf(12120,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk138 )
    | ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12097]) ).

thf(2878,plain,
    sk187 @ v10_lattices,
    inference(cnfConj,[status(thm)],[2869]) ).

thf(581,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_lattice2 @ k1_lattice2 )
        = ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_filter_2) ).

thf(4331,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)],[581]) ).

thf(3009,plain,
    sk197 @ v8_lattices,
    inference(cnfConj,[status(thm)],[2999]) ).

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 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
                = ( B @ ( C @ ( A @ k9_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_filter_0) ).

thf(5688,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( 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)],[861]) ).

thf(37905,plain,
    ( ( ( sk297 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[4370,31369]) ).

thf(37906,plain,
    ( ( ( sk297 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[37905]) ).

thf(38088,plain,
    ( ( sk297 != k1_xboole_0 )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[37906]) ).

thf(595,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v16_lattices )
        & ( A @ v15_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v3_filter_0 )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
             => ( ( A @ ( B @ ( C @ v3_lattice4 ) ) )
               => ( ( C @ ( A @ ( B @ r1_lattice4 ) ) )
                  & ( A @ v3_filter_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_lattice4) ).

thf(4405,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)],[595]) ).

thf(683,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( B @ ( A @ k4_lattices ) ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_lattices) ).

thf(4907,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)],[683]) ).

thf(823,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ k1_setwiseo @ ( A @ k1_lattice4 ) )
        = ( A @ k5_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_lattice4) ).

thf(5538,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)],[823]) ).

thf(835,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
               => ! [D: $i] :
                    ( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ! [E: $i] :
                        ( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                       => ( ( ( C = E )
                            & ( B = D ) )
                         => ( D @ ( E @ ( A @ k1_lattice2 @ r3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_lattice2) ).

thf(5587,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( 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)],[835]) ).

thf(498,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( E @ ( D @ ( A @ ( C @ k3_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
                       => ! [F: $i] :
                            ( ( C @ ( F @ m1_subset_1 ) )
                           => ( ( D @ ( F @ r2_hidden ) )
                             => ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_lattice2) ).

thf(3936,plain,
    ! [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)],[498]) ).

thf(900,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ~ ( ( ( B @ ( A @ k2_filter_0 ) )
                = ( A @ u1_struct_0 ) )
              & ~ ! [C: $i] :
                    ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                   => ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                      = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_filter_0) ).

thf(5886,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)],[900]) ).

thf(14798,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( C @ ( B @ k4_tarski ) @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3676,2366]) ).

thf(14799,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( C @ ( B @ k4_tarski ) @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[14798]) ).

thf(14813,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ sk249 )
     != ( C @ ( B @ k4_tarski ) ) ),
    inference(simp,[status(thm)],[14799]) ).

thf(2665,plain,
    sk157 @ v12_lattices,
    inference(cnfConj,[status(thm)],[2661]) ).

thf(679,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v14_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( A @ ( F @ m1_subset_1 ) )
                           => ( ( B @ ( F @ r2_hidden ) )
                             => ( F @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
                       => ( E @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( D @ ( B @ ( C @ ( A @ k3_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_lattice2) ).

thf(4868,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)],[679]) ).

thf(89,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
        = ( A @ k1_tarski ) )
    <=> ( ( ( A = B )
          | ( C @ ( B @ r2_hidden ) ) )
        & ~ ( C @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_zfmisc_1) ).

thf(1467,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(2994,plain,
    sk196 @ v4_lattices,
    inference(cnfConj,[status(thm)],[2983]) ).

thf(8122,plain,
    ( ( ( sk197 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3001,7813]) ).

thf(8123,plain,
    ( ( ( sk197 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8122]) ).

thf(8155,plain,
    ( ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8123]) ).

thf(16023,plain,
    ( ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[8155,2222]) ).

thf(16024,plain,
    ( ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16023]) ).

thf(16070,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,8691]) ).

thf(16071,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16070]) ).

thf(16221,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk295 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16071]) ).

thf(16285,plain,
    ( ( sk295 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16221]) ).

thf(507,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( B @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( B @ k1_lattice2 @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( B @ k1_lattice2 @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( D = E )
                       => ( ( ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) )
                            = ( E @ ( C @ ( B @ k1_lattice2 @ ( A @ k2_lattice2 ) ) ) ) )
                          & ( ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) )
                            = ( E @ ( C @ ( B @ k1_lattice2 @ ( A @ k3_lattice2 ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_lattice2) ).

thf(3975,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)],[507]) ).

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/sandbox/benchmark/theBenchmark.p',t64_partfun1) ).

thf(2629,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(166,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( B @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
        & ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 )
        & ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_binop_1) ).

thf(1990,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(858,axiom,
    ( ( k6_nat_lat @ l3_lattices )
    & ( k6_nat_lat @ v10_lattices )
    & ~ ( k6_nat_lat @ v3_struct_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_nat_lat) ).

thf(5678,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)],[858]) ).

thf(494,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ( B
            = ( B @ ( A @ a_2_1_domain_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_domain_1) ).

thf(3921,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)],[494]) ).

thf(70,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ( ( ( ( A @ k2_relat_1 )
            = k1_xboole_0 )
          | ( ( A @ k1_relat_1 )
            = k1_xboole_0 ) )
       => ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).

thf(1340,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(1142,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)],[1141]) ).

thf(1145,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)],[1142]) ).

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/sandbox/benchmark/theBenchmark.p',t27_relset_1) ).

thf(2256,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(297,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
       => ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
          & ( D @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_partfun1) ).

thf(2846,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)],[297]) ).

thf(1018,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
      | ( A @ ( A @ ( B @ ( C @ sk6 ) ) @ m1_subset_1 ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
      | ~ ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( A @ ( B @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[1016]) ).

thf(40639,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( sk297 @ sk18 @ v1_funct_1 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,33118]) ).

thf(40640,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( sk297 @ sk18 @ v1_funct_1 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[40639]) ).

thf(40641,plain,
    ( ( sk297 @ sk18 @ v1_funct_1 )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[40640:[bind(A,$thf( sk1 ))]]) ).

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 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( ( C = E )
                          & ( B = D ) )
                       => ( ( ( C @ ( B @ ( A @ k3_lattices ) ) )
                            = ( E @ ( D @ ( A @ k1_lattice2 @ k4_lattices ) ) ) )
                          & ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                            = ( E @ ( D @ ( A @ k1_lattice2 @ k3_lattices ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_lattice2) ).

thf(5807,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[889]) ).

thf(932,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_2 ) )
        <=> ( A @ ( B @ m1_filter_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_filter_2) ).

thf(6008,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)],[932]) ).

thf(304,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).

thf(2899,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)],[304]) ).

thf(647,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                    & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                        & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ! [F: $i] :
                          ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
                            & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
                            & ( F @ v1_funct_1 ) )
                         => ( ( ( D @ ( C @ ( A @ r1_lattice2 ) ) )
                              & ( F
                                = ( B @ ( D @ k1_realset1 ) ) )
                              & ( E
                                = ( B @ ( C @ k1_realset1 ) ) ) )
                           => ( F @ ( E @ ( B @ r1_lattice2 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_filter_2) ).

thf(4722,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)],[647]) ).

thf(547,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
         => ! [D: $i] :
              ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
             => ( ! [E: $i] :
                    ( ( A @ ( E @ m1_subset_1 ) )
                   => ( ( B @ ( E @ r2_hidden ) )
                    <=> ( ~ ( D @ ( E @ r2_hidden ) )
                        & ( C @ ( E @ r2_hidden ) ) ) ) )
               => ( B
                  = ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_subset_1) ).

thf(4168,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)],[547]) ).

thf(956,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v1_lattice2 )
      <=> ( ( A @ v13_lattices )
          & ( A @ v3_filter_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_lattice2) ).

thf(6132,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)],[956]) ).

thf(928,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k2_filter_0 ) )
            = ( B @ ( A @ a_2_0_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_filter_0) ).

thf(5991,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)],[928]) ).

thf(420,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( B @ ( F @ m1_subset_1 ) )
                           => ( ( C @ ( F @ r2_hidden ) )
                             => ( F @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) )
                       => ( ( E @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) )
                          | ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_lattice2) ).

thf(3571,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)],[420]) ).

thf(566,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l2_lattices )
        & ( A @ v4_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k3_lattices ) ) )
        = ( C @ ( B @ ( A @ k1_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_lattices) ).

thf(4255,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)],[566]) ).

thf(282,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ? [C: $i] :
          ( ! [D: $i] :
              ( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
             => ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
          & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
          & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
          & ( C @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_realset1) ).

thf(2715,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)],[282]) ).

thf(971,plain,
    sk1 @ ( sk2 @ ( sk1 @ u1_struct_0 @ k6_domain_1 ) @ m2_filter_2 ),
    inference(cnfConj,[status(thm)],[969]) ).

thf(31852,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ ( B @ k1_funct_2 ) ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,15329]) ).

thf(31853,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ ( B @ k1_funct_2 ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[31852]) ).

thf(31854,plain,
    ! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ sk18 @ v1_funct_1 ),
    inference(pattern_uni,[status(thm)],[31853:[bind(A,$thf( D @ ( D @ k1_funct_2 ) )),bind(B,$thf( D ))]]) ).

thf(33666,plain,
    ! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ sk18 @ v1_funct_1 ),
    inference(simp,[status(thm)],[31854]) ).

thf(5941,plain,
    ( ( k13_nat_lat @ l3_lattices )
    & ( k13_nat_lat @ v10_lattices )
    & ~ ( k13_nat_lat @ v3_struct_0 ) ),
    inference(cnf,[status(esa)],[5940]) ).

thf(5944,plain,
    k13_nat_lat @ l3_lattices,
    inference(cnfConj,[status(thm)],[5941]) ).

thf(30122,plain,
    ! [A: $i] :
      ( ( A != sk196 )
      | ( k1_xboole_0 @ v15_lattices )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,2985]) ).

thf(30123,plain,
    ( ( k1_xboole_0 @ v15_lattices )
    | ( sk196 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[30122:[bind(A,$thf( sk196 ))]]) ).

thf(7754,plain,
    ( ( ( sk341 @ v1_xboole_0 )
     != ( k1_xboole_0 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3050,4839]) ).

thf(7755,plain,
    ( ( sk341 @ v1_xboole_0 )
   != ( k1_xboole_0 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[7754]) ).

thf(7772,plain,
    sk341 != k1_xboole_0,
    inference(simp,[status(thm)],[7755]) ).

thf(33068,plain,
    ! [A: $i] :
      ( ( A != sk341 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,7772]) ).

thf(33069,plain,
    ! [A: $i] :
      ( ( A != sk341 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[33068]) ).

thf(33070,plain,
    sk341 @ sk18 @ v1_funct_1,
    inference(pattern_uni,[status(thm)],[33069:[bind(A,$thf( sk341 ))]]) ).

thf(606,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_4_domain_1 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ( ( ( D @ ( E @ r2_hidden ) )
                & ~ ( C @ ( E @ r2_hidden ) ) )
              | ( ~ ( D @ ( E @ r2_hidden ) )
                & ( C @ ( E @ r2_hidden ) ) ) )
            & ( A = E )
            & ( B @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_4_domain_1) ).

thf(4469,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)],[606]) ).

thf(2882,plain,
    sk187 @ v9_lattices,
    inference(cnfConj,[status(thm)],[2869]) ).

thf(38082,plain,
    ( ( ( sk187 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[2881,31369]) ).

thf(38083,plain,
    ( ( ( sk187 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[38082]) ).

thf(38091,plain,
    ( ( sk187 != k1_xboole_0 )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[38083]) ).

thf(27136,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk216 @ k2_relat_1 @ ( A @ ( sk216 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[27092,1030]) ).

thf(27137,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk216 @ k2_relat_1 @ ( A @ ( sk216 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[27136]) ).

thf(27138,plain,
    ! [B: $i,A: $i] : ( sk216 @ k2_relat_1 @ ( A @ ( B @ ( sk216 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[27137:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk216 @ k9_relat_1 ) )),bind(C,$thf( sk216 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(27152,plain,
    ! [B: $i,A: $i] : ( sk216 @ k2_relat_1 @ ( A @ ( B @ ( sk216 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[27138]) ).

thf(801,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k7_lattices ) )
                = ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_lattices) ).

thf(5452,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)],[801]) ).

thf(122,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) )
         => ( ( C @ ( B @ ( A @ r4_binop_1 ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ! [E: $i] :
                    ( ( A @ ( E @ m1_subset_1 ) )
                   => ! [F: $i] :
                        ( ( A @ ( F @ m1_subset_1 ) )
                       => ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
                          = ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_binop_1) ).

thf(1748,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(32356,plain,
    ! [A: $i] :
      ( ( A != sk197 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,16024]) ).

thf(32357,plain,
    ! [A: $i] :
      ( ( A != sk197 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[32356]) ).

thf(32358,plain,
    ( ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ( sk197 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[32357:[bind(A,$thf( sk197 ))]]) ).

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/sandbox/benchmark/theBenchmark.p',rc1_funct_2) ).

thf(2294,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(2295,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( A @ ( B @ sk111 ) @ v1_funct_2 ) ) )
      & ( A @ ( B @ sk111 ) @ v1_funct_1 )
      & ( A @ ( B @ sk111 ) @ v1_relat_1 )
      & ( B @ ( A @ ( A @ ( B @ sk111 ) @ m1_relset_1 ) ) ) ),
    inference(cnf,[status(esa)],[2294]) ).

thf(2298,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ sk111 ) @ v1_funct_1 ),
    inference(cnfConj,[status(thm)],[2295]) ).

thf(946,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) )
                    = ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lattices) ).

thf(6069,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)],[946]) ).

thf(390,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
        = ( k1_xboole_0 @ k1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t176_partfun1) ).

thf(3391,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)],[390]) ).

thf(6348,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk138 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2471,999]) ).

thf(6349,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk138 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[6348]) ).

thf(6350,plain,
    ! [A: $i] : ( sk138 @ k1_relat_1 @ ( sk138 @ k9_relat_1 ) @ ( A @ ( sk138 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[6349:[bind(A,$thf( A )),bind(B,$thf( sk138 ))]]) ).

thf(21193,plain,
    ! [A: $i] : ( sk138 @ k2_relat_1 @ ( A @ ( sk138 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(rewrite,[status(thm)],[6350,15487]) ).

thf(4360,plain,
    sk297 @ v3_lattices,
    inference(cnfConj,[status(thm)],[4356]) ).

thf(16039,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( sk197 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,7375]) ).

thf(16040,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( sk197 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16039]) ).

thf(16232,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk71 != k1_xboole_0 )
      | ( sk197 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16040]) ).

thf(16298,plain,
    ( ( sk71 != k1_xboole_0 )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16232]) ).

thf(761,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_filter_0) ).

thf(5250,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)],[761]) ).

thf(3112,plain,
    k6_nat_lat @ v5_lattices,
    inference(cnfConj,[status(thm)],[3103]) ).

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

thf(2375,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(8150,plain,
    ( ( ( sk157 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2672,7813]) ).

thf(8151,plain,
    ( ( ( sk157 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8150]) ).

thf(8157,plain,
    ( ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ m2_relset_1 ) ) ) ),
    inference(simp,[status(thm)],[8151]) ).

thf(16031,plain,
    ( ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[8157,2222]) ).

thf(16032,plain,
    ( ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16031]) ).

thf(690,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( C @ u1_struct_0 @ ( A @ ( E @ m2_relset_1 ) ) )
                        & ( C @ u1_struct_0 @ ( A @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( A @ ( F @ m1_subset_1 ) )
                           => ( ( B @ ( F @ r2_hidden ) )
                             => ( F @ ( E @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( C @ u1_struct_0 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r3_lattices ) ) ) ) )
                       => ( E @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( C @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_lattice2) ).

thf(4939,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)],[690]) ).

thf(4366,plain,
    sk297 @ v15_lattices,
    inference(cnfConj,[status(thm)],[4356]) ).

thf(812,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m2_filter_2 ) )
         => ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_filter_2) ).

thf(5499,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)],[812]) ).

thf(878,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_nat_lat ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k24_filter_2 ) )
        = ( B @ k1_lattice2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k24_filter_2) ).

thf(5748,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)],[878]) ).

thf(111,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( ( A @ ( B @ v1_binop_1 ) )
      <=> ! [C: $i] :
            ( ( A @ ( C @ m1_subset_1 ) )
           => ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
                  = ( C @ ( D @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_binop_1) ).

thf(1647,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(346,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ( A @ k1_zfmisc_1 @ ( B @ ( A @ k3_subset_1 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).

thf(3129,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)],[346]) ).

thf(29940,plain,
    ! [A: $i] :
      ( ( A != sk157 )
      | ( k1_xboole_0 @ v5_lattices )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,2671]) ).

thf(29941,plain,
    ( ( k1_xboole_0 @ v5_lattices )
    | ( sk157 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[29940:[bind(A,$thf( sk157 ))]]) ).

thf(2407,plain,
    k13_nat_lat @ v9_lattices,
    inference(cnfConj,[status(thm)],[2398]) ).

thf(681,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
                & ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ! [E: $i] :
                        ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                       => ( ( ( E @ ( D @ ( A @ k4_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
                            = ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_lattices ) ) ) )
                          & ( ( E @ ( D @ ( A @ k3_lattices ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
                            = ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k3_lattices ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattice4) ).

thf(4894,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)],[681]) ).

thf(298,axiom,
    ! [A: $i] :
      ( ( A @ v1_funct_1 )
    <=> ! [B: $i,C: $i,D: $i] :
          ( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
            & ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
         => ( C = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_1) ).

thf(2850,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)],[298]) ).

thf(2160,plain,
    sk94 @ v10_lattices,
    inference(cnfConj,[status(thm)],[2154]) ).

thf(627,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v8_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( B @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r1_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_lattices) ).

thf(4593,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)],[627]) ).

thf(2888,plain,
    sk188 @ v7_lattices,
    inference(cnfConj,[status(thm)],[2884]) ).

thf(1186,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ r1_tarski ) )
      | ~ ( C @ v2_funct_1 )
      | ~ ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
      | ~ ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( C @ v1_relat_1 ) ),
    inference(cnf,[status(esa)],[1185]) ).

thf(1038,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)],[1032]) ).

thf(16102,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,8677]) ).

thf(16103,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16102]) ).

thf(16217,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk295 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[16103]) ).

thf(16281,plain,
    ( ( sk295 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[16217]) ).

thf(915,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k2_filter_0 ) @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_filter_0) ).

thf(5948,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)],[915]) ).

thf(655,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ( A @ ( I @ m1_subset_1 ) )
        & ( A @ ( H @ m1_subset_1 ) )
        & ( A @ ( G @ m1_subset_1 ) )
        & ( A @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( A @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_domain_1) ).

thf(4781,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)],[655]) ).

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/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).

thf(2656,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(918,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( B @ ( D @ ( A @ k4_lattices ) ) @ ( D @ ( C @ ( A @ k4_lattices ) ) @ ( C @ ( B @ ( A @ k4_lattices ) ) @ ( A @ k3_lattices ) ) @ ( A @ k3_lattices ) ) )
                      = ( B @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( C @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) )
       => ( A @ v11_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_lattices) ).

thf(5955,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[918]) ).

thf(596,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v17_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v16_lattices )
          & ( A @ v15_lattices )
          & ( A @ v14_lattices )
          & ( A @ v13_lattices )
          & ( A @ v11_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_lattices) ).

thf(4409,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)],[596]) ).

thf(367,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ ( D @ m1_subset_1 ) )
                   => ( ( B @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                      = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_binop_1) ).

thf(3246,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)],[367]) ).

thf(3636,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)],[3635]) ).

thf(3637,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)],[3636]) ).

thf(3638,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ r1_tarski ) )
      | ( A != B ) ),
    inference(cnfConj,[status(thm)],[3637]) ).

thf(3641,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ r1_tarski ) )
      | ( A != B ) ),
    inference(lifteq,[status(thm)],[3638]) ).

thf(3642,plain,
    ! [A: $i] : ( A @ ( A @ r1_tarski ) ),
    inference(simp,[status(thm)],[3641]) ).

thf(586,axiom,
    ! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(4346,plain,
    ! [A: $i] : ( A @ ( A @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(593,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
                & ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( B @ ( A @ ( C @ v1_lattice4 ) ) )
              <=> ( C @ v2_funct_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice4) ).

thf(4398,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)],[593]) ).

thf(562,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( B @ ( A @ k1_lattices ) ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_lattices) ).

thf(4240,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)],[562]) ).

thf(529,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( B @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ( ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) )
                    = ( D @ ( C @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice2) ).

thf(4092,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)],[529]) ).

thf(795,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ ( B @ m2_lattice4 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( A @ ( B @ m2_filter_2 ) )
          <=> ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( ( B @ ( D @ r2_hidden ) )
                        & ( B @ ( C @ r2_hidden ) ) )
                    <=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_filter_2) ).

thf(5418,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)],[795]) ).

thf(805,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ u1_struct_0 @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_filter_0) ).

thf(5467,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)],[805]) ).

thf(16043,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,6900]) ).

thf(16044,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16043]) ).

thf(16229,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk71 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ v13_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16044]) ).

thf(16295,plain,
    ( ( sk71 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ v13_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16229]) ).

thf(65,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ( A @ v2_funct_1 )
       => ( ( A @ k2_funct_1 @ k2_funct_1 )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funct_1) ).

thf(1300,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(85,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_subset_1 ) )
         => ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
          <=> ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ( ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
                    = D )
                  & ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
                    = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_binop_1) ).

thf(1452,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(465,axiom,
    ! [A: $i] :
      ( ( A @ l2_struct_0 )
     => ( ( A @ v2_struct_0 )
       => ( A
          = ( A @ u2_struct_0 @ ( A @ u1_struct_0 @ g2_struct_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v2_struct_0) ).

thf(3791,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)],[465]) ).

thf(828,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ r1_lattice2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_lattice2) ).

thf(5555,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)],[828]) ).

thf(141,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ v1_funct_1 )
        & ( C @ v1_relat_1 ) )
     => ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
      <=> ( ( B
            = ( A @ ( C @ k1_funct_1 ) ) )
          & ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).

thf(1869,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(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/sandbox/benchmark/theBenchmark.p',dt_k4_filter_2) ).

thf(3475,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(651,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( A @ ( G @ m1_subset_1 ) )
        & ( A @ ( F @ m1_subset_1 ) )
        & ( A @ ( E @ m1_subset_1 ) )
        & ( A @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_domain_1 ) ) ) ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_domain_1) ).

thf(4768,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)],[651]) ).

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/sandbox/benchmark/theBenchmark.p',commutativity_k7_domain_1) ).

thf(2276,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(207,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ v1_relat_1 )
     => ( ( B @ ( A @ r1_tarski ) )
       => ( A @ v1_relat_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_relat_1) ).

thf(2219,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)],[207]) ).

thf(769,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_filter_2 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k16_filter_2 ) )
        = ( B @ ( A @ k8_filter_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k16_filter_2) ).

thf(5309,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)],[769]) ).

thf(460,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
       => ( B @ ( C @ ( A @ r1_filter_2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_filter_2) ).

thf(3774,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)],[460]) ).

thf(125,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ v1_relat_1 )
        & ( A @ v1_relat_1 ) )
     => ( B @ ( A @ k4_xboole_0 ) @ v1_relat_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).

thf(1763,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(417,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ( ( ( A @ u1_lattices @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) )
              = ( B @ u1_lattices @ ( B @ u2_lattices @ ( B @ u1_struct_0 @ g3_lattices ) ) ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ! [E: $i] :
                        ( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                       => ! [F: $i] :
                            ( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                           => ( ( ( D = F )
                                & ( C = E ) )
                             => ( ( ( F @ ( E @ ( B @ r1_lattices ) ) )
                                 => ( D @ ( C @ ( A @ r1_lattices ) ) ) )
                                & ( ( D @ ( C @ ( A @ r1_lattices ) ) )
                                 => ( F @ ( E @ ( B @ r1_lattices ) ) ) )
                                & ( ( D @ ( C @ ( A @ k2_lattices ) ) )
                                  = ( F @ ( E @ ( B @ k2_lattices ) ) ) )
                                & ( ( D @ ( C @ ( A @ k1_lattices ) ) )
                                  = ( F @ ( E @ ( B @ k1_lattices ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_filter_2) ).

thf(3544,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)],[417]) ).

thf(825,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m2_filter_2 ) )
                 => ( ( D @ ( B @ r2_hidden ) )
                   => ( ( D @ ( B @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) )
                      & ( D @ ( C @ ( B @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_filter_2) ).

thf(5543,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[825]) ).

thf(113,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( ( A @ ( B @ v2_binop_1 ) )
      <=> ! [C: $i] :
            ( ( A @ ( C @ m1_subset_1 ) )
           => ! [D: $i] :
                ( ( A @ ( D @ m1_subset_1 ) )
               => ! [E: $i] :
                    ( ( A @ ( E @ m1_subset_1 ) )
                   => ( ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ k1_binop_1 ) ) )
                      = ( E @ ( D @ ( C @ ( B @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_binop_1) ).

thf(1658,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(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/sandbox/benchmark/theBenchmark.p',t49_funct_2) ).

thf(2322,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(663,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v9_lattices )
        & ( A @ v8_lattices )
        & ( A @ v7_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( C @ ( B @ ( A @ r1_lattices ) ) )
                   => ( D @ ( C @ ( A @ k2_lattices ) ) @ ( D @ ( B @ ( A @ k2_lattices ) ) @ ( A @ r1_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_lattices) ).

thf(4800,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)],[663]) ).

thf(8630,plain,
    ( ( ( sk341 @ v1_xboole_0 )
     != ( sk278 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4083,4839]) ).

thf(8631,plain,
    ( ( sk341 @ v1_xboole_0 )
   != ( sk278 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8630]) ).

thf(8644,plain,
    sk341 != sk278,
    inference(simp,[status(thm)],[8631]) ).

thf(699,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                = ( C @ ( B @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattices) ).

thf(4982,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)],[699]) ).

thf(394,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v7_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( D @ ( C @ ( A @ k2_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
                      = ( D @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k2_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_lattices) ).

thf(3412,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)],[394]) ).

thf(849,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( B @ ( A @ ( E @ m1_lattice4 ) ) )
                     => ( ( D @ ( C @ ( A @ r3_lattices ) ) )
                       => ( D @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_lattice4) ).

thf(5638,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)],[849]) ).

thf(101,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ v1_xboole_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
         => ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
              & ( C @ v1_funct_1 ) )
           => ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
              & ( B @ ( A @ ( C @ v1_partfun1 ) ) )
              & ~ ( C @ v1_xboole_0 )
              & ( C @ v1_funct_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_funct_2) ).

thf(1579,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(727,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r1_lattices ) ) )
              <=> ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                  = C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattices) ).

thf(5106,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)],[727]) ).

thf(16148,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( sk187 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,6956]) ).

thf(16149,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
      | ( sk187 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16148]) ).

thf(16249,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk71 != k1_xboole_0 )
      | ( sk187 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16149]) ).

thf(16318,plain,
    ( ( sk71 != k1_xboole_0 )
    | ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16249]) ).

thf(695,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) )
      <=> ? [E: $i] :
            ( ~ ( ( C @ ( E @ r2_hidden ) )
              <=> ( D @ ( E @ r2_hidden ) ) )
            & ( A = E )
            & ( B @ ( E @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_7_domain_1) ).

thf(4959,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)],[695]) ).

thf(697,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ( A @ v5_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( ( D @ ( C @ ( A @ r1_lattices ) ) )
                      & ( C @ ( B @ ( A @ r1_lattices ) ) ) )
                   => ( D @ ( B @ ( A @ r1_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_lattices) ).

thf(4976,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)],[697]) ).

thf(599,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( C @ ( F @ m1_subset_1 ) )
                           => ( ( D @ ( F @ r2_hidden ) )
                             => ( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) )
                                = B ) ) )
                       => ( ( ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) )
                            = B )
                          | ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_lattice2) ).

thf(4431,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ! [F: $i] :
                            ( ( C @ ( F @ m1_subset_1 ) )
                           => ( ( D @ ( F @ r2_hidden ) )
                             => ( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) )
                                = B ) ) )
                       => ( ( ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) )
                            = B )
                          | ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(3007,plain,
    sk197 @ v1_lattice2,
    inference(cnfConj,[status(thm)],[2999]) ).

thf(2675,plain,
    sk157 @ v14_lattices,
    inference(cnfConj,[status(thm)],[2661]) ).

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

thf(2056,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(3196,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
    inference(cnf,[status(esa)],[3195]) ).

thf(23256,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ),
    inference(rewrite,[status(thm)],[3196,2476]) ).

thf(7854,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)],[3098,999]) ).

thf(7855,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)],[7854]) ).

thf(7856,plain,
    ! [A: $i] : ( k1_xboole_0 @ k1_relat_1 @ ( k1_xboole_0 @ k9_relat_1 ) @ ( A @ ( k1_xboole_0 @ k9_relat_1 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[7855:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).

thf(26757,plain,
    k1_xboole_0 @ ( k1_xboole_0 @ r1_tarski ),
    inference(rewrite,[status(thm)],[7856,3053]) ).

thf(664,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                    & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
                        & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ! [F: $i] :
                          ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
                            & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
                            & ( F @ v1_funct_1 ) )
                         => ( ( ( D @ ( C @ ( A @ r6_binop_1 ) ) )
                              & ( F
                                = ( B @ ( D @ k1_realset1 ) ) )
                              & ( E
                                = ( B @ ( C @ k1_realset1 ) ) ) )
                           => ( F @ ( E @ ( B @ r6_binop_1 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_filter_2) ).

thf(4802,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)],[664]) ).

thf(3107,plain,
    k6_nat_lat @ v8_lattices,
    inference(cnfConj,[status(thm)],[3103]) ).

thf(904,axiom,
    ! [A: $i] :
      ( ( A @ l2_struct_0 )
     => ( A @ u1_struct_0 @ ( A @ u2_struct_0 @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_struct_0) ).

thf(5902,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)],[904]) ).

thf(50592,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk138 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2471,1179]) ).

thf(50593,plain,
    ! [B: $i,A: $i] :
      ( ( ( sk138 @ v1_relat_1 )
       != ( B @ v1_relat_1 ) )
      | ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[50592]) ).

thf(50594,plain,
    ! [A: $i] : ( A @ ( sk138 @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[50593:[bind(A,$thf( A )),bind(B,$thf( sk138 ))]]) ).

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

thf(1257,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(27216,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk218 @ k2_relat_1 @ ( A @ ( sk218 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[27172,1030]) ).

thf(27217,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk218 @ k2_relat_1 @ ( A @ ( sk218 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[27216]) ).

thf(27218,plain,
    ! [B: $i,A: $i] : ( sk218 @ k2_relat_1 @ ( A @ ( B @ ( sk218 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[27217:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk218 @ k9_relat_1 ) )),bind(C,$thf( sk218 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(27238,plain,
    ! [B: $i,A: $i] : ( sk218 @ k2_relat_1 @ ( A @ ( B @ ( sk218 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[27218]) ).

thf(874,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k8_filter_0 ) @ l3_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v10_lattices )
        & ~ ( B @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_filter_0) ).

thf(5736,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)],[874]) ).

thf(752,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k3_lattice4 ) @ m3_lattice4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_lattice4) ).

thf(5223,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)],[752]) ).

thf(2992,plain,
    sk196 @ v7_lattices,
    inference(cnfConj,[status(thm)],[2983]) ).

thf(13584,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)],[1902,2109]) ).

thf(13585,plain,
    k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ m1_subset_1 ),
    inference(pattern_uni,[status(thm)],[13584:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(384,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ v1_relat_1 )
     => ( B @ k2_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).

thf(3356,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)],[384]) ).

thf(842,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( B @ ( A @ k11_filter_2 ) @ m2_lattice4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_filter_2) ).

thf(5613,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)],[842]) ).

thf(756,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_filter_0) ).

thf(5240,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)],[756]) ).

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/sandbox/benchmark/theBenchmark.p',t117_zfmisc_1) ).

thf(2279,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(159,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( B @ ( A @ a_2_3_domain_1 ) @ m1_subset_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_domain_1) ).

thf(1955,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(296,axiom,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).

thf(2843,plain,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( A @ r1_tarski ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(92,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ( A @ k2_funct_1 @ v1_funct_1 )
        & ( A @ k2_funct_1 @ v1_relat_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).

thf(1485,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(1052,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(cnf,[status(esa)],[1051]) ).

thf(102,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ? [C: $i] : ( B @ ( A @ ( C @ m1_realset1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_realset1) ).

thf(1585,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(1093,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)],[1092]) ).

thf(1094,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)],[1093]) ).

thf(643,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
     => ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_funct_2) ).

thf(4695,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)],[643]) ).

thf(327,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v11_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v12_lattices )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_lattices) ).

thf(3024,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)],[327]) ).

thf(12939,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ sk249 @ v1_xboole_0 )
       != ( B @ k1_tarski @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3676,4906]) ).

thf(12940,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk249 @ v1_xboole_0 )
     != ( B @ k1_tarski @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[12939]) ).

thf(12952,plain,
    ! [B: $i,A: $i] :
      ( ( A @ sk249 )
     != ( B @ k1_tarski ) ),
    inference(simp,[status(thm)],[12940]) ).

thf(779,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k5_lattices )
        = ( A @ u2_lattices @ ( A @ u1_struct_0 @ k3_binop_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_lattice2) ).

thf(5364,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)],[779]) ).

thf(1008,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( B @ ( C @ ( D @ ( E @ sk5 ) ) ) ) @ r2_hidden ) )
      | ~ ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) )
      | ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
      | ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
      | ~ ( D @ v1_funct_1 ) ),
    inference(cnfConj,[status(thm)],[1006]) ).

thf(3943,plain,
    ! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
    inference(cnf,[status(esa)],[3942]) ).

thf(585,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != D )
        & ( A != C )
        & ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_zfmisc_1) ).

thf(4342,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)],[585]) ).

thf(312,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( B @ v2_funct_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_partfun1) ).

thf(2939,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)],[312]) ).

thf(2892,plain,
    sk188 @ v10_lattices,
    inference(cnfConj,[status(thm)],[2884]) ).

thf(14745,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk393 @ 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)],[5329,1080]) ).

thf(14746,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( sk393 @ 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)],[14745]) ).

thf(14747,plain,
    ( ( f2_s11_funct_2 @ ( sk393 @ k2_relat_1 @ r1_tarski ) )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(pattern_uni,[status(thm)],[14746:[bind(A,$thf( f1_s11_funct_2 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( sk393 ))]]) ).

thf(661,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ u1_struct_0 @ ( A @ ( D @ m1_relset_1 ) ) )
        & ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 )
        & ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_lattice2) ).

thf(4795,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)],[661]) ).

thf(351,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ? [C: $i] :
          ( ! [D: $i] :
              ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
             => ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
          & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
          & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
          & ( C @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_realset1) ).

thf(3156,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)],[351]) ).

thf(491,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v11_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_lattice2) ).

thf(3914,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)],[491]) ).

thf(29944,plain,
    ! [A: $i] :
      ( ( A != sk197 )
      | ( k1_xboole_0 @ v3_lattices )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,3012]) ).

thf(29945,plain,
    ( ( k1_xboole_0 @ v3_lattices )
    | ( sk197 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[29944:[bind(A,$thf( sk197 ))]]) ).

thf(4669,plain,
    ! [A: $i] :
      ( ( ( ( A @ ( sk328 @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
          = ( A @ f3_s13_funct_2 ) )
        | ~ ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
        | ~ sk326 )
      & ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk328 @ m2_relset_1 ) ) )
        | ~ sk326 )
      & ( ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( sk328 @ v1_funct_2 ) ) )
        | ~ sk326 )
      & ( ( sk328 @ v1_funct_1 )
        | ~ sk326 )
      & ( sk326
        | ~ ( f2_s13_funct_2 @ ( sk327 @ f3_s13_funct_2 @ m1_subset_1 ) ) )
      & ( sk326
        | ( f1_s13_funct_2 @ ( sk327 @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[4668]) ).

thf(4671,plain,
    ( sk326
    | ( f1_s13_funct_2 @ ( sk327 @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[4669]) ).

thf(533,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( A @ ( C @ r2_hidden ) )
        <=> ( B @ ( C @ r2_hidden ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).

thf(4111,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)],[533]) ).

thf(439,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
     => ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_subset_1) ).

thf(3684,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)],[439]) ).

thf(572,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l2_lattices )
        & ( A @ v4_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k3_lattices ) ) )
        = ( B @ ( C @ ( A @ k3_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_lattices) ).

thf(4278,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)],[572]) ).

thf(924,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( A @ ( E @ m1_filter_0 ) )
                     => ( ( ( E @ ( D @ ( C @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
                          & ( E @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) )
                       => ( E @ ( D @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_filter_0) ).

thf(5981,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)],[924]) ).

thf(32414,plain,
    ! [A: $i] :
      ( ( A != sk157 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,16032]) ).

thf(32415,plain,
    ! [A: $i] :
      ( ( A != sk157 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[32414]) ).

thf(32416,plain,
    ( ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ( sk157 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[32415:[bind(A,$thf( sk157 ))]]) ).

thf(423,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
     => ( ( B @ ( A @ k2_tarski ) )
        = ( C @ k1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_zfmisc_1) ).

thf(3589,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)],[423]) ).

thf(652,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k2_lattice4 ) )
                = ( C @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_lattice4) ).

thf(4770,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)],[652]) ).

thf(2885,plain,
    sk188 @ v4_lattices,
    inference(cnfConj,[status(thm)],[2884]) ).

thf(38084,plain,
    ( ( ( sk157 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ~ $true
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[2672,31369]) ).

thf(38085,plain,
    ( ( ( sk157 @ v13_lattices )
     != ( k1_xboole_0 @ v13_lattices ) )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[38084]) ).

thf(38094,plain,
    ( ( sk157 != k1_xboole_0 )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[38085]) ).

thf(920,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ? [B: $i] : ( A @ ( B @ m2_lattice4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_lattice4) ).

thf(5966,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)],[920]) ).

thf(2347,plain,
    sk118 @ v7_lattices,
    inference(cnfConj,[status(thm)],[2342]) ).

thf(654,axiom,
    ? [A: $i] : ( A @ l2_struct_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_struct_0) ).

thf(4779,plain,
    ? [A: $i] : ( A @ l2_struct_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(4780,plain,
    sk337 @ l2_struct_0,
    inference(cnf,[status(esa)],[4779]) ).

thf(452,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
              <=> ( ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k4_lattices ) ) )
                  = ( A @ k5_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_filter_0) ).

thf(3725,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)],[452]) ).

thf(717,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ? [C: $i] :
              ( ( B @ ( C @ r2_hidden ) )
              & ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_filter_0) ).

thf(5068,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)],[717]) ).

thf(14771,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( sk295 @ 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)],[14759,1044]) ).

thf(14772,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s4_funct_2 @ ( sk295 @ 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)],[14771]) ).

thf(14773,plain,
    ! [A: $i] : ( sk295 @ k2_relat_1 @ ( A @ k4_xboole_0 ) @ ( f2_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[14772:[bind(A,$thf( sk295 @ k2_relat_1 )),bind(B,$thf( f2_s4_funct_2 )),bind(C,$thf( C ))]]) ).

thf(14791,plain,
    ! [A: $i] : ( sk295 @ k2_relat_1 @ ( A @ k4_xboole_0 ) @ ( f2_s4_funct_2 @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[14773]) ).

thf(300,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
        & ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
        & ( F @ v1_funct_1 ) )
     => ( ( ( B @ ( E @ r2_hidden ) )
          & ( A @ ( D @ r2_hidden ) ) )
       => ( ( C @ ( E @ ( D @ k4_tarski ) @ ( F @ k1_funct_1 ) @ r2_hidden ) )
          | ( C = k1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_funct_2) ).

thf(2865,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)],[300]) ).

thf(2875,plain,
    sk187 @ v15_lattices,
    inference(cnfConj,[status(thm)],[2869]) ).

thf(18084,plain,
    ! [B: $i,A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( B @ k1_zfmisc_1 ) )
      | ( ( A @ sk249 )
       != ( k1_xboole_0 @ k1_tarski ) ) ),
    inference(paramod_ordered,[status(thm)],[1902,12950]) ).

thf(18085,plain,
    ! [A: $i] :
      ( ( A @ sk249 )
     != ( k1_xboole_0 @ k1_tarski ) ),
    inference(pattern_uni,[status(thm)],[18084:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).

thf(4639,plain,
    sk322 @ l1_lattices,
    inference(cnf,[status(esa)],[4638]) ).

thf(373,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_partfun1 ) ) )
        & ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_binop_1 ) )
        & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_lattices @ v1_funct_2 ) ) )
        & ( A @ u1_lattices @ v1_funct_1 )
        & ( A @ u1_lattices @ v1_relat_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_lattice2) ).

thf(3284,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)],[373]) ).

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/sandbox/benchmark/theBenchmark.p',t175_partfun1) ).

thf(2626,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(4138,plain,
    sk282 @ l1_struct_0,
    inference(cnf,[status(esa)],[4137]) ).

thf(403,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k4_lattices ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattices) ).

thf(3457,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)],[403]) ).

thf(2352,plain,
    sk118 @ v6_lattices,
    inference(cnfConj,[status(thm)],[2342]) ).

thf(334,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
     => ( ( ( D @ ( B @ r1_tarski ) )
          & ( C @ ( A @ r1_tarski ) ) )
        | ( ( B @ ( A @ k2_zfmisc_1 ) )
          = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).

thf(3067,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)],[334]) ).

thf(2870,plain,
    sk187 @ v3_lattices,
    inference(cnfConj,[status(thm)],[2869]) ).

thf(546,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k1_lattices ) ) )
                = ( C @ ( B @ ( A @ u2_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattices) ).

thf(4165,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)],[546]) ).

thf(184,axiom,
    ! [A: $i] :
      ( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ m1_relset_1 ) ) )
     => ( ( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
          & ( A @ v1_funct_1 ) )
       => ( ( k1_xboole_0 @ ( A @ v2_binop_1 ) )
          & ( k1_xboole_0 @ ( A @ v1_binop_1 ) )
          & ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
          & ( A @ v1_xboole_0 )
          & ( A @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_binop_1) ).

thf(2078,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(691,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( B @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( B @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( ( C @ ( D @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) )
                          = ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k2_partfun1 ) ) ) ) )
                       => ( ( ( D @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) )
                            = ( E @ ( C @ ( A @ ( B @ k2_lattice2 ) ) ) ) )
                          | ( C = k1_xboole_0 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_lattice2) ).

thf(4944,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)],[691]) ).

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/sandbox/benchmark/theBenchmark.p',d14_binop_1) ).

thf(2310,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(136,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ! [E: $i] :
          ~ ( ! [F: $i] :
                ~ ( ( E
                    = ( F @ ( D @ k1_funct_1 ) ) )
                  & ( C @ ( F @ r2_hidden ) )
                  & ( A @ ( F @ r2_hidden ) ) )
            & ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_funct_2) ).

thf(1844,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(957,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( B @ ( A @ k4_lattice4 ) )
            = ( B @ ( A @ a_2_0_lattice4 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_lattice4) ).

thf(6137,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)],[957]) ).

thf(484,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ( ! [C: $i] :
            ( ( A @ ( C @ m1_subset_1 ) )
           => ( B @ ( C @ r2_hidden ) ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_subset_1) ).

thf(3874,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)],[484]) ).

thf(2997,plain,
    sk196 @ l3_lattices,
    inference(cnfConj,[status(thm)],[2983]) ).

thf(201,axiom,
    ! [A: $i] :
      ~ ( ! [B: $i] :
            ~ ( ! [C: $i,D: $i] :
                  ~ ( ( B
                      = ( D @ ( C @ k4_tarski ) ) )
                    & ( ( A @ ( D @ r2_hidden ) )
                      | ( A @ ( C @ r2_hidden ) ) ) )
              & ( A @ ( B @ r2_hidden ) ) )
        & ( A != k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_mcart_1) ).

thf(2187,plain,
    ! [A: $i] :
      ~ ( ! [B: $i] :
            ~ ( ! [C: $i,D: $i] :
                  ~ ( ( B
                      = ( D @ ( C @ k4_tarski ) ) )
                    & ( ( A @ ( D @ r2_hidden ) )
                      | ( A @ ( C @ r2_hidden ) ) ) )
              & ( A @ ( B @ r2_hidden ) ) )
        & ( A != k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(192,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
     => ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).

thf(2110,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(1009,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E
        = ( A @ ( B @ ( C @ ( D @ ( E @ sk5 ) ) ) ) @ ( D @ k1_funct_1 ) ) )
      | ~ ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) )
      | ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
      | ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
      | ~ ( D @ v1_funct_1 ) ),
    inference(cnfConj,[status(thm)],[1006]) ).

thf(1010,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) )
      | ~ ( B @ ( A @ ( D @ m2_relset_1 ) ) )
      | ~ ( B @ ( A @ ( D @ v1_funct_2 ) ) )
      | ~ ( D @ v1_funct_1 )
      | ( ( A @ ( B @ ( C @ ( D @ ( E @ sk5 ) ) ) ) @ ( D @ k1_funct_1 ) )
        = E ) ),
    inference(lifteq,[status(thm)],[1009]) ).

thf(12015,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,8677]) ).

thf(12016,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( k1_xboole_0 @ l3_lattices )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12015]) ).

thf(12145,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk295 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12016]) ).

thf(12226,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[12145]) ).

thf(5325,plain,
    ( ( sk393 @ v1_funct_1 )
    | ( f3_s11_funct_2 = f4_s11_funct_2 ) ),
    inference(cnfConj,[status(thm)],[5322]) ).

thf(5332,plain,
    ( ( sk393 @ v1_funct_1 )
    | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(lifteq,[status(thm)],[5325]) ).

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

thf(1866,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(496,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k11_filter_0 ) )
        = ( B @ ( A @ k10_filter_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k11_filter_0) ).

thf(3929,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)],[496]) ).

thf(649,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ( A @ ( B @ m1_filter_0 ) )
          <=> ( ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ! [D: $i] :
                      ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                     => ( ( ( D @ ( C @ ( A @ r3_lattices ) ) )
                          & ( B @ ( C @ r2_hidden ) ) )
                       => ( B @ ( D @ r2_hidden ) ) ) ) )
              & ! [C: $i] :
                  ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
                 => ! [D: $i] :
                      ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                     => ( ( ( B @ ( D @ r2_hidden ) )
                          & ( B @ ( C @ r2_hidden ) ) )
                       => ( B @ ( D @ ( C @ ( A @ k4_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_filter_0) ).

thf(4730,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)],[649]) ).

thf(622,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ u1_struct_0 @ ( A @ ( D @ m1_relset_1 ) ) )
        & ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 )
        & ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
        & ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ u1_struct_0 @ ( D @ ( C @ ( B @ ( A @ k2_lattice2 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattice2) ).

thf(4574,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)],[622]) ).

thf(40395,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( sk157 @ sk18 @ v1_funct_1 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,32846]) ).

thf(40396,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( sk157 @ sk18 @ v1_funct_1 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[40395]) ).

thf(40397,plain,
    ( ( sk157 @ sk18 @ v1_funct_1 )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[40396:[bind(A,$thf( sk1 ))]]) ).

thf(2167,plain,
    sk95 @ l2_struct_0,
    inference(cnfConj,[status(thm)],[2166]) ).

thf(4611,plain,
    ! [A: $i] :
      ( ( ( ( A @ ( sk320 @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
          = ( A @ f3_s12_funct_2 ) )
        | ~ ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
        | ~ sk318 )
      & ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk320 @ m2_relset_1 ) ) )
        | ~ sk318 )
      & ( ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( sk320 @ v1_funct_2 ) ) )
        | ~ sk318 )
      & ( ( sk320 @ v1_funct_1 )
        | ~ sk318 )
      & ( sk318
        | ~ ( f2_s12_funct_2 @ ( sk319 @ f3_s12_funct_2 @ r2_hidden ) ) )
      & ( sk318
        | ( f1_s12_funct_2 @ ( sk319 @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[4610]) ).

thf(4615,plain,
    ( sk318
    | ( f1_s12_funct_2 @ ( sk319 @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[4611]) ).

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/sandbox/benchmark/theBenchmark.p',d8_relat_2) ).

thf(2532,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(903,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k7_lattices ) )
                = ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_lattices) ).

thf(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 @ k3_lattices ) ) @ ( A @ k7_lattices ) )
                = ( C @ ( A @ k7_lattices ) @ ( B @ ( A @ k7_lattices ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

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 ) )
     => ( ( A @ ( C @ r2_hidden ) )
       => ( ( D @ k2_relat_1 @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
          | ( B = k1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_2) ).

thf(3235,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)],[364]) ).

thf(603,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( D @ ( C @ r2_hidden ) )
                       => ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( A @ ( B @ k3_lattice2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_lattice2) ).

thf(4451,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)],[603]) ).

thf(16072,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( sk157 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,7051]) ).

thf(16073,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( sk157 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16072]) ).

thf(16251,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk138 != k1_xboole_0 )
      | ( sk157 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16073]) ).

thf(16320,plain,
    ( ( sk138 != k1_xboole_0 )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16251]) ).

thf(490,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
                = ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_lattice4) ).

thf(3911,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)],[490]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ( ( A @ k3_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
        & ( A @ k3_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_relat_1) ).

thf(1253,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(2988,plain,
    sk196 @ v8_lattices,
    inference(cnfConj,[status(thm)],[2983]) ).

thf(481,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
     => ( ( ( D @ ( C @ r1_tarski ) )
          & ( B @ ( A @ r1_tarski ) ) )
       => ( D @ ( B @ ( E @ m2_relset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_relset_1) ).

thf(3864,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)],[481]) ).

thf(869,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( A @ u2_lattices @ v3_binop_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_lattice2) ).

thf(5724,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)],[869]) ).

thf(665,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( A @ ( D @ m1_subset_1 ) )
        & ( A @ ( C @ m1_subset_1 ) )
        & ( A @ ( B @ m1_subset_1 ) )
        & ~ ( A @ v1_xboole_0 ) )
     => ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_domain_1 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_domain_1) ).

thf(4806,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)],[665]) ).

thf(409,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ v1_xboole_0 )
       => ( ( A @ ( B @ m1_subset_1 ) )
        <=> ( B @ v1_xboole_0 ) ) )
      & ( ~ ( A @ v1_xboole_0 )
       => ( ( A @ ( B @ m1_subset_1 ) )
        <=> ( A @ ( B @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).

thf(3484,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)],[409]) ).

thf(115,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ v1_relat_1 )
     => ~ ( ! [C: $i] :
              ~ ( B @ k2_relat_1 @ ( C @ r2_hidden ) )
          & ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_relat_1) ).

thf(1674,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(447,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ m2_relset_1 ) ) )
                    & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ( ( D @ ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) )
                    = ( C @ ( D @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ u1_struct_0 @ k2_lattice2 ) ) ) @ ( A @ k3_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_lattice4) ).

thf(3709,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)],[447]) ).

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

thf(1903,plain,
    ! [A: $i,B: $i] :
      ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
         => ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ m2_relset_1 ) ) )
            & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ v1_funct_2 ) ) )
            & ( B @ ( C @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(4666,plain,
    sk325 @ l3_lattices,
    inference(cnfConj,[status(thm)],[4665]) ).

thf(2406,plain,
    k13_nat_lat @ v6_lattices,
    inference(cnfConj,[status(thm)],[2398]) ).

thf(528,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_tarski )
        = ( C @ ( B @ k2_tarski ) ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).

thf(4089,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_tarski )
        = ( C @ ( B @ k2_tarski ) ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(937,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( C @ ( B @ r1_tarski ) )
               => ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ k3_filter_0 ) @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_filter_0) ).

thf(6030,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)],[937]) ).

thf(362,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
    <=> ( ( D @ ( B @ r2_hidden ) )
        & ( C @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).

thf(3220,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)],[362]) ).

thf(518,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ~ ( B @ v1_xboole_0 )
         => ! [C: $i] :
              ( ( B @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( B @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( B @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ( D @ ( C @ r2_hidden ) )
                       => ( E @ ( D @ ( A @ ( B @ k2_lattice2 ) ) ) @ ( C @ ( E @ ( A @ u1_struct_0 @ ( B @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_lattice2) ).

thf(4042,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)],[518]) ).

thf(108,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
        & ( A @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_partfun1) ).

thf(1629,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(3104,plain,
    k6_nat_lat @ v9_lattices,
    inference(cnfConj,[status(thm)],[3103]) ).

thf(3003,plain,
    sk197 @ v5_lattices,
    inference(cnfConj,[status(thm)],[2999]) ).

thf(881,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
                & ~ ( C @ v1_xboole_0 ) )
             => ( ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
                  = ( C @ ( A @ k3_filter_0 ) @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) )
                & ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
                  = ( C @ ( B @ ( A @ k3_filter_0 ) @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_filter_0) ).

thf(5756,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)],[881]) ).

thf(380,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ v1_relat_1 )
     => ( ( B @ ( A @ r1_tarski ) )
       => ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_relat_1) ).

thf(3331,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)],[380]) ).

thf(12080,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,7374]) ).

thf(12081,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12080]) ).

thf(12113,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk138 )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12081]) ).

thf(39097,plain,
    ! [A: $i] :
      ( ( A != k6_nat_lat )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( sk1 @ sk18 @ v1_funct_1 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,31868]) ).

thf(39098,plain,
    ! [A: $i] :
      ( ( A != k6_nat_lat )
      | ( sk1 @ sk18 @ v1_funct_1 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[39097]) ).

thf(39099,plain,
    ( ( sk1 @ sk18 @ v1_funct_1 )
    | ( k6_nat_lat @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[39098:[bind(A,$thf( k6_nat_lat ))]]) ).

thf(814,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_filter_2 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ k1_lattice2 @ ( B @ ( A @ k15_filter_2 ) @ m1_filter_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_filter_2) ).

thf(5505,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)],[814]) ).

thf(434,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m2_relset_1 ) ) )
            & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ( ( B
              = ( A @ k5_lattice4 ) )
          <=> ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
                  = ( C @ ( A @ k7_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_lattice4) ).

thf(3662,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)],[434]) ).

thf(16150,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,8192]) ).

thf(16151,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16150]) ).

thf(16223,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk207 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[16151]) ).

thf(16288,plain,
    ( ( sk207 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[16223]) ).

thf(16141,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( sk297 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,9407]) ).

thf(16142,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( sk297 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16141]) ).

thf(16253,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk216 != k1_xboole_0 )
      | ( sk297 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16142]) ).

thf(16322,plain,
    ( ( sk216 != k1_xboole_0 )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16253]) ).

thf(767,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ v3_filter_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_filter_0) ).

thf(5304,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)],[767]) ).

thf(441,axiom,
    f1_s7_domain_1 @ k1_zfmisc_1 @ ( a_0_0_domain_1 @ m1_subset_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s7_domain_1) ).

thf(3694,plain,
    f1_s7_domain_1 @ k1_zfmisc_1 @ ( a_0_0_domain_1 @ m1_subset_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(742,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v13_lattices )
      <=> ? [B: $i] :
            ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( ( B @ ( C @ ( A @ k2_lattices ) ) )
                    = B )
                  & ( ( C @ ( B @ ( A @ k2_lattices ) ) )
                    = B ) ) )
            & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_lattices) ).

thf(5162,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)],[742]) ).

thf(45764,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)],[28608,1194]) ).

thf(45765,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)],[45764]) ).

thf(45796,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)],[45765]) ).

thf(45817,plain,
    ! [B: $i,A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != ( k1_xboole_0 @ k1_tarski @ ( B @ k4_xboole_0 ) ) ),
    inference(simp,[status(thm)],[45796]) ).

thf(411,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_struct_0 )
        & ~ ( A @ v3_struct_0 ) )
     => ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).

thf(3497,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)],[411]) ).

thf(414,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( C @ ( B @ a_2_1_domain_1 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i] :
            ( ( C @ ( D @ r2_hidden ) )
            & ( A = D )
            & ( B @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_domain_1) ).

thf(3529,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)],[414]) ).

thf(30083,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ sk80 ) )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,15299]) ).

thf(30084,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( B @ sk80 ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[30083]) ).

thf(30085,plain,
    ! [A: $i] : ( A @ sk80 @ sk18 @ v1_funct_1 ),
    inference(pattern_uni,[status(thm)],[30084:[bind(A,$thf( C @ sk80 )),bind(B,$thf( C ))]]) ).

thf(33449,plain,
    ! [A: $i] : ( A @ sk80 @ sk18 @ v1_funct_1 ),
    inference(simp,[status(thm)],[30085]) ).

thf(188,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
                = ( D @ ( B @ ( A @ k5_partfun1 ) ) ) )
              & ! [E: $i] :
                  ( B
                 != ( E @ k1_tarski ) ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t168_funct_2) ).

thf(2095,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(631,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
                & ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
              <=> ( ( C @ k2_relat_1 )
                  = ( B @ u1_struct_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice4) ).

thf(4619,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)],[631]) ).

thf(1159,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)],[1158]) ).

thf(1161,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)],[1159]) ).

thf(548,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( A @ ( D @ m1_subset_1 ) )
        & ( B @ ( A @ ( C @ m1_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 )
        & ~ ( A @ v1_xboole_0 ) )
     => ( B @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_funct_2) ).

thf(4182,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)],[548]) ).

thf(893,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ u1_struct_0 @ m3_lattice4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_lattice4) ).

thf(5828,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)],[893]) ).

thf(8364,plain,
    ! [A: $i] :
      ( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
       != ( sk216 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3244,3815]) ).

thf(8365,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8364]) ).

thf(8369,plain,
    ! [A: $i] :
      ( ( A @ k1_zfmisc_1 )
     != sk216 ),
    inference(simp,[status(thm)],[8365]) ).

thf(377,axiom,
    k1_xboole_0 @ v1_xboole_0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(3324,plain,
    k1_xboole_0 @ v1_xboole_0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(820,axiom,
    f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s8_domain_1) ).

thf(5532,plain,
    f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(579,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( A @ k2_lattice4 ) @ ( B @ ( A @ k2_lattice4 ) @ ( A @ k4_lattices ) ) )
                = ( C @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k2_lattice4 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_lattice4) ).

thf(4321,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)],[579]) ).

thf(2399,plain,
    k13_nat_lat @ v5_lattices,
    inference(cnfConj,[status(thm)],[2398]) ).

thf(478,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C
                  = ( B @ ( A @ k3_filter_0 ) ) )
              <=> ( ! [D: $i] :
                      ( ( A @ ( D @ m1_filter_0 ) )
                     => ( ( D @ ( B @ r1_tarski ) )
                       => ( D @ ( C @ r1_tarski ) ) ) )
                  & ( C @ ( B @ r1_tarski ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_filter_0) ).

thf(3844,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)],[478]) ).

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/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).

thf(2648,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(398,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( C @ r1_tarski ) )
                & ( C @ ( B @ ( A @ k5_filter_0 ) ) @ ( B @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_filter_0) ).

thf(3430,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)],[398]) ).

thf(129,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
        = ( B @ ( A @ k2_tarski ) ) )
    <=> ( ~ ( C @ ( B @ r2_hidden ) )
        & ~ ( C @ ( A @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).

thf(1777,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(791,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_filter_0 ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_filter_0) ).

thf(5409,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)],[791]) ).

thf(437,axiom,
    ! [A: $i] :
      ( ( A @ l1_struct_0 )
     => ( ( A @ v3_struct_0 )
      <=> ( A @ u1_struct_0 @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_struct_0) ).

thf(3677,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)],[437]) ).

thf(6273,plain,
    ( ( ( sk152 @ v1_xboole_0 )
     != ( sk14 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2587,1167]) ).

thf(6274,plain,
    ( ( sk152 @ v1_xboole_0 )
   != ( sk14 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[6273]) ).

thf(6277,plain,
    sk152 != sk14,
    inference(simp,[status(thm)],[6274]) ).

thf(2162,plain,
    sk94 @ v7_lattices,
    inference(cnfConj,[status(thm)],[2154]) ).

thf(827,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ m1_subset_1 ) )
     => ! [C: $i,D: $i] :
          ( ( ( B @ ( A @ g2_struct_0 ) )
            = ( D @ ( C @ g2_struct_0 ) ) )
         => ( ( B = D )
            & ( A = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g2_struct_0) ).

thf(5549,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)],[827]) ).

thf(944,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ k1_lattice2 @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k7_filter_2 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_filter_2) ).

thf(6062,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)],[944]) ).

thf(718,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                  = C ) )
           => ( B
              = ( A @ k6_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_lattice2) ).

thf(5072,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( 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)],[718]) ).

thf(967,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( ( D @ ( A @ k6_filter_2 ) @ ( E @ ( A @ k6_filter_2 ) @ ( A @ r3_lattices ) ) )
                         => ( E @ ( D @ ( A @ k1_lattice2 @ r3_lattices ) ) ) )
                        & ( ( E @ ( D @ ( A @ k1_lattice2 @ r3_lattices ) ) )
                         => ( D @ ( A @ k6_filter_2 ) @ ( E @ ( A @ k6_filter_2 ) @ ( A @ r3_lattices ) ) ) )
                        & ( ( B @ ( A @ k5_filter_2 ) @ ( C @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ r3_lattices ) ) )
                         => ( C @ ( B @ ( A @ r3_lattices ) ) ) )
                        & ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                         => ( B @ ( A @ k5_filter_2 ) @ ( C @ ( A @ k5_filter_2 ) @ ( A @ k1_lattice2 @ r3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_filter_2) ).

thf(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 @ 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)],[967]) ).

thf(856,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ r6_binop_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_lattice2) ).

thf(5672,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)],[856]) ).

thf(733,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( ( B @ ( D @ r2_hidden ) )
                        & ( B @ ( C @ r2_hidden ) ) )
                    <=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) )
           => ( A @ ( B @ m2_lattice4 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_filter_2) ).

thf(5128,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)],[733]) ).

thf(16132,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( sk187 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,9142]) ).

thf(16133,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( sk187 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16132]) ).

thf(16237,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk216 != k1_xboole_0 )
      | ( sk187 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16133]) ).

thf(16303,plain,
    ( ( sk216 != k1_xboole_0 )
    | ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16237]) ).

thf(308,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ( ( A @ ( B @ v1_binop_1 ) )
          <=> ! [C: $i] :
                ( ( A @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ ( D @ m1_subset_1 ) )
                   => ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                      = ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_binop_1) ).

thf(2917,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)],[308]) ).

thf(4372,plain,
    sk297 @ l3_lattices,
    inference(cnfConj,[status(thm)],[4356]) ).

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/sandbox/benchmark/theBenchmark.p',t56_subset_1) ).

thf(2623,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(13361,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,10678]) ).

thf(13362,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[13361]) ).

thf(13384,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk295 )
    | ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[13362]) ).

thf(13389,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( k6_nat_lat != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[13384]) ).

thf(688,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v11_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( E @ ( C @ k4_lattices ) ) )
                        = ( D @ ( E @ ( C @ u1_lattices @ ( A @ ( C @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_lattice2) ).

thf(4927,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)],[688]) ).

thf(149,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_lattice2 @ v10_lattices )
        & ( A @ k1_lattice2 @ v9_lattices )
        & ( A @ k1_lattice2 @ v8_lattices )
        & ( A @ k1_lattice2 @ v7_lattices )
        & ( A @ k1_lattice2 @ v6_lattices )
        & ( A @ k1_lattice2 @ v5_lattices )
        & ( A @ k1_lattice2 @ v4_lattices )
        & ( A @ k1_lattice2 @ v3_lattices )
        & ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_lattice2) ).

thf(1908,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_lattice2 @ v10_lattices )
        & ( A @ k1_lattice2 @ v9_lattices )
        & ( A @ k1_lattice2 @ v8_lattices )
        & ( A @ k1_lattice2 @ v7_lattices )
        & ( A @ k1_lattice2 @ v6_lattices )
        & ( A @ k1_lattice2 @ v5_lattices )
        & ( A @ k1_lattice2 @ v4_lattices )
        & ( A @ k1_lattice2 @ v3_lattices )
        & ~ ( A @ k1_lattice2 @ v3_struct_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(16199,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( sk196 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,7171]) ).

thf(16200,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( sk196 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16199]) ).

thf(16228,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk138 != k1_xboole_0 )
      | ( sk196 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16200]) ).

thf(16294,plain,
    ( ( sk138 != k1_xboole_0 )
    | ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16228]) ).

thf(509,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v16_lattices )
        & ( A @ v15_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v3_filter_0 )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
             => ! [D: $i] :
                  ( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( B @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( B @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ( ( F @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
                              & ( A @ ( B @ ( C @ v1_lattice4 ) ) ) )
                           => ( F @ ( D @ ( B @ k4_filter_0 ) ) @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_lattice4) ).

thf(3987,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)],[509]) ).

thf(370,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( B != k1_xboole_0 )
       => ! [E: $i] :
            ( ? [F: $i] :
                ( ( E
                  = ( F @ ( D @ k1_funct_1 ) ) )
                & ( C @ ( F @ r2_hidden ) )
                & ( A @ ( F @ r2_hidden ) ) )
           => ( C @ ( D @ k9_relat_1 ) @ ( E @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funct_2) ).

thf(3264,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)],[370]) ).

thf(796,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v11_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( D @ ( C @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k2_lattices ) ) )
                      = ( D @ ( B @ ( A @ k2_lattices ) ) @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k1_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_lattices) ).

thf(5430,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)],[796]) ).

thf(708,axiom,
    ! [A: $i] :
      ( ( A @ l2_lattices )
     => ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ m2_relset_1 ) ) )
        & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u2_lattices @ v1_funct_2 ) ) )
        & ( A @ u2_lattices @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).

thf(5041,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)],[708]) ).

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

thf(2517,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(160,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
    <=> ( ( B = D )
        & ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_zfmisc_1) ).

thf(1957,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(16203,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( sk187 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,7050]) ).

thf(16204,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( sk187 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16203]) ).

thf(16224,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk138 != k1_xboole_0 )
      | ( sk187 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16204]) ).

thf(16289,plain,
    ( ( sk138 != k1_xboole_0 )
    | ( sk187 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16224]) ).

thf(640,axiom,
    ! [A: $i] :
      ( ( A @ l2_struct_0 )
     => ( A @ l1_struct_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_struct_0) ).

thf(4687,plain,
    ! [A: $i] :
      ( ( A @ l2_struct_0 )
     => ( A @ l1_struct_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(2155,plain,
    sk94 @ v5_lattices,
    inference(cnfConj,[status(thm)],[2154]) ).

thf(922,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( ( B @ ( A @ k5_lattices @ r2_hidden ) )
              & ( A @ l3_lattices )
              & ( A @ v13_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( ( B
                = ( A @ u1_struct_0 ) )
              & ( B
                = ( A @ k1_filter_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_filter_0) ).

thf(5971,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)],[922]) ).

thf(6007,plain,
    sk445 @ v3_lattices,
    inference(cnfConj,[status(thm)],[6004]) ).

thf(374,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( C @ ( B @ ( A @ r4_binop_1 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ ( D @ m1_subset_1 ) )
                   => ! [E: $i] :
                        ( ( A @ ( E @ m1_subset_1 ) )
                       => ! [F: $i] :
                            ( ( A @ ( F @ m1_subset_1 ) )
                           => ( ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                              = ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_binop_1) ).

thf(3291,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)],[374]) ).

thf(511,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_zfmisc_1) ).

thf(3997,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(454,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k6_lattices )
        = ( A @ k1_lattice2 @ k5_lattices ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_lattice2) ).

thf(3733,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)],[454]) ).

thf(21227,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk138 @ k2_relat_1 @ ( A @ ( sk138 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21193,1030]) ).

thf(21228,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( sk138 @ k2_relat_1 @ ( A @ ( sk138 @ k9_relat_1 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[21227]) ).

thf(21229,plain,
    ! [B: $i,A: $i] : ( sk138 @ k2_relat_1 @ ( A @ ( B @ ( sk138 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[21228:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk138 @ k9_relat_1 ) )),bind(C,$thf( sk138 @ k2_relat_1 )),bind(D,$thf( D ))]]) ).

thf(21248,plain,
    ! [B: $i,A: $i] : ( sk138 @ k2_relat_1 @ ( A @ ( B @ ( sk138 @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[21229]) ).

thf(55,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ! [B: $i] :
          ( ( B @ v1_relat_1 )
         => ( B @ ( A @ k4_xboole_0 ) @ k2_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_relat_1) ).

thf(1229,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(105,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ k2_tarski ) @ ( A @ k4_xboole_0 ) )
        = k1_xboole_0 )
    <=> ~ ( ( A
           != ( C @ ( B @ k2_tarski ) ) )
          & ( A
           != ( C @ k1_tarski ) )
          & ( A
           != ( B @ k1_tarski ) )
          & ( A != k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_zfmisc_1) ).

thf(1593,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(75,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ ( C @ r1_tarski ) )
        & ( B @ ( A @ r1_tarski ) ) )
     => ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_xboole_1) ).

thf(1380,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(719,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k1_lattices ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattices) ).

thf(5078,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)],[719]) ).

thf(27653,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 )
       != sk278 ) ),
    inference(paramod_ordered,[status(thm)],[1994,15654]) ).

thf(27654,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk278 ),
    inference(pattern_uni,[status(thm)],[27653:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).

thf(27686,plain,
    ! [A: $i] :
      ( ( A @ k1_tarski @ k1_zfmisc_1 )
     != sk278 ),
    inference(simp,[status(thm)],[27654]) ).

thf(31090,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 @ v10_lattices )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,974]) ).

thf(31091,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[31090:[bind(A,$thf( sk1 ))]]) ).

thf(674,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k12_filter_0 ) )
        = ( B @ ( A @ k10_filter_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k12_filter_0) ).

thf(4843,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)],[674]) ).

thf(658,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ m1_filter_0 ) )
        & ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k6_filter_0 ) ) )
        = ( C @ ( B @ ( A @ k5_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_filter_0) ).

thf(4787,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)],[658]) ).

thf(66,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( A @ ( C @ v1_binop_1 ) )
               => ( ( B @ ( C @ ( A @ r5_binop_1 ) ) )
                <=> ( B @ ( C @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_binop_1) ).

thf(1303,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(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 @ ( C @ m1_filter_0 ) )
                 => ~ ( ( A @ ( C @ v1_filter_0 ) )
                      & ( C @ ( B @ r2_hidden ) ) ) )
              & ( B
               != ( A @ k5_lattices ) )
              & ( A @ l3_lattices )
              & ( A @ v13_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_filter_0) ).

thf(5477,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ~ ( ! [C: $i] :
                  ( ( A @ ( 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)],[807]) ).

thf(781,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ? [B: $i] : ( A @ ( B @ m3_lattice4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_lattice4) ).

thf(5371,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)],[781]) ).

thf(839,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ! [E: $i] :
                      ( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ! [F: $i] :
                          ( ( D @ ( A @ k8_filter_0 ) @ u1_struct_0 @ ( F @ m1_subset_1 ) )
                         => ( ( ( C = F )
                              & ( B = E ) )
                           => ( ( ( C @ ( B @ ( A @ k4_lattices ) ) )
                                = ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k4_lattices ) ) ) )
                              & ( ( C @ ( B @ ( A @ k3_lattices ) ) )
                                = ( F @ ( E @ ( D @ ( A @ k8_filter_0 ) @ k3_lattices ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_filter_0) ).

thf(5601,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[839]) ).

thf(4357,plain,
    sk297 @ v7_lattices,
    inference(cnfConj,[status(thm)],[4356]) ).

thf(610,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( ( B @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( B @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ( ( D @ ( C @ ( B @ ( A @ k3_lattice2 ) ) ) )
                    = ( D @ ( C @ ( B @ u1_lattices @ ( B @ u1_struct_0 @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lattice2) ).

thf(4491,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)],[610]) ).

thf(123,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( B @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
        = ( A @ k1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_zfmisc_1) ).

thf(1757,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(14806,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( sk278 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4083,2366]) ).

thf(14807,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( sk278 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[14806]) ).

thf(14814,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != sk278 ),
    inference(simp,[status(thm)],[14807]) ).

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 @ k5_filter_2 ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_filter_2) ).

thf(6150,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)],[961]) ).

thf(4577,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( sk314 @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) )
        | ~ ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
        | ~ sk312 )
      & ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk314 @ m2_relset_1 ) ) )
        | ~ sk312 )
      & ( ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( sk314 @ v1_funct_2 ) ) )
        | ~ sk312 )
      & ( ( sk314 @ v1_funct_1 )
        | ~ sk312 )
      & ( sk312
        | ~ ( A @ ( sk313 @ p1_s14_funct_2 ) )
        | ~ ( f2_s14_funct_2 @ ( A @ m1_subset_1 ) ) )
      & ( sk312
        | ( f1_s14_funct_2 @ ( sk313 @ m1_subset_1 ) ) ) ),
    inference(cnf,[status(esa)],[4576]) ).

thf(4579,plain,
    ( sk312
    | ( f1_s14_funct_2 @ ( sk313 @ m1_subset_1 ) ) ),
    inference(cnfConj,[status(thm)],[4577]) ).

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

thf(1480,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(787,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( B @ ( A @ k4_filter_0 ) ) )
            = ( A @ k6_lattices ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_filter_0) ).

thf(5398,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)],[787]) ).

thf(4367,plain,
    sk297 @ v16_lattices,
    inference(cnfConj,[status(thm)],[4356]) ).

thf(910,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ k1_lattice2 @ u1_struct_0 @ ( B @ ( A @ k5_filter_2 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_filter_2) ).

thf(5926,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)],[910]) ).

thf(8356,plain,
    ( ( ( sk341 @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3244,4839]) ).

thf(8357,plain,
    ( ( sk341 @ v1_xboole_0 )
   != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8356]) ).

thf(8368,plain,
    sk341 != sk216,
    inference(simp,[status(thm)],[8357]) ).

thf(15154,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( A @ ( sk295 @ 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)],[14351,1030]) ).

thf(15155,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( f1_s4_funct_2 @ ( A @ ( sk295 @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
       != ( C @ ( B @ r1_tarski ) ) )
      | ( C @ ( D @ ( B @ k4_xboole_0 ) @ r1_tarski ) ) ),
    inference(simp,[status(thm)],[15154]) ).

thf(15156,plain,
    ! [B: $i,A: $i] : ( f1_s4_funct_2 @ ( A @ ( B @ ( sk295 @ k1_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(pattern_uni,[status(thm)],[15155:[bind(A,$thf( F )),bind(B,$thf( F @ ( sk295 @ k1_relat_1 @ k4_xboole_0 ) )),bind(C,$thf( f1_s4_funct_2 )),bind(D,$thf( D ))]]) ).

thf(15172,plain,
    ! [B: $i,A: $i] : ( f1_s4_funct_2 @ ( A @ ( B @ ( sk295 @ k1_relat_1 @ k4_xboole_0 ) @ k4_xboole_0 ) @ r1_tarski ) ),
    inference(simp,[status(thm)],[15156]) ).

thf(379,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( A
        = ( A @ a_1_0_domain_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_domain_1) ).

thf(3328,plain,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ( A
        = ( A @ a_1_0_domain_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(621,axiom,
    ! [A: $i] :
      ( ( ( A @ l2_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v5_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( D @ ( C @ ( A @ k1_lattices ) ) @ ( B @ ( A @ k1_lattices ) ) )
                      = ( D @ ( C @ ( B @ ( A @ k1_lattices ) ) @ ( A @ k1_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_lattices) ).

thf(4565,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)],[621]) ).

thf(418,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( C @ ( B @ a_2_0_domain_1 ) @ ( A @ r2_hidden ) )
      <=> ? [D: $i,E: $i] :
            ( ( A
              = ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
            & ( C @ ( E @ m1_subset_1 ) )
            & ( B @ ( D @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_domain_1) ).

thf(3558,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)],[418]) ).

thf(793,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_filter_0 )
        = ( A @ u1_struct_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_filter_0) ).

thf(5413,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)],[793]) ).

thf(16080,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,8397]) ).

thf(16081,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16080]) ).

thf(16252,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk216 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[16081]) ).

thf(16321,plain,
    ( ( sk216 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[16252]) ).

thf(2404,plain,
    k13_nat_lat @ v4_lattices,
    inference(cnfConj,[status(thm)],[2398]) ).

thf(397,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v14_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( A @ ( B @ ( C @ m1_lattice4 ) ) )
             => ( ( A @ ( B @ ( C @ v2_lattice4 ) ) )
               => ( ( C @ ( A @ ( B @ r2_lattice4 ) ) )
                  & ( A @ v14_lattices ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_lattice4) ).

thf(3426,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)],[397]) ).

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/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).

thf(2223,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(940,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v11_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ k3_lattices ) ) )
                    = ( D @ ( B @ ( A @ k3_lattices ) ) @ ( C @ ( B @ ( A @ k3_lattices ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_lattices) ).

thf(6040,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)],[940]) ).

thf(121,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ( A @ v2_funct_1 )
       => ( ( ( A @ k1_relat_1 )
            = ( A @ k2_funct_1 @ k2_relat_1 ) )
          & ( ( A @ k2_relat_1 )
            = ( A @ k2_funct_1 @ k1_relat_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).

thf(1742,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(830,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( B @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ k1_lattice4 ) )
                = ( C @ ( B @ ( A @ k1_lattice4 ) @ ( A @ k3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_lattice4) ).

thf(5559,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)],[830]) ).

thf(30077,plain,
    ! [A: $i] :
      ( ( A != sk197 )
      | ( k1_xboole_0 @ v4_lattices )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,3004]) ).

thf(30078,plain,
    ( ( k1_xboole_0 @ v4_lattices )
    | ( sk197 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[30077:[bind(A,$thf( sk197 ))]]) ).

thf(324,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i,C: $i,D: $i] :
          ( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
            | ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
         => ( D @ ( B @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_zfmisc_1) ).

thf(3015,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)],[324]) ).

thf(47019,plain,
    ( ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2587,46818]) ).

thf(47020,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) @ v1_xboole_0 )
   != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[47019]) ).

thf(47027,plain,
    ( ( sk14 @ k8_subset_1 @ k1_tarski @ ( sk14 @ k4_xboole_0 ) )
   != sk152 ),
    inference(simp,[status(thm)],[47020]) ).

thf(30901,plain,
    ! [A: $i] :
      ( ( A != sk297 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,16016]) ).

thf(30902,plain,
    ! [A: $i] :
      ( ( A != sk297 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[30901]) ).

thf(30903,plain,
    ( ~ ( k1_xboole_0 @ ( sk1 @ ( k1_xboole_0 @ v1_partfun1 ) ) )
    | ( sk297 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[30902:[bind(A,$thf( sk297 ))]]) ).

thf(138,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
         != ( B @ ( A @ k2_tarski ) ) )
        & ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
         != ( B @ k1_tarski ) )
        & ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
         != ( A @ k1_tarski ) )
        & ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
         != k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_zfmisc_1) ).

thf(1859,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(542,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
        & ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
     => ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
        = ( B @ ( C @ ( A @ k4_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).

thf(4146,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)],[542]) ).

thf(68,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = ( A @ k1_tarski ) )
      | ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_zfmisc_1) ).

thf(1314,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(866,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ k1_filter_2 @ m1_filter_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_filter_2) ).

thf(5709,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)],[866]) ).

thf(573,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ( A @ ( A @ k1_funct_2 ) @ ( B @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_2) ).

thf(4281,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)],[573]) ).

thf(953,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( A @ u1_lattices @ v1_setwiseo ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_lattice2) ).

thf(6114,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)],[953]) ).

thf(11400,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)],[1902,7770]) ).

thf(11401,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != k1_xboole_0 ),
    inference(pattern_uni,[status(thm)],[11400:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(11414,plain,
    ! [A: $i] :
      ( ( ( k1_xboole_0 @ k1_zfmisc_1 )
       != ( A @ k1_zfmisc_1 ) )
      | ( ( k1_xboole_0 @ k1_tarski )
       != sk216 ) ),
    inference(paramod_ordered,[status(thm)],[1902,8369]) ).

thf(11415,plain,
    ( ( k1_xboole_0 @ k1_tarski )
   != sk216 ),
    inference(pattern_uni,[status(thm)],[11414:[bind(A,$thf( k1_xboole_0 ))]]) ).

thf(1325,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( B @ sk25 ) @ k1_relat_1 ) )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1319]) ).

thf(1334,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ sk25 ) @ k1_relat_1 )
        = B )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1325]) ).

thf(1335,plain,
    ! [A: $i] :
      ( ( A @ ( k1_xboole_0 @ sk25 ) @ k1_relat_1 )
      = k1_xboole_0 ),
    inference(simp,[status(thm)],[1334]) ).

thf(5564,plain,
    sk410 @ l2_struct_0,
    inference(cnfConj,[status(thm)],[5563]) ).

thf(875,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( ( D @ ( B @ ( A @ r3_lattices ) ) )
                      & ( C @ ( B @ ( A @ r3_lattices ) ) ) )
                   => ( D @ ( C @ ( A @ k4_lattices ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_filter_0) ).

thf(5741,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( ( 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)],[875]) ).

thf(1033,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)],[1032]) ).

thf(49,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
          = ( C @ k2_relat_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_funct_2) ).

thf(1197,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(678,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_lattices )
        & ( A @ v6_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( C @ ( B @ ( A @ k4_lattices ) ) )
        = ( B @ ( C @ ( A @ k4_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_lattices) ).

thf(4865,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)],[678]) ).

thf(783,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
             => ( ( C @ ( B @ ( A @ r1_lattice4 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ! [E: $i] :
                        ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                       => ( ( E @ ( D @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) )
                          = ( E @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k8_funct_2 ) ) ) @ ( B @ k4_filter_0 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_lattice4) ).

thf(5378,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)],[783]) ).

thf(601,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_lattice2 @ k1_lattice2 )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_lattice2) ).

thf(4442,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)],[601]) ).

thf(851,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( B @ ( A @ k1_lattice4 ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice4) ).

thf(5642,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)],[851]) ).

thf(11961,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,7375]) ).

thf(11962,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk71 @ m2_relset_1 ) ) ) )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[11961]) ).

thf(12121,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk71 )
    | ( sk197 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk71 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[11962]) ).

thf(16057,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,8674]) ).

thf(16058,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ v10_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16057]) ).

thf(16233,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk295 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[16058]) ).

thf(16299,plain,
    ( ( sk295 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ v10_lattices ) ),
    inference(simp,[status(thm)],[16233]) ).

thf(2668,plain,
    sk157 @ v9_lattices,
    inference(cnfConj,[status(thm)],[2661]) ).

thf(750,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v13_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v1_lattice2 )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ? [D: $i] :
                    ( ! [E: $i] :
                        ( ( A @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                       => ( ( C @ ( E @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
                         => ( D @ ( E @ ( A @ r3_lattices ) ) ) ) )
                    & ( C @ ( D @ ( B @ ( A @ k4_lattices ) ) @ ( A @ r3_lattices ) ) )
                    & ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_lattice2) ).

thf(5200,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)],[750]) ).

thf(2021,plain,
    ! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
    inference(cnf,[status(esa)],[2020]) ).

thf(71,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ! [B: $i,C: $i] :
          ( ( ~ ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
           => ( ( C
                = ( B @ ( A @ k1_funct_1 ) ) )
            <=> ( C = k1_xboole_0 ) ) )
          & ( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
           => ( ( C
                = ( B @ ( A @ k1_funct_1 ) ) )
            <=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).

thf(1346,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(106,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
        = ( A @ k1_tarski ) )
    <=> ~ ( B @ ( A @ r2_hidden ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_zfmisc_1) ).

thf(1610,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(2159,plain,
    sk94 @ v6_lattices,
    inference(cnfConj,[status(thm)],[2154]) ).

thf(887,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
        & ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
        & ( A @ l1_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( C @ ( B @ ( A @ k2_lattices ) ) @ m1_subset_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattices) ).

thf(5803,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)],[887]) ).

thf(714,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ v14_lattices ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_filter_0) ).

thf(5061,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)],[714]) ).

thf(755,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ k1_lattice2 @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( A @ k1_lattice2 @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( ( C = E )
                          & ( B = D )
                          & ( E @ ( D @ ( A @ k1_lattice2 @ r3_lattices ) ) ) )
                       => ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_lattice2) ).

thf(5236,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[755]) ).

thf(16401,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( sk393 @ 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)],[14747,1030]) ).

thf(16402,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( f2_s11_funct_2 @ ( sk393 @ 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)],[16401]) ).

thf(16403,plain,
    ! [A: $i] :
      ( ( f2_s11_funct_2 @ ( A @ ( sk393 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(pattern_uni,[status(thm)],[16402:[bind(A,$thf( sk393 @ k2_relat_1 )),bind(B,$thf( f2_s11_funct_2 )),bind(C,$thf( C ))]]) ).

thf(16412,plain,
    ! [A: $i] :
      ( ( f2_s11_funct_2 @ ( A @ ( sk393 @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) )
      | ( f4_s11_funct_2 = f3_s11_funct_2 ) ),
    inference(simp,[status(thm)],[16403]) ).

thf(4363,plain,
    sk297 @ v8_lattices,
    inference(cnfConj,[status(thm)],[4356]) ).

thf(153,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_2) ).

thf(1930,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ v1_xboole_0 )
     => ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(227,axiom,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A @ v1_relat_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).

thf(2353,plain,
    ! [A: $i] :
      ( ( A @ v1_xboole_0 )
     => ( A @ v1_relat_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(987,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
      | ~ ( B @ ( A @ ( C @ sk3 ) ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( C @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[985]) ).

thf(914,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v14_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k6_lattices @ ( A @ k4_lattices ) ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_lattices) ).

thf(5945,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)],[914]) ).

thf(194,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k8_filter_0 ) @ v10_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v9_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v8_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v7_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v6_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v5_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v4_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v3_lattices )
        & ~ ( B @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_filter_0) ).

thf(2127,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m1_filter_0 ) )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k8_filter_0 ) @ v10_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v9_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v8_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v7_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v6_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v5_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v4_lattices )
        & ( B @ ( A @ k8_filter_0 ) @ v3_lattices )
        & ~ ( B @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

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

thf(1829,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(318,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
         => ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( D @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t168_partfun1) ).

thf(2966,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)],[318]) ).

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/sandbox/benchmark/theBenchmark.p',dt_k3_binop_1) ).

thf(2430,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(31618,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 @ l3_lattices )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,975]) ).

thf(31619,plain,
    ( ( k1_xboole_0 @ l3_lattices )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[31618:[bind(A,$thf( sk1 ))]]) ).

thf(12050,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,9407]) ).

thf(12051,plain,
    ( ( ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) )
     != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12050]) ).

thf(12134,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk216 )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12051]) ).

thf(738,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v3_filter_0 )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ( ( ( D @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ r2_hidden ) )
                      & ( D @ ( B @ r2_hidden ) ) )
                   => ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_filter_0) ).

thf(5151,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)],[738]) ).

thf(16078,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( sk196 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,8927]) ).

thf(16079,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk207 @ m2_relset_1 ) ) ) )
      | ( sk196 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16078]) ).

thf(16246,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk207 != k1_xboole_0 )
      | ( sk196 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16079]) ).

thf(16314,plain,
    ( ( sk207 != k1_xboole_0 )
    | ( sk196 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk207 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16246]) ).

thf(855,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( A @ k2_filter_0 ) @ ( B @ r2_hidden ) )
              <=> ( B @ ( C @ ( A @ r3_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_filter_0) ).

thf(5668,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( 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)],[855]) ).

thf(332,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
              <=> ! [D: $i] :
                    ( ( A @ ( D @ m1_subset_1 ) )
                   => ( ( D @ ( B @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                      = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_binop_1) ).

thf(3057,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)],[332]) ).

thf(963,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( B @ l3_lattices )
            & ( B @ v10_lattices )
            & ~ ( B @ v3_struct_0 ) )
         => ! [C: $i] :
              ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
             => ( ( B @ ( A @ ( C @ v3_lattice4 ) ) )
              <=> ( ( B @ ( A @ ( C @ v2_lattice4 ) ) )
                  & ( B @ ( A @ ( C @ v1_lattice4 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lattice4) ).

thf(6155,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)],[963]) ).

thf(96,axiom,
    ! [A: $i] :
      ( ( ( A @ v1_funct_1 )
        & ( A @ v1_relat_1 ) )
     => ( ! [B: $i,C: $i] :
            ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k9_relat_1 ) )
            = ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k4_xboole_0 ) ) )
       => ( A @ v2_funct_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_funct_1) ).

thf(1532,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(735,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                 => ( ( C @ ( B @ ( A @ r3_lattices ) ) )
                   => ( ( D @ ( C @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
                      & ( C @ ( D @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
                      & ( D @ ( C @ ( A @ k3_lattices ) ) @ ( D @ ( B @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) )
                      & ( C @ ( D @ ( A @ k3_lattices ) ) @ ( B @ ( D @ ( A @ k3_lattices ) ) @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_filter_0) ).

thf(5140,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[735]) ).

thf(15310,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( sk71 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1924,3056]) ).

thf(15311,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( sk71 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[15310]) ).

thf(15324,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != sk71 ),
    inference(simp,[status(thm)],[15311]) ).

thf(8634,plain,
    ( ( ( sk278 @ v1_xboole_0 )
     != ( sk14 @ v1_xboole_0 ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4083,1167]) ).

thf(8635,plain,
    ( ( sk278 @ v1_xboole_0 )
   != ( sk14 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[8634]) ).

thf(8643,plain,
    sk278 != sk14,
    inference(simp,[status(thm)],[8635]) ).

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/sandbox/benchmark/theBenchmark.p',t110_zfmisc_1) ).

thf(2265,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(483,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ l3_lattices )
        & ( B @ v10_lattices )
        & ~ ( B @ v3_struct_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [C: $i] :
          ( ( B @ ( A @ ( C @ m1_lattice4 ) ) )
         => ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ m2_relset_1 ) ) )
            & ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( C @ v1_funct_2 ) ) )
            & ( C @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_lattice4) ).

thf(3869,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)],[483]) ).

thf(833,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ( ( C @ ( B @ ( A @ k9_filter_0 ) ) )
                = ( B @ ( C @ ( A @ k4_filter_0 ) ) @ ( C @ ( B @ ( A @ k4_filter_0 ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_filter_0) ).

thf(5581,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( 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)],[833]) ).

thf(607,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( A @ k1_lattice2 )
        = ( A @ u2_lattices @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ g3_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattice2) ).

thf(4484,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)],[607]) ).

thf(989,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ sk3 ) ) )
      | ( A @ ( A @ ( B @ ( C @ sk4 ) ) @ r2_hidden ) )
      | ( ( C @ k1_relat_1 )
       != A )
      | ~ ( C @ v1_funct_1 )
      | ~ ( C @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[985]) ).

thf(991,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( C @ sk3 ) ) )
      | ( A @ ( A @ ( B @ ( C @ sk4 ) ) @ r2_hidden ) )
      | ~ ( C @ v1_funct_1 )
      | ~ ( C @ v1_relat_1 )
      | ( ( C @ k1_relat_1 )
       != A ) ),
    inference(lifteq,[status(thm)],[989]) ).

thf(992,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ k1_relat_1 @ ( B @ sk3 ) ) )
      | ( B @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ ( B @ sk4 ) ) @ r2_hidden ) )
      | ~ ( B @ v1_funct_1 )
      | ~ ( B @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[991]) ).

thf(1923,plain,
    sk71 @ v2_funct_1,
    inference(cnfConj,[status(thm)],[1920]) ).

thf(36012,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( k1_xboole_0 != k1_xboole_0 )
      | ( sk187 @ sk18 @ v1_funct_1 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,30771]) ).

thf(36013,plain,
    ! [A: $i] :
      ( ( A != sk1 )
      | ( sk187 @ sk18 @ v1_funct_1 )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(simp,[status(thm)],[36012]) ).

thf(36014,plain,
    ( ( sk187 @ sk18 @ v1_funct_1 )
    | ( sk1 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[36013:[bind(A,$thf( sk1 ))]]) ).

thf(16100,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( sk157 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,9145]) ).

thf(16101,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk216 @ m2_relset_1 ) ) ) )
      | ( sk157 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16100]) ).

thf(16242,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk216 != k1_xboole_0 )
      | ( sk157 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16101]) ).

thf(16309,plain,
    ( ( sk216 != k1_xboole_0 )
    | ( sk157 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk216 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16242]) ).

thf(29858,plain,
    ! [A: $i] :
      ( ( A != sk197 )
      | ( k1_xboole_0 @ v10_lattices )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,3008]) ).

thf(29859,plain,
    ( ( k1_xboole_0 @ v10_lattices )
    | ( sk197 @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[29858:[bind(A,$thf( sk197 ))]]) ).

thf(846,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( B @ ( A @ u1_lattices @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
                  = C ) )
           => ( B
              = ( A @ k6_lattices ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_lattice2) ).

thf(5623,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( 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)],[846]) ).

thf(709,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
            & ( D @ v1_funct_1 ) )
         => ( C = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_2) ).

thf(5046,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)],[709]) ).

thf(415,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_tarski ) )
      = ( A @ ( B @ k2_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

thf(3538,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_tarski ) )
      = ( A @ ( B @ k2_tarski ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(151,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( B != k1_xboole_0 )
       => ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_2) ).

thf(1925,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( B != k1_xboole_0 )
       => ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(950,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( ( A @ l3_lattices )
          & ( A @ v13_lattices )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ k1_filter_0 )
          = ( A @ k5_lattices @ ( A @ k2_filter_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_filter_0) ).

thf(6104,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)],[950]) ).

thf(592,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
             => ( ( A @ k5_lattice4 @ ( B @ ( A @ u1_struct_0 @ k2_setwiseo ) @ ( C @ ( A @ u1_struct_0 @ k5_setwiseo ) ) @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) )
                = ( B @ ( A @ k7_lattices ) @ ( A @ k5_lattice4 @ ( C @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) @ ( A @ k4_lattices ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_lattice4) ).

thf(4395,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)],[592]) ).

thf(456,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ m2_lattice4 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( B @ ( A @ k10_filter_2 ) )
        = ( B @ ( A @ k7_filter_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_filter_2) ).

thf(3740,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)],[456]) ).

thf(343,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
        & ( B @ v1_funct_1 ) )
     => ! [C: $i] :
          ( ( A @ ( C @ m1_subset_1 ) )
         => ( ( A @ ( B @ v1_binop_1 ) )
           => ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
            <=> ! [D: $i] :
                  ( ( A @ ( D @ m1_subset_1 ) )
                 => ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
                    = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_binop_1) ).

thf(3113,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)],[343]) ).

thf(391,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ! [C: $i] :
              ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
                & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
                & ( C @ v1_funct_1 ) )
             => ! [D: $i] :
                  ( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
                    & ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ( ( D
                      = ( B @ ( C @ k1_realset1 ) ) )
                   => ( ( ( A @ ( C @ v2_binop_1 ) )
                       => ( B @ ( D @ v2_binop_1 ) ) )
                      & ( ( A @ ( C @ v3_binop_1 ) )
                       => ( B @ ( D @ v3_binop_1 ) ) )
                      & ( ( A @ ( C @ v1_binop_1 ) )
                       => ( B @ ( D @ v1_binop_1 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_filter_2) ).

thf(3394,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)],[391]) ).

thf(144,axiom,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v3_filter_0 )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v12_lattices )
          & ( A @ v11_lattices )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_filter_0) ).

thf(1885,plain,
    ! [A: $i] :
      ( ( A @ l3_lattices )
     => ( ( ( A @ v3_filter_0 )
          & ( A @ v10_lattices )
          & ~ ( A @ v3_struct_0 ) )
       => ( ( A @ v12_lattices )
          & ( A @ v11_lattices )
          & ( A @ v10_lattices )
          & ( A @ v9_lattices )
          & ( A @ v8_lattices )
          & ( A @ v7_lattices )
          & ( A @ v6_lattices )
          & ( A @ v5_lattices )
          & ( A @ v4_lattices )
          & ~ ( A @ v3_struct_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(642,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( C @ r1_tarski ) )
                & ( C @ ( B @ ( A @ u1_struct_0 @ k1_zfmisc_1 @ k1_finsub_1 ) ) @ ( A @ k3_filter_0 ) @ ( B @ r1_tarski ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_lattice4) ).

thf(4691,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)],[642]) ).

thf(410,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( ( C @ l3_lattices )
                & ( C @ v13_lattices )
                & ( C @ v11_lattices )
                & ( C @ v10_lattices )
                & ~ ( C @ v3_struct_0 ) )
             => ! [D: $i] :
                  ( ( ( C @ u1_struct_0 @ ( A @ ( D @ m2_relset_1 ) ) )
                    & ( C @ u1_struct_0 @ ( A @ ( D @ v1_funct_2 ) ) )
                    & ( D @ v1_funct_1 ) )
                 => ! [E: $i] :
                      ( ( C @ u1_struct_0 @ ( E @ m1_subset_1 ) )
                     => ( ( D @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) @ ( E @ ( C @ u1_lattices @ ( C @ u1_struct_0 @ ( C @ u1_struct_0 @ ( C @ u1_struct_0 @ k2_binop_1 ) ) ) ) ) )
                        = ( D @ ( E @ ( C @ u1_lattices @ ( A @ ( C @ u1_struct_0 @ k8_funcop_1 ) ) ) ) @ ( B @ ( C @ ( A @ k2_lattice2 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_lattice2) ).

thf(3494,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)],[410]) ).

thf(16123,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2222,7687]) ).

thf(16124,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
       != ( k1_xboole_0 @ ( sk1 @ ( sk138 @ m2_relset_1 ) ) ) )
      | ( k1_xboole_0 @ l3_lattices )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[16123]) ).

thf(16218,plain,
    ! [B: $i,A: $i] :
      ( ( B != k1_xboole_0 )
      | ( A != sk1 )
      | ( sk138 != k1_xboole_0 )
      | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
      | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[16124]) ).

thf(16282,plain,
    ( ( sk138 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk138 @ v1_partfun1 ) ) )
    | ( k1_xboole_0 @ l3_lattices ) ),
    inference(simp,[status(thm)],[16218]) ).

thf(776,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ v8_lattices )
      <=> ! [B: $i] :
            ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
           => ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( C @ ( B @ ( A @ k2_lattices ) ) @ ( A @ k1_lattices ) ) )
                  = C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattices) ).

thf(5344,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)],[776]) ).

thf(195,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( C @ v2_funct_1 )
        <=> ! [D: $i,E: $i] :
              ( ( ( ( D @ ( C @ k1_funct_1 ) )
                  = ( E @ ( C @ k1_funct_1 ) ) )
                & ( A @ ( E @ r2_hidden ) )
                & ( A @ ( D @ r2_hidden ) ) )
             => ( D = E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_funct_2) ).

thf(2138,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( ! [D: $i,E: $i] :
                ( ( ( ( D @ ( C @ k1_funct_1 ) )
                    = ( E @ ( C @ k1_funct_1 ) ) )
                  & ( A @ ( E @ r2_hidden ) )
                  & ( A @ ( D @ r2_hidden ) ) )
               => ( D = E ) )
           => ( C @ v2_funct_1 ) )
          & ( ( C @ v2_funct_1 )
           => ! [D: $i,E: $i] :
                ( ( ( ( D @ ( C @ k1_funct_1 ) )
                    = ( E @ ( C @ k1_funct_1 ) ) )
                  & ( A @ ( E @ r2_hidden ) )
                  & ( A @ ( D @ r2_hidden ) ) )
               => ( D = E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(323,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_partfun1) ).

thf(3013,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)],[323]) ).

thf(1323,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ sk25 ) @ k2_relat_1 @ r1_tarski ) )
      | ( B != k1_xboole_0 ) ),
    inference(cnfConj,[status(thm)],[1319]) ).

thf(1330,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ sk25 ) @ k2_relat_1 @ r1_tarski ) )
      | ( B != k1_xboole_0 ) ),
    inference(lifteq,[status(thm)],[1323]) ).

thf(1331,plain,
    ! [A: $i] : ( A @ ( A @ ( k1_xboole_0 @ sk25 ) @ k2_relat_1 @ r1_tarski ) ),
    inference(simp,[status(thm)],[1330]) ).

thf(836,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ( A @ v3_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ k1_filter_0 @ ( A @ k8_filter_0 ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_filter_0) ).

thf(5591,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)],[836]) ).

thf(12021,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4328,9825]) ).

thf(12022,plain,
    ( ( ( k1_xboole_0 @ ( sk1 @ ( sk295 @ m2_relset_1 ) ) )
     != ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( sk295 @ m2_relset_1 ) ) ) )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12021]) ).

thf(12182,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk295 != sk295 )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12022]) ).

thf(12203,plain,
    ( ( f2_s4_funct_2 != k1_xboole_0 )
    | ( sk1 != f1_s4_funct_2 )
    | ( sk297 != k1_xboole_0 )
    | ~ ( k1_xboole_0 @ ( sk1 @ ( sk295 @ v1_partfun1 ) ) ) ),
    inference(simp,[status(thm)],[12182]) ).

thf(363,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ! [B: $i] :
          ( ( B @ ( A @ r1_relat_2 ) )
        <=> ! [C: $i] :
              ( ( B @ ( C @ r2_hidden ) )
             => ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_2) ).

thf(3227,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)],[363]) ).

thf(157,axiom,
    ! [A: $i] :
      ( ( ( A @ l1_lattices )
        & ( A @ v7_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( A @ u1_lattices @ v2_binop_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_lattice2) ).

thf(1945,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(170,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ v1_relat_1 )
     => ! [D: $i] :
          ( ( D @ v1_relat_1 )
         => ( ( ( B @ ( A @ r1_tarski ) )
              & ( D @ ( C @ r1_tarski ) ) )
           => ( B @ ( D @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_relat_1) ).

thf(2018,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(190,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
        & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
        & ( C @ v1_funct_1 ) )
     => ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r2_hidden ) )
       => ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_realset1) ).

thf(2106,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(451,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( B @ v1_xboole_0 )
        & ( A != B )
        & ( A @ v1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

thf(3721,plain,
    ! [A: $i,B: $i] :
      ~ ( ( B @ v1_xboole_0 )
        & ( A != B )
        & ( A @ v1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(2879,plain,
    sk187 @ v4_lattices,
    inference(cnfConj,[status(thm)],[2869]) ).

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/sandbox/benchmark/theBenchmark.p',t135_zfmisc_1) ).

thf(2640,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(740,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ! [C: $i] :
              ( ( A @ ( C @ m1_filter_0 ) )
             => ( ( C @ ( B @ ( A @ u1_struct_0 @ k4_subset_1 ) ) @ ( A @ k3_filter_0 ) )
                = ( C @ ( B @ ( A @ a_3_1_filter_0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_filter_0) ).

thf(5155,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)],[740]) ).

thf(707,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( C @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
        & ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
        & ~ ( C @ v1_xboole_0 )
        & ~ ( B @ v1_xboole_0 ) )
     => ( ( E @ ( D @ ( C @ ( B @ a_4_1_domain_1 ) ) ) @ ( A @ r2_hidden ) )
      <=> ? [F: $i,G: $i] :
            ( ( E @ ( G @ r2_hidden ) )
            & ( D @ ( F @ r2_hidden ) )
            & ( A
              = ( G @ ( F @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
            & ( C @ ( G @ m1_subset_1 ) )
            & ( B @ ( F @ m1_subset_1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_1_domain_1) ).

thf(5029,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)],[707]) ).

thf(495,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
        & ( C @ v1_funct_1 ) )
     => ! [D: $i] :
          ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
         => ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
            & ( D @ v1_funct_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_funct_2) ).

thf(3924,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)],[495]) ).

thf(50497,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ sk25 ) @ v1_relat_1 )
       != ( C @ v1_relat_1 ) )
      | ( B @ ( C @ k4_xboole_0 ) @ v1_relat_1 )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1337,1179]) ).

thf(50498,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( k1_xboole_0 @ sk25 ) @ v1_relat_1 )
       != ( C @ v1_relat_1 ) )
      | ( B @ ( C @ k4_xboole_0 ) @ v1_relat_1 ) ),
    inference(simp,[status(thm)],[50497]) ).

thf(50499,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( k1_xboole_0 @ sk25 ) @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(pattern_uni,[status(thm)],[50498:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( k1_xboole_0 @ sk25 ) ))]]) ).

thf(50634,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( k1_xboole_0 @ sk25 ) @ k4_xboole_0 ) @ v1_relat_1 ),
    inference(simp,[status(thm)],[50499]) ).

thf(770,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
            & ~ ( B @ v1_xboole_0 ) )
         => ( ! [C: $i] :
                ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
               => ! [D: $i] :
                    ( ( A @ u1_struct_0 @ ( D @ m1_subset_1 ) )
                   => ( ( ( B @ ( D @ r2_hidden ) )
                        & ( B @ ( C @ r2_hidden ) ) )
                    <=> ( B @ ( D @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) )
           => ( A @ ( B @ m2_filter_2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_filter_2) ).

thf(5312,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)],[770]) ).

thf(810,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ ( B @ m1_filter_0 ) )
         => ( ( A @ v12_lattices )
           => ( B @ ( A @ k8_filter_0 ) @ v12_lattices ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_filter_0) ).

thf(5494,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)],[810]) ).

thf(619,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ? [F: $i] :
                            ( ( F @ ( E @ ( A @ u1_struct_0 @ ( C @ k8_funct_2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) )
                            & ( D @ ( F @ r2_hidden ) )
                            & ( C @ ( F @ m1_subset_1 ) ) )
                       => ( E @ ( D @ ( A @ ( C @ k2_lattice2 ) ) ) @ ( B @ ( A @ r3_lattices ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_lattice2) ).

thf(4555,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ~ ( C @ v1_xboole_0 )
             => ! [D: $i] :
                  ( ( C @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
                 => ! [E: $i] :
                      ( ( ( A @ u1_struct_0 @ ( C @ ( E @ m2_relset_1 ) ) )
                        & ( A @ u1_struct_0 @ ( C @ ( E @ v1_funct_2 ) ) )
                        & ( E @ v1_funct_1 ) )
                     => ( ? [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)],[619]) ).

thf(885,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( ( A @ l3_lattices )
              & ( A @ v12_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 )
              & ( A @ l3_lattices )
              & ( A @ v16_lattices )
              & ( A @ v15_lattices )
              & ( A @ v10_lattices )
              & ~ ( A @ v3_struct_0 ) )
           => ( ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ l3_lattices )
              & ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v16_lattices )
              & ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v15_lattices )
              & ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v10_lattices )
              & ~ ( B @ ( A @ k2_filter_0 ) @ ( A @ k8_filter_0 ) @ v3_struct_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_filter_0) ).

thf(5789,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)],[885]) ).

thf(844,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k2_lattice4 ) )
            = ( A @ k7_grcat_1 @ ( B @ ( A @ ( A @ u1_struct_0 @ k3_lattice2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_lattice4) ).

thf(5618,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)],[844]) ).

thf(2887,plain,
    sk188 @ v9_lattices,
    inference(cnfConj,[status(thm)],[2884]) ).

thf(693,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ k1_lattice2 @ ( B @ m2_lattice4 ) )
        & ~ ( B @ v1_xboole_0 )
        & ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ ( B @ ( A @ k12_filter_2 ) @ m2_lattice4 ) )
        & ~ ( B @ ( A @ k12_filter_2 ) @ v1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_filter_2) ).

thf(4949,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)],[693]) ).

thf(1184,plain,
    ! [A: $i] :
      ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
      | ~ ( A @ v1_funct_1 )
      | ~ ( A @ v1_relat_1 ) ),
    inference(cnfConj,[status(thm)],[1181]) ).

thf(392,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
     => ( B @ v1_finset_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_finsub_1) ).

thf(3405,plain,
    ! [A: $i,B: $i] :
      ( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
     => ( B @ v1_finset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(14804,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
       != ( sk152 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2587,2366]) ).

thf(14805,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
     != ( sk152 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[14804]) ).

thf(14811,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ k4_tarski ) )
     != sk152 ),
    inference(simp,[status(thm)],[14805]) ).

thf(87,axiom,
    ! [A: $i] :
      ( ( A @ v1_relat_1 )
     => ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).

thf(1463,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(746,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ ( A @ k1_filter_0 @ m1_filter_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_filter_0) ).

thf(5183,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)],[746]) ).

thf(2297,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ sk111 ) @ v1_relat_1 ),
    inference(cnfConj,[status(thm)],[2295]) ).

thf(400,axiom,
    ! [A: $i] :
      ( ~ ( A @ v1_xboole_0 )
     => ! [B: $i] :
          ( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
            & ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
            & ( B @ v1_funct_1 ) )
         => ( ( A @ ( B @ v3_binop_1 ) )
          <=> ! [C: $i] :
                ( ( A @ ( C @ m1_subset_1 ) )
               => ( ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
                  = C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_binop_1) ).

thf(3443,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)],[400]) ).

thf(799,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ( ( B @ ( A @ k7_lattices ) @ ( A @ k7_lattices ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_lattices) ).

thf(5445,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)],[799]) ).

thf(947,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ? [B: $i] : ( A @ ( B @ m2_nat_lat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_nat_lat) ).

thf(6072,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)],[947]) ).

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

thf(1416,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(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/sandbox/benchmark/theBenchmark.p',t39_subset_1) ).

thf(2453,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(521,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
        & ( B @ ( A @ ( D @ v1_funct_2 ) ) )
        & ( D @ v1_funct_1 ) )
     => ( ( C @ ( B @ r1_tarski ) )
       => ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
            & ( C @ ( A @ ( D @ v1_funct_2 ) ) )
            & ( D @ v1_funct_1 ) )
          | ( ( A != k1_xboole_0 )
            & ( B = k1_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_2) ).

thf(4056,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)],[521]) ).

thf(854,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ! [B: $i] :
          ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
         => ! [C: $i] :
              ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
             => ! [D: $i] :
                  ( ( A @ ( D @ m1_filter_0 ) )
                 => ( ( D @ ( B @ r2_hidden ) )
                   => ( ( D @ ( B @ ( C @ ( A @ k3_lattices ) ) @ r2_hidden ) )
                      & ( D @ ( C @ ( B @ ( A @ k3_lattices ) ) @ r2_hidden ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_filter_0) ).

thf(5664,plain,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_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)],[854]) ).

thf(2351,plain,
    sk118 @ v1_lattice2,
    inference(cnfConj,[status(thm)],[2342]) ).

thf(551,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v17_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ m2_relset_1 ) ) )
        & ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k5_lattice4 @ v1_funct_2 ) ) )
        & ( A @ k5_lattice4 @ v1_funct_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattice4) ).

thf(4189,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)],[551]) ).

thf(872,axiom,
    ! [A: $i] :
      ( ( ( A @ l3_lattices )
        & ( A @ v10_lattices )
        & ~ ( A @ v3_struct_0 ) )
     => ( A @ u1_struct_0 @ ( A @ u1_lattices @ v3_binop_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_lattice2) ).

thf(5732,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)],[872]) ).

thf(2993,plain,
    sk196 @ v5_lattices,
    inference(cnfConj,[status(thm)],[2983]) ).

thf(50,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_zfmisc_1) ).

thf(1204,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(15322,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
       != ( sk216 @ v1_xboole_0 ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3244,3056]) ).

thf(15323,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
     != ( sk216 @ v1_xboole_0 ) ),
    inference(simp,[status(thm)],[15322]) ).

thf(15327,plain,
    ! [A: $i] :
      ( ( A @ ( A @ k1_funct_2 ) )
     != sk216 ),
    inference(simp,[status(thm)],[15323]) ).

thf(29826,plain,
    ! [A: $i] :
      ( ( A != k6_nat_lat )
      | ( k1_xboole_0 @ v13_lattices )
      | ( A @ sk18 @ v1_funct_1 ) ),
    inference(paramod_ordered,[status(thm)],[1246,5390]) ).

thf(29827,plain,
    ( ( k1_xboole_0 @ v13_lattices )
    | ( k6_nat_lat @ sk18 @ v1_funct_1 ) ),
    inference(pattern_uni,[status(thm)],[29826:[bind(A,$thf( k6_nat_lat ))]]) ).

thf(328,axiom,
    ! [A: $i,B: $i] :
      ( ( A != k1_xboole_0 )
     => ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
         != k1_xboole_0 )
        & ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
         != k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_zfmisc_1) ).

thf(3035,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)],[328]) ).

thf(1014,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)],[1013]) ).

thf(69186,plain,
    $false,
    inference(e,[status(thm)],[2163,5116,1024,1633,4022,1083,8646,1179,6014,4904,2250,7375,3021,5686,1036,4201,7373,45907,1337,5469,3944,5088,29780,1369,4835,2889,1190,1168,2341,3053,4101,2336,3008,2109,4262,5329,1995,12116,3798,33118,5950,3434,2876,1237,3477,3698,1031,5390,1899,5654,2595,4015,6074,6263,5028,6142,6057,3681,1924,4515,10679,3012,2099,2837,4487,12949,4376,1406,5225,5820,4339,19142,1882,6162,1068,3858,3813,2381,5644,2395,2062,5242,16308,1618,994,2527,6900,30125,3098,16280,29195,1073,2671,2676,48319,3108,4326,15325,1971,5691,8928,5529,27696,1041,3382,3217,3794,3942,1164,31369,2901,3895,6278,4234,23438,1655,3120,5565,3745,1137,11399,5906,3004,4839,15651,15217,15299,16283,4638,5146,8370,2476,2168,1260,5674,1919,3253,4247,5005,5178,5636,1095,2432,2020,973,5921,4124,1386,5874,4610,2405,1482,5621,5533,12447,7168,50613,2348,3350,5227,33326,4142,1127,33463,2548,12141,3502,16304,2985,1576,5123,4371,4079,5938,1921,2886,16319,33775,46859,47103,4030,4137,50610,2400,4760,1967,2067,2825,3880,27700,4511,5024,5352,5342,2603,5306,2667,5284,16287,14351,16022,5188,3776,3125,4275,47030,5836,3820,3891,2654,3204,5953,5765,4439,1287,3938,3195,4348,6034,9410,9828,12122,1760,3131,4334,7771,5640,3089,6006,6332,1992,5706,3353,27092,1059,1132,3043,5461,4243,17154,4353,4664,26795,3919,1013,3084,2024,4265,1494,3180,4793,1100,4595,1922,33322,3099,5338,3374,23383,5868,2169,2403,1087,5521,16300,1147,4194,4358,2049,2635,2929,28875,4551,3902,29943,1568,4368,2520,2730,5746,8674,3951,2158,2989,16315,4302,2388,3866,4253,3268,2007,1489,1465,5892,2027,5333,3453,3983,4815,2925,1051,5787,2222,3524,15500,5526,12362,5597,14815,1450,2090,5027,4857,33898,4258,2996,1040,16018,2893,2469,2259,4001,2880,8929,1136,47026,47105,31019,5541,16293,1151,1020,8642,1677,5805,2034,5985,3300,3093,5457,4783,35770,5360,1183,14812,5401,5220,3421,27697,16312,3808,4924,33623,7051,16276,47104,8924,981,2964,5059,1169,15494,2367,1928,5448,4935,6110,30771,3712,15328,4364,11413,1394,4996,5296,5246,3676,5321,4307,16028,8691,998,3243,988,2286,12133,5629,4519,5137,50511,3606,3906,3184,2982,7170,4082,4065,5695,1863,1074,5174,16279,5017,6064,5968,4557,8397,2093,16324,4700,3011,4604,3450,4199,3459,4216,2910,2204,3303,5530,6020,2473,5751,6183,4589,8927,30659,15655,5411,6731,27695,3635,2364,2164,5562,7357,15650,5416,4370,4576,3054,4910,16297,16292,6741,12205,1067,2660,1768,1057,1163,2673,1900,1021,1042,6032,26868,3989,2937,4044,5049,2589,12110,5611,5734,1091,2601,2428,2560,2805,3972,8645,1217,3022,5455,1502,5815,4785,2606,16016,3134,1824,5754,3816,2032,5507,4821,2986,30479,12115,2890,5594,4160,4661,3207,16307,3514,3948,3271,3618,12321,1178,2872,4553,1687,1210,5729,4461,2464,1938,31868,5391,2873,30246,5983,8371,2670,3810,4053,4585,2477,2663,2332,6043,4155,4994,4947,3137,3499,5988,3894,16026,4327,2200,2609,4402,1836,1787,5566,6060,1079,2213,1027,16274,4417,3050,2345,2344,1128,3647,2112,1291,9829,1740,47108,16301,1573,5330,974,1012,5066,4063,1106,3731,1983,5053,6153,4974,5615,1111,4429,1425,3102,3963,4930,16284,15729,3001,3087,4808,1936,3105,3467,28611,2300,5904,1089,2498,3831,2157,2840,1143,5609,8677,2946,2990,1851,9145,4668,2801,33342,2895,1375,6955,1121,8414,2577,14353,50597,1587,12950,23837,5889,4095,5373,4840,12142,10678,4219,32084,5830,2877,3143,1361,5818,3000,3714,2868,5743,3010,41987,2666,7682,2460,1683,1028,47029,5080,5496,3407,6116,11403,33740,1461,2053,2196,5547,6164,5865,3194,2349,2108,2038,1207,3671,2085,2472,1039,970,14318,9825,1974,6129,1050,1246,3064,4086,3162,3703,1825,5063,4846,997,5850,1150,5726,1297,29762,3541,3787,1382,2487,2598,6331,2153,1231,1131,3743,2355,1932,984,2505,4237,4829,1947,5683,4231,9144,3628,6005,1429,3967,2862,4135,5801,3333,4953,3109,1979,4689,3005,28608,4361,12138,1333,5711,48802,4889,2883,7687,3592,2408,1167,2529,1732,30107,5112,5557,4184,12201,2788,16275,5153,7770,1086,4625,6160,5090,3999,47101,2368,1071,2402,1187,4906,2915,16296,2221,5198,2995,46818,5909,3841,5249,5126,2662,1185,2338,3675,12953,4921,4919,5722,6026,1103,38087,2941,12119,16311,4797,5928,4489,4453,1146,2292,3358,5762,42009,2585,8195,3257,1219,9404,3839,15474,4359,5979,3111,3686,4017,2894,4365,975,3768,1125,4122,5962,4709,26238,1154,6140,4786,4144,50516,2970,1007,33324,12951,9142,6617,4283,5488,4494,3255,5395,6108,16030,3609,16302,5067,4309,5923,12143,3736,3081,5940,16323,4677,2674,1535,16278,2991,16313,30127,1403,5097,1795,4328,4590,2817,1124,5503,38089,5535,2161,4978,4127,16291,3002,1058,5148,15329,5997,2474,3568,3170,1139,3796,5185,7191,4186,5118,2293,3051,2891,4837,3651,3695,4149,5331,3594,5086,3783,1092,3700,5703,3579,1765,1090,4854,1897,2557,4640,4273,5158,3719,2319,4790,2721,27172,3631,4369,3815,10675,3779,16317,1589,2955,1122,1194,30105,6144,2346,4716,29793,6024,3238,5244,12227,2987,2637,4305,5848,1011,10677,5491,3106,29216,2669,4139,2943,5407,4213,9146,3197,5093,4667,6154,3138,3182,2896,3384,4773,15654,2871,4509,4107,1307,2065,29825,1175,2742,4445,9830,12111,3192,5392,47028,3583,1293,1177,2974,6956,3893,1112,9407,1667,2180,4635,5367,6087,5584,1877,7768,8192,1080,2632,12114,2343,16020,5082,15497,5994,3073,47107,5335,5439,3800,4264,3932,1162,4985,5286,2785,3006,1149,15487,8372,2874,2289,5180,1022,4726,2664,3861,5254,2350,2401,3917,5299,2156,2207,7356,4084,3480,1171,983,4832,5340,5057,5442,2171,3423,1044,19093,1066,2620,6628,32846,3110,15326,6738,4373,1643,2369,4362,1015,3241,1113,2797,1000,2752,1775,2592,2022,3363,3706,3325,1102,5403,4497,4209,2984,16305,1076,12120,5528,9826,2878,4336,4331,3009,5688,38088,4405,4907,5538,5587,3936,5886,14813,2665,4868,1467,2994,16024,2471,16285,1081,3975,2629,1990,5678,3921,1340,1145,2256,2846,1018,14810,4355,40641,5807,6008,2899,968,4722,4168,6132,5991,3571,4255,2715,15479,971,33666,5944,30123,33070,4469,4324,2882,38091,27152,5452,1748,32358,10672,2298,6069,3391,1003,21193,1025,4360,2397,1070,16298,5250,3112,2375,16032,4939,4366,2588,5499,5748,1647,3129,29941,2407,4894,2850,2160,4593,2888,1186,1038,16281,5948,4781,2468,2656,3019,1053,5955,4409,14795,3246,3642,4346,4398,4240,4092,5418,5467,2165,16295,1300,1452,3791,5555,1869,3475,4768,2276,2219,5309,3774,1317,1763,3544,1901,7769,5543,1658,2322,4800,8644,4982,3412,5638,1579,3095,5106,16318,4959,4976,7374,4431,3007,2675,2056,23256,26757,4802,3107,5902,50594,1257,27238,5736,5223,2992,13585,3356,5613,5240,2279,1955,2843,1485,1052,1585,1094,1140,4695,3024,9406,12952,5364,1008,3943,4342,2939,7192,3256,2892,14747,4795,3156,3914,10674,29945,4671,4111,14496,3684,6622,4278,5981,32416,3589,4770,2885,38094,5966,2347,4780,3725,3056,5068,14791,2865,2875,18085,4639,3284,2626,4138,3457,2352,1084,3067,1180,2870,4165,1157,4873,2078,5386,4944,2310,976,1844,6137,3874,2997,2187,2110,1010,12226,5332,1866,2071,3929,1108,4730,4574,40397,2167,4615,2532,5899,6003,4338,3235,995,4451,16320,3911,6903,1253,2988,3864,5724,4806,6341,3484,1674,3709,1903,4666,2406,4089,6030,3220,4042,1629,3104,3003,5756,1822,3331,3136,12113,39099,5505,3662,16288,16322,1030,5304,3694,5162,45817,3497,3529,33449,2095,4619,1161,4182,5828,8369,3324,5532,4321,2399,3844,2648,3430,1777,15653,5409,1077,3677,6277,2162,5549,6062,5072,6166,2294,5672,5128,16303,41985,2917,4372,2623,1994,13389,4927,15652,1045,1908,1133,5852,999,16294,3987,3264,5430,5041,2517,8209,1957,16289,4687,2155,5971,6007,3291,3997,3733,2587,21248,1229,7171,1593,1380,5078,27686,31091,4843,4787,1303,5477,5371,5601,4357,4491,1757,14814,6150,4579,1480,5398,4367,5926,8368,15172,3328,4565,3558,5413,16321,2366,2404,3426,2223,6040,1742,5559,30078,3015,47027,30903,7772,1859,4146,8400,1314,5709,4281,6114,11401,11415,7050,1335,4083,1172,5564,5741,1033,2961,1197,4865,5378,4442,5642,12121,16299,2668,1165,9409,5200,3673,2021,1346,1610,3244,2159,5803,5061,5236,16412,30155,4363,1930,2353,987,5945,2127,1829,1129,2966,2430,31619,12134,1152,5151,16314,5668,3057,6155,1532,5140,15324,8643,2265,3869,5581,2467,4484,992,1923,3245,36014,16309,29859,5623,5046,3538,1925,4713,6104,4395,3740,14759,1004,3113,1902,3394,1885,4691,3494,16282,5344,2138,3013,1331,47031,5591,12203,3227,1945,2018,2106,3721,2672,2879,2640,5155,4779,5029,3924,50634,2881,5312,5494,4555,5789,5618,2887,4949,1184,3405,14811,1463,5183,2998,2297,3443,5445,6072,1416,2453,4056,5664,2351,4189,5732,2993,1204,15327,29827,3035,1014,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LAT303+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.59  % Computer : n015.cluster.edu
% 0.13/0.59  % Model    : x86_64 x86_64
% 0.13/0.59  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.59  % Memory   : 8046.5625MB
% 0.13/0.59  % OS       : Linux 6.8.0-71-generic
% 0.13/0.59  % CPULimit : 300
% 0.13/0.59  % WCLimit  : 300
% 0.13/0.59  % DateTime : Fri Sep 25 20:41:59 UTC 2026
% 0.13/0.59  % CPUTime  : 
% 0.13/0.59  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.96/1.17  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 3.31/1.87  % [INFO] 	 Parsing done (688ms). 
% 3.31/1.88  % [INFO] 	 Running in sequential loop mode. 
% 4.17/2.18  % [INFO] 	 eprover registered as external prover. 
% 4.17/2.19  % [INFO] 	 Scanning for conjecture ... 
% 4.77/2.38  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2950 axioms. Running axiom selection ... 
% 7.45/2.93  % [INFO] 	 Axiom selection finished. Selected 965 axioms (removed 1985 axioms). 
% 9.03/3.36  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 9.48/3.40  % [INFO] 	 Type checking passed. 
% 9.48/3.40  % [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 ... 
% 169.12/46.12  % External prover 'e' found a proof!
% 169.12/46.12  % [INFO] 	 Killing All external provers ... 
% 169.12/46.12  % Time passed: 45388ms (effective reasoning time: 44233ms)
% 169.12/46.12  % 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)>
% 169.12/46.13  % Axioms used in derivation (965): t31_lattice2, 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, d13_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, 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, t53_subset_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, 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, 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, d1_lattice2, t56_partfun1, t59_partfun1, s12_funct_2, t43_lattices, s3_funct_2, t42_filter_0, cc6_lattices, t57_lattice2, t33_lattice2, t16_funct_2, d16_lattices, t113_zfmisc_1, t67_lattice2, t7_lattice2, t48_domain_1, t111_zfmisc_1, dt_k2_subset_1, t8_subset_1, t80_lattice2, t9_filter_2, existence_l1_lattices, t32_lattice4, d5_tarski, t15_funct_1, dt_k11_domain_1, t26_lattices, fc4_relat_1, t19_lattices, t4_ordinal1, t1_subset, dt_k1_lattice4, t147_relat_1, t10_partfun1, t47_lattice2, d5_xboole_0, t4_lattice4, t9_lattice2, fc4_subset_1, t12_filter_2, t168_funct_2, t10_relset_1, dt_k15_filter_2, fc3_relat_1, d8_funct_1, t69_filter_0, t144_relat_1, t57_domain_1, existence_l3_lattices, dt_k6_nat_lat, 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, 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, fraenkel_a_3_3_domain_1, t50_funct_2, t70_zfmisc_1, t69_zfmisc_1, cc4_lattices, redefinition_k11_filter_0, fc2_filter_2, rc3_funct_1, 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, redefinition_k2_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, 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, d11_filter_0, t26_filter_2, t31_lattices, s13_funct_2, fraenkel_a_2_2_domain_1, t129_zfmisc_1, d4_subset_1, t2_binop_1, d6_binop_1, dt_m1_filter_2, t27_lattices, t64_funct_2, reflexivity_r3_lattices, t20_filter_2, d1_xboole_0, d9_lattices, t56_filter_0, t72_filter_0, fraenkel_a_3_0_filter_0, t130_zfmisc_1, t3_filter_2, t175_partfun1, t15_relat_1, t48_funct_2, fraenkel_a_3_7_domain_1, d16_lattice4, t70_filter_0, t46_filter_0, t40_lattice2, t64_relat_1, t138_zfmisc_1, t25_subset_1, t37_filter_0, rc11_lattices, rc3_lattices, t52_filter_0, t108_zfmisc_1, t165_funct_2, t57_filter_0, dt_l1_lattices, dt_k12_filter_2, dt_k4_lattice4, t60_partfun1, existence_m1_realset1, dt_k11_filter_2, t31_partfun1, dt_k7_lattices, t3_funct_2, rc2_subset_1, existence_l2_lattices, t27_relset_1, t52_domain_1, t118_zfmisc_1, t55_partfun1, s4_subset_1, t8_funct_2, t118_funct_2, t29_lattice4, t76_nat_lat, t14_relset_1, t39_lattice4, t16_relset_1, t38_lattice4, d13_relat_1, t28_lattice2, t164_funct_2, d15_lattice4, fc2_funct_2, t6_boole, t12_funct_1, dt_k6_subset_1, t10_relat_1, d1_relat_1, t59_filter_0, t1_xboole_1, t26_relset_1, cc6_lattice2, t64_partfun1, t47_lattice4, d5_filter_2, existence_l2_struct_0, t32_lattices, t5_lattice4, t19_filter_0, t44_lattice4, t49_filter_0, t5_subset, t17_filter_2, redefinition_k12_filter_0, t29_relat_1, d14_lattice4, t77_funct_2, t59_domain_1, t34_filter_0, d4_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_nat_lat, fc2_subset_1, t45_funct_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, t50_lattices, s8_domain_1, dt_l3_lattices, t48_lattice2, t79_zfmisc_1, t12_lattice2, t5_funct_2, dt_k8_funct_2, d12_lattice4, t16_filter_2, t167_funct_2, dt_m1_struct_0, t17_lattices, t11_funct_2, t40_funct_2, fraenkel_a_0_0_domain_1, t102_zfmisc_1, t24_binop_1, t27_lattice4, t75_lattice2, t4_filter_0, t89_filter_0, dt_l2_lattices, redefinition_k7_domain_1, t40_filter_0, d3_filter_2, t72_partfun1, t8_funct_1, t2_tarski, t16_funct_1, t28_zfmisc_1, t72_zfmisc_1, t82_funct_2, dt_k4_filter_0, t33_xboole_1, s9_domain_1, t84_lattice2, t47_lattices, d7_filter_2, d20_lattices, t8_zfmisc_1, d6_realset1, t67_zfmisc_1, t38_filter_0, d3_lattices, t23_zfmisc_1, t34_lattice4, cc5_lattices, t4_subset, t38_subset_1, d18_lattices, t169_funct_2, t44_lattices, dt_k2_funct_1, cc1_funct_2, t39_subset_1, d8_filter_0, t32_xboole_1, 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, t15_lattice4, t74_zfmisc_1, dt_k8_filter_0, t14_funct_1, t5_filter_2, t9_zfmisc_1, d7_filter_0, existence_m2_realset1, existence_m3_realset1, t56_subset_1, dt_k1_domain_1, t17_funct_2, t85_lattice2, redefinition_k14_filter_2, t75_filter_0, t13_lattice2, fc1_realset1, t25_filter_2, t132_funct_2, t45_lattices, t49_lattice4, t51_funct_2, d12_binop_1, t21_lattices, t12_zfmisc_1, d2_lattice4, t38_lattice2, t139_zfmisc_1, t16_lattice2, cc1_funct_1, t4_funct_2, redefinition_k1_filter_2, d10_lattice4, s11_funct_2, d3_relat_2, s2_domain_1, rc3_struct_0, t3_ordinal1, t9_domain_1, d6_filter_2, t25_lattices, t7_boole, dt_k14_filter_2, dt_k5_lattice4, t11_binop_1, t55_filter_0, t143_relat_1, d2_subset_1, t27_lattice2, commutativity_k4_lattices, redefinition_k9_filter_2, t66_zfmisc_1, fc1_subset_1, t33_zfmisc_1, rc2_lattice2, commutativity_k2_struct_0, t7_filter_2, t23_filter_2, dt_k6_domain_1, t157_funct_1, t31_lattice4, fc5_lattice2, d17_lattices, dt_k2_partfun1, rc2_funct_1, t158_funct_2, dt_k9_filter_0, t90_filter_0, redefinition_k15_filter_2, t4_subset_1, redefinition_k1_domain_1, rc1_funct_2, t26_zfmisc_1, t6_filter_2, t69_partfun1, t7_ordinal1, dt_k10_filter_2, t9_funct_2, t31_funct_2, rc1_subset_1, t48_lattice4, t68_filter_0, fc6_lattice2, t8_lattice2, t18_lattices, cc1_lattices, t5_filter_0, t64_zfmisc_1, fc5_relat_1, dt_k3_lattice2, t30_filter_0, t40_lattice4, t13_filter_2, redefinition_r3_lattices, t40_lattices, t65_funct_1, t4_filter_2, t113_funct_2, t71_partfun1, d21_lattices, t41_lattices, t159_funct_2, t116_zfmisc_1, d4_lattices, existence_m1_filter_0, t2_lattice2, redefinition_m1_filter_2, dt_k2_struct_0, t49_lattices, t14_funct_2, t27_binop_1, t48_lattices, dt_k2_lattice4, t9_filter_0, fc1_nat_lat, fraenkel_a_3_1_domain_1, t60_funct_2, t7_lattice4, 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, 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, t15_subset_1, t44_filter_0, t118_funct_1, d9_binop_1, t19_lattice2, t146_relat_1, t35_xboole_1, t49_domain_1, d17_binop_1, dt_k2_filter_0, dt_k2_funct_2, d2_filter_0, rc1_nat_lat, t5_lattice2, free_g2_struct_0, dt_k20_filter_2, t17_relset_1, cc3_lattices, d5_subset_1, t99_partfun1, t107_zfmisc_1, t9_realset1, t121_funct_2, t114_zfmisc_1, dt_k23_filter_2, t58_partfun1, d1_zfmisc_1, t27_filter_0, t15_filter_2, t11_lattice4, rc2_relat_1, t36_lattice2, existence_m2_relset_1, d4_binop_1, t64_filter_0, t38_zfmisc_1, t75_nat_lat, t9_lattice4, t69_enumset1, t82_lattice2, t22_zfmisc_1, t14_filter_2, d1_filter_0, redefinition_k7_filter_0, t43_funct_2, t1_filter_0, commutativity_k4_subset_1, t62_lattice2, t39_filter_0, t74_lattice2, t11_filter_0, existence_m2_lattice4, t23_lattice4, d4_lattice2, t116_funct_2, fraenkel_a_3_6_domain_1, t168_partfun1, s14_funct_2, t51_filter_0, t14_lattice4, t37_lattice4, redefinition_k2_binop_1, t74_filter_0, t65_lattice2, d5_filter_0, t60_nat_lat, t61_lattice2, t6_funct_2, redefinition_k24_filter_2, t44_lattice2, t41_subset_1, fc3_nat_lat, d3_lattice4, t157_relat_1, cc3_finsub_1, t51_subset_1, t21_subset_1, existence_m1_lattice4, 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, 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, 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, d7_lattice4, t58_filter_0, redefinition_k2_filter_2, d4_xboole_0, t47_filter_0, t39_lattice2, t20_relat_1, dt_k1_lattices, t73_zfmisc_1, t69_lattice2, dt_k12_domain_1, t18_lattice4, d5_binop_1, t54_subset_1, t123_funct_1, t29_lattices, t88_filter_0, d1_relat_2, t82_filter_0, 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, 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, t37_zfmisc_1, 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, 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, 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, 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, t16_binop_1, t66_filter_0, 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, 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
% 169.12/46.13  % No. of inferences in proof: 3424
% 169.12/46.13  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 45388 ms resp. 44233 ms w/o parsing
% 174.56/47.30  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 174.56/47.33  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------