%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SEU424+3 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 11:58:54 EDT 2023

% Result   : Theorem 60.78s 21.27s
% Output   : Refutation 63.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      : 3177
% Syntax   : Number of formulae    : 5770 ( 697 unt; 586 typ;   0 def)
%            Number of atoms       : 27448 (5499 equ;   0 cnn)
%            Maximal formula atoms :   47 (   5 avg)
%            Number of connectives : 105453 (4278   ~; 276   |;10869   &;78911   @)
%                                         ( 444 <=>;10675  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   35 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  : 1220 (1220   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  588 ( 586 usr; 127 con; 0-10 aty)
%            Number of variables   : 17816 (   0   ^;16898   !; 918   ?;17816   :)

% Comments : 
%------------------------------------------------------------------------------
thf(v1_xboole_0_type,type,
    v1_xboole_0: $i > $o ).

thf(m1_subset_1_type,type,
    m1_subset_1: $i > $i > $o ).

thf(k1_zfmisc_1_type,type,
    k1_zfmisc_1: $i > $i ).

thf(m2_relset_1_type,type,
    m2_relset_1: $i > $i > $i > $o ).

thf(a_4_0_relset_2_type,type,
    a_4_0_relset_2: $i > $i > $i > $i > $i ).

thf(k5_finsub_1_type,type,
    k5_finsub_1: $i > $i ).

thf(k6_setwiseo_type,type,
    k6_setwiseo: $i > $i > $i > $i ).

thf(k4_xboole_0_type,type,
    k4_xboole_0: $i > $i > $i ).

thf(v1_funct_1_type,type,
    v1_funct_1: $i > $o ).

thf(v1_funct_2_type,type,
    v1_funct_2: $i > $i > $i > $o ).

thf(k2_zfmisc_1_type,type,
    k2_zfmisc_1: $i > $i > $i ).

thf(v9_monoid_0_type,type,
    v9_monoid_0: $i > $i > $o ).

thf(v1_setwiseo_type,type,
    v1_setwiseo: $i > $i > $o ).

thf(k2_binop_1_type,type,
    k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).

thf(k3_binop_1_type,type,
    k3_binop_1: $i > $i > $i ).

thf(v1_relat_1_type,type,
    v1_relat_1: $i > $o ).

thf(r2_hidden_type,type,
    r2_hidden: $i > $i > $o ).

thf(k1_relat_1_type,type,
    k1_relat_1: $i > $i ).

thf(k5_relat_1_type,type,
    k5_relat_1: $i > $i > $i ).

thf(k1_funct_1_type,type,
    k1_funct_1: $i > $i > $i ).

thf(k2_relat_1_type,type,
    k2_relat_1: $i > $i ).

thf(k7_relat_1_type,type,
    k7_relat_1: $i > $i > $i ).

thf(k3_xboole_0_type,type,
    k3_xboole_0: $i > $i > $i ).

thf(k1_xboole_0_type,type,
    k1_xboole_0: $i ).

thf(k10_finseq_1_type,type,
    k10_finseq_1: $i > $i > $i ).

thf(k2_tarski_type,type,
    k2_tarski: $i > $i > $i ).

thf(k1_tarski_type,type,
    k1_tarski: $i > $i ).

thf(k1_mcart_1_type,type,
    k1_mcart_1: $i > $i ).

thf(k2_mcart_1_type,type,
    k2_mcart_1: $i > $i ).

thf(k4_tarski_type,type,
    k4_tarski: $i > $i > $i ).

thf(k2_funct_4_type,type,
    k2_funct_4: $i > $i ).

thf(v1_binop_1_type,type,
    v1_binop_1: $i > $i > $o ).

thf(k9_setwiseo_type,type,
    k9_setwiseo: $i > $i ).

thf(v2_funct_1_type,type,
    v2_funct_1: $i > $o ).

thf(r1_tarski_type,type,
    r1_tarski: $i > $i > $o ).

thf(k13_funct_3_type,type,
    k13_funct_3: $i > $i > $i ).

thf(v1_finset_1_type,type,
    v1_finset_1: $i > $o ).

thf(k1_cat_1_type,type,
    k1_cat_1: $i > $i > $i > $i ).

thf(k1_numbers_type,type,
    k1_numbers: $i ).

thf(k9_binop_2_type,type,
    k9_binop_2: $i > $i > $i ).

thf(k4_funcop_1_type,type,
    k4_funcop_1: $i > $i > $i > $i ).

thf(k3_funcop_1_type,type,
    k3_funcop_1: $i > $i > $i > $i ).

thf(k2_funcop_1_type,type,
    k2_funcop_1: $i > $i > $i ).

thf(m2_pua2mss1_type,type,
    m2_pua2mss1: $i > $i > $o ).

thf(m2_subset_1_type,type,
    m2_subset_1: $i > $i > $i > $o ).

thf(k5_numbers_type,type,
    k5_numbers: $i ).

thf(m2_finseq_2_type,type,
    m2_finseq_2: $i > $i > $i > $o ).

thf(k4_finseq_2_type,type,
    k4_finseq_2: $i > $i > $i ).

thf(k4_finseq_1_type,type,
    k4_finseq_1: $i > $i ).

thf(k2_finseq_1_type,type,
    k2_finseq_1: $i > $i ).

thf(k9_relat_1_type,type,
    k9_relat_1: $i > $i > $i ).

thf(k4_relat_1_type,type,
    k4_relat_1: $i > $i ).

thf(k6_relat_1_type,type,
    k6_relat_1: $i > $i ).

thf(k19_mcart_1_type,type,
    k19_mcart_1: $i > $i ).

thf(k4_funct_4_type,type,
    k4_funct_4: $i > $i > $i > $i > $i ).

thf(k2_xboole_0_type,type,
    k2_xboole_0: $i > $i > $i ).

thf(r6_binop_1_type,type,
    r6_binop_1: $i > $i > $i > $o ).

thf(k1_binop_1_type,type,
    k1_binop_1: $i > $i > $i > $i ).

thf(m1_pboole_type,type,
    m1_pboole: $i > $i > $o ).

thf(k1_setwiseo_type,type,
    k1_setwiseo: $i > $i ).

thf(r1_binop_1_type,type,
    r1_binop_1: $i > $i > $i > $o ).

thf(m3_pboole_type,type,
    m3_pboole: $i > $i > $i > $i > $o ).

thf(v5_monoid_0_type,type,
    v5_monoid_0: $i > $i > $o ).

thf(v3_monoid_0_type,type,
    v3_monoid_0: $i > $i > $o ).

thf(v4_monoid_0_type,type,
    v4_monoid_0: $i > $i > $o ).

thf(k1_funct_4_type,type,
    k1_funct_4: $i > $i > $i ).

thf(v2_binop_1_type,type,
    v2_binop_1: $i > $i > $o ).

thf(k7_setwiseo_type,type,
    k7_setwiseo: $i > $i > $i > $i > $i > $i ).

thf(k8_funct_2_type,type,
    k8_funct_2: $i > $i > $i > $i > $i ).

thf(r3_binop_1_type,type,
    r3_binop_1: $i > $i > $i > $o ).

thf(k2_setwiseo_type,type,
    k2_setwiseo: $i > $i > $i ).

thf(k5_setwiseo_type,type,
    k5_setwiseo: $i > $i > $i > $i ).

thf(k4_card_3_type,type,
    k4_card_3: $i > $i ).

thf(r1_xboole_0_type,type,
    r1_xboole_0: $i > $i > $o ).

thf(m2_finseq_1_type,type,
    m2_finseq_1: $i > $i > $o ).

thf(k12_finseq_1_type,type,
    k12_finseq_1: $i > $i > $i ).

thf(k11_binop_2_type,type,
    k11_binop_2: $i > $i > $i ).

thf(m1_relset_1_type,type,
    m1_relset_1: $i > $i > $i > $o ).

thf(k10_binop_2_type,type,
    k10_binop_2: $i > $i > $i ).

thf(r1_partfun1_type,type,
    r1_partfun1: $i > $i > $o ).

thf(k1_funct_2_type,type,
    k1_funct_2: $i > $i > $i ).

thf(k7_pboole_type,type,
    k7_pboole: $i > $i > $i > $i > $i ).

thf(k11_finseq_1_type,type,
    k11_finseq_1: $i > $i > $i > $i ).

thf(k3_funct_4_type,type,
    k3_funct_4: $i > $i > $i ).

thf(v3_binop_1_type,type,
    v3_binop_1: $i > $i > $o ).

thf(k4_setwiseo_type,type,
    k4_setwiseo: $i > $i > $i > $i > $i ).

thf(k18_mcart_1_type,type,
    k18_mcart_1: $i > $i ).

thf(k1_closure2_type,type,
    k1_closure2: $i > $i > $i ).

thf(k4_closure2_type,type,
    k4_closure2: $i > $i > $i > $i ).

thf(k9_finseq_1_type,type,
    k9_finseq_1: $i > $i ).

thf(v2_funct_2_type,type,
    v2_funct_2: $i > $i > $i > $o ).

thf(k1_functor0_type,type,
    k1_functor0: $i > $i > $i > $i > $i ).

thf(k3_cqc_lang_type,type,
    k3_cqc_lang: $i > $i > $i ).

thf(k7_funct_2_type,type,
    k7_funct_2: $i > $i > $i > $i > $i > $i ).

thf(k2_funct_1_type,type,
    k2_funct_1: $i > $i ).

thf(k9_funct_2_type,type,
    k9_funct_2: $i > $i > $i > $i ).

thf(k1_funct_5_type,type,
    k1_funct_5: $i > $i ).

thf(k2_funct_5_type,type,
    k2_funct_5: $i > $i ).

thf(k2_ens_1_type,type,
    k2_ens_1: $i > $i ).

thf(k3_ens_1_type,type,
    k3_ens_1: $i > $i > $i ).

thf(k4_ens_1_type,type,
    k4_ens_1: $i > $i > $i ).

thf(k6_ens_1_type,type,
    k6_ens_1: $i > $i > $i > $i ).

thf(v1_finseq_1_type,type,
    v1_finseq_1: $i > $o ).

thf(k7_funcop_1_type,type,
    k7_funcop_1: $i > $i > $i > $i > $i > $i ).

thf(m1_eqrel_1_type,type,
    m1_eqrel_1: $i > $i > $o ).

thf(k2_partfun1_type,type,
    k2_partfun1: $i > $i > $i > $i > $i ).

thf(r6_pboole_type,type,
    r6_pboole: $i > $i > $i > $o ).

thf(k2_midsp_1_type,type,
    k2_midsp_1: $i ).

thf(k7_vectsp_2_type,type,
    k7_vectsp_2: $i ).

thf(k8_vectsp_2_type,type,
    k8_vectsp_2: $i ).

thf(k5_funcop_1_type,type,
    k5_funcop_1: $i > $i > $i > $i ).

thf(r2_binop_1_type,type,
    r2_binop_1: $i > $i > $i > $o ).

thf(k3_urysohn1_type,type,
    k3_urysohn1: $i > $i ).

thf(v1_membered_type,type,
    v1_membered: $i > $o ).

thf(v2_membered_type,type,
    v2_membered: $i > $o ).

thf(k10_ens_1_type,type,
    k10_ens_1: $i > $i ).

thf(k1_domain_1_type,type,
    k1_domain_1: $i > $i > $i > $i > $i ).

thf(k2_funct_2_type,type,
    k2_funct_2: $i > $i > $i > $i > $i ).

thf(k8_setwiseo_type,type,
    k8_setwiseo: $i > $i > $i > $i > $i ).

thf(k1_partfun1_type,type,
    k1_partfun1: $i > $i > $i > $i > $i > $i > $i ).

thf(k15_funct_3_type,type,
    k15_funct_3: $i > $i > $i ).

thf(k33_binop_2_type,type,
    k33_binop_2: $i ).

thf(k6_funcop_1_type,type,
    k6_funcop_1: $i > $i > $i > $i > $i > $i ).

thf(k8_funcop_1_type,type,
    k8_funcop_1: $i > $i > $i > $i > $i > $i ).

thf(k12_mcart_1_type,type,
    k12_mcart_1: $i > $i > $i > $i > $i ).

thf(k6_partfun1_type,type,
    k6_partfun1: $i > $i ).

thf(k7_filter_1_type,type,
    k7_filter_1: $i > $i > $i > $i > $i ).

thf(v1_classes2_type,type,
    v1_classes2: $i > $o ).

thf(k9_funct_3_type,type,
    k9_funct_3: $i > $i > $i ).

thf(k35_binop_2_type,type,
    k35_binop_2: $i ).

thf(m2_filter_1_type,type,
    m2_filter_1: $i > $i > $i > $o ).

thf(k1_funct_3_type,type,
    k1_funct_3: $i > $i ).

thf(k4_relset_1_type,type,
    k4_relset_1: $i > $i > $i > $i ).

thf(v8_monoid_0_type,type,
    v8_monoid_0: $i > $i > $o ).

thf(v6_monoid_0_type,type,
    v6_monoid_0: $i > $i > $o ).

thf(v7_monoid_0_type,type,
    v7_monoid_0: $i > $i > $o ).

thf(k17_mcart_1_type,type,
    k17_mcart_1: $i > $i ).

thf(k3_setwiseo_type,type,
    k3_setwiseo: $i > $i > $i > $i ).

thf(k4_partfun1_type,type,
    k4_partfun1: $i > $i > $i ).

thf(k1_enumset1_type,type,
    k1_enumset1: $i > $i > $i > $i ).

thf(k1_metric_1_type,type,
    k1_metric_1: $i > $i > $i > $i > $i > $i ).

thf(k12_binop_2_type,type,
    k12_binop_2: $i > $i > $i ).

thf(k3_tarski_type,type,
    k3_tarski: $i > $i ).

thf(k12_funct_3_type,type,
    k12_funct_3: $i > $i ).

thf(k10_setwiseo_type,type,
    k10_setwiseo: $i > $i > $i > $i > $i ).

thf(k16_funct_3_type,type,
    k16_funct_3: $i > $i > $i > $i > $i > $i > $i ).

thf(k1_realset1_type,type,
    k1_realset1: $i > $i > $i ).

thf(k6_enumset1_type,type,
    k6_enumset1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(k4_enumset1_type,type,
    k4_enumset1: $i > $i > $i > $i > $i > $i > $i ).

thf(m1_card_fil_type,type,
    m1_card_fil: $i > $i > $o ).

thf(v2_card_fil_type,type,
    v2_card_fil: $i > $i > $o ).

thf(v3_card_fil_type,type,
    v3_card_fil: $i > $i > $o ).

thf(k5_enumset1_type,type,
    k5_enumset1: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(k3_enumset1_type,type,
    k3_enumset1: $i > $i > $i > $i > $i > $i ).

thf(k4_zfmisc_1_type,type,
    k4_zfmisc_1: $i > $i > $i > $i > $i ).

thf(k4_mcart_1_type,type,
    k4_mcart_1: $i > $i > $i > $i > $i ).

thf(v1_realset1_type,type,
    v1_realset1: $i > $o ).

thf(m4_realset1_type,type,
    m4_realset1: $i > $i > $o ).

thf(k8_mcart_1_type,type,
    k8_mcart_1: $i > $i > $i > $i > $i > $i ).

thf(k3_zfmisc_1_type,type,
    k3_zfmisc_1: $i > $i > $i > $i ).

thf(k3_mcart_1_type,type,
    k3_mcart_1: $i > $i > $i > $i ).

thf(k5_xboole_0_type,type,
    k5_xboole_0: $i > $i > $i ).

thf(k5_relset_1_type,type,
    k5_relset_1: $i > $i > $i > $i ).

thf(k1_setfam_1_type,type,
    k1_setfam_1: $i > $i ).

thf(v6_ordinal1_type,type,
    v6_ordinal1: $i > $o ).

thf(a_1_0_lattice5_type,type,
    a_1_0_lattice5: $i > $i ).

thf(k5_setfam_1_type,type,
    k5_setfam_1: $i > $i > $i ).

thf(a_3_0_relset_2_type,type,
    a_3_0_relset_2: $i > $i > $i > $i ).

thf(k1_relset_2_type,type,
    k1_relset_2: $i > $i > $i > $i ).

thf(k3_setfam_1_type,type,
    k3_setfam_1: $i > $i > $i ).

thf(v1_partfun1_type,type,
    v1_partfun1: $i > $i > $i > $o ).

thf(v4_finsub_1_type,type,
    v4_finsub_1: $i > $o ).

thf(k1_finsub_1_type,type,
    k1_finsub_1: $i > $i > $i > $i ).

thf(k9_mcart_1_type,type,
    k9_mcart_1: $i > $i > $i > $i > $i > $i ).

thf(k3_funct_2_type,type,
    k3_funct_2: $i > $i > $i > $i > $i ).

thf(k8_binop_2_type,type,
    k8_binop_2: $i > $i ).

thf(k3_subset_1_type,type,
    k3_subset_1: $i > $i > $i ).

thf(k5_mcart_1_type,type,
    k5_mcart_1: $i > $i > $i > $i > $i ).

thf(k6_mcart_1_type,type,
    k6_mcart_1: $i > $i > $i > $i > $i ).

thf(k7_mcart_1_type,type,
    k7_mcart_1: $i > $i > $i > $i > $i ).

thf(v1_setfam_1_type,type,
    v1_setfam_1: $i > $o ).

thf(k5_partfun1_type,type,
    k5_partfun1: $i > $i > $i > $i ).

thf(k6_subset_1_type,type,
    k6_subset_1: $i > $i > $i > $i ).

thf(k6_pralg_1_type,type,
    k6_pralg_1: $i > $i > $i ).

thf(k10_mcart_1_type,type,
    k10_mcart_1: $i > $i > $i > $i > $i > $i ).

thf(k11_mcart_1_type,type,
    k11_mcart_1: $i > $i > $i > $i > $i > $i ).

thf(k12_ens_1_type,type,
    k12_ens_1: $i > $i ).

thf(g1_cat_1_type,type,
    g1_cat_1: $i > $i > $i > $i > $i > $i > $i ).

thf(k8_ens_1_type,type,
    k8_ens_1: $i > $i ).

thf(k9_ens_1_type,type,
    k9_ens_1: $i > $i ).

thf(k11_ens_1_type,type,
    k11_ens_1: $i > $i ).

thf(k4_qc_lang1_type,type,
    k4_qc_lang1: $i ).

thf(k2_qc_lang1_type,type,
    k2_qc_lang1: $i ).

thf(k6_cqc_lang_type,type,
    k6_cqc_lang: $i > $i > $i ).

thf(k18_group_2_type,type,
    k18_group_2: $i > $i > $i ).

thf(m3_realset1_type,type,
    m3_realset1: $i > $i > $i > $o ).

thf(k4_realset1_type,type,
    k4_realset1: $i > $i > $i > $i ).

thf(k2_borsuk_1_type,type,
    k2_borsuk_1: $i > $i > $i ).

thf(k6_domain_1_type,type,
    k6_domain_1: $i > $i > $i ).

thf(k7_cat_1_type,type,
    k7_cat_1: $i > $i > $i ).

thf(a_0_0_altcat_2_type,type,
    a_0_0_altcat_2: $i ).

thf(k10_funct_3_type,type,
    k10_funct_3: $i > $i > $i ).

thf(k5_domain_1_type,type,
    k5_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(k10_relset_1_type,type,
    k10_relset_1: $i > $i > $i > $i > $i ).

thf(k11_relset_1_type,type,
    k11_relset_1: $i > $i > $i > $i > $i ).

thf(m1_functor0_type,type,
    m1_functor0: $i > $i > $i > $i > $i > $i > $o ).

thf(k4_urysohn1_type,type,
    k4_urysohn1: $i ).

thf(m1_realset1_type,type,
    m1_realset1: $i > $i > $i > $o ).

thf(k4_funct_2_type,type,
    k4_funct_2: $i > $i > $i > $i ).

thf(v1_fraenkel_type,type,
    v1_fraenkel: $i > $o ).

thf(k2_cantor_1_type,type,
    k2_cantor_1: $i > $i > $i ).

thf(a_3_1_pua2mss1_type,type,
    a_3_1_pua2mss1: $i > $i > $i > $i ).

thf(k2_enumset1_type,type,
    k2_enumset1: $i > $i > $i > $i > $i ).

thf(k36_binop_2_type,type,
    k36_binop_2: $i ).

thf(k10_pboole_type,type,
    k10_pboole: $i > $i > $i ).

thf(k13_pboole_type,type,
    k13_pboole: $i > $i > $i ).

thf(k7_ens_1_type,type,
    k7_ens_1: $i > $i > $i > $i ).

thf(r4_nattra_1_type,type,
    r4_nattra_1: $i > $i > $i > $i > $i > $i > $o ).

thf(k2_card_fil_type,type,
    k2_card_fil: $i > $i > $i ).

thf(m1_fraenkel_type,type,
    m1_fraenkel: $i > $i > $i > $o ).

thf(k1_cat_2_type,type,
    k1_cat_2: $i > $i > $i > $i > $i > $i > $i ).

thf(m1_filter_1_type,type,
    m1_filter_1: $i > $i > $i > $o ).

thf(k7_metric_1_type,type,
    k7_metric_1: $i ).

thf(k4_subset_1_type,type,
    k4_subset_1: $i > $i > $i > $i ).

thf(k9_cat_2_type,type,
    k9_cat_2: $i > $i > $i > $i > $i > $i > $i ).

thf(k9_funcop_1_type,type,
    k9_funcop_1: $i > $i > $i > $i > $i ).

thf(k11_setwiseo_type,type,
    k11_setwiseo: $i > $i ).

thf(k2_nattra_1_type,type,
    k2_nattra_1: $i > $i > $i > $i > $i > $i > $i ).

thf(k10_cat_2_type,type,
    k10_cat_2: $i > $i > $i > $i > $i ).

thf(k14_funct_3_type,type,
    k14_funct_3: $i > $i > $i > $i > $i > $i ).

thf(r2_realset1_type,type,
    r2_realset1: $i > $i > $i > $o ).

thf(k7_binop_2_type,type,
    k7_binop_2: $i > $i ).

thf(k4_domain_1_type,type,
    k4_domain_1: $i > $i > $i > $i > $i > $i > $i ).

thf(k5_subset_1_type,type,
    k5_subset_1: $i > $i > $i > $i ).

thf(k5_ens_1_type,type,
    k5_ens_1: $i > $i > $i ).

thf(k1_multop_1_type,type,
    k1_multop_1: $i > $i > $i > $i > $i ).

thf(k20_mcart_1_type,type,
    k20_mcart_1: $i > $i ).

thf(a_2_0_domain_1_type,type,
    a_2_0_domain_1: $i > $i > $i ).

thf(k3_multop_1_type,type,
    k3_multop_1: $i > $i > $i > $i > $i > $i ).

thf(r2_subset_1_type,type,
    r2_subset_1: $i > $i > $o ).

thf(k2_monoid_0_type,type,
    k2_monoid_0: $i > $i > $i > $i ).

thf(k3_cantor_1_type,type,
    k3_cantor_1: $i > $i > $i > $i > $i > $i ).

thf(k1_pcomps_1_type,type,
    k1_pcomps_1: $i > $i ).

thf(k14_borsuk_1_type,type,
    k14_borsuk_1: $i > $i > $i > $i > $i ).

thf(k1_card_fil_type,type,
    k1_card_fil: $i > $i > $i ).

thf(k6_setfam_1_type,type,
    k6_setfam_1: $i > $i > $i ).

thf(a_1_0_ens_1_type,type,
    a_1_0_ens_1: $i > $i ).

thf(m1_finseq_2_type,type,
    m1_finseq_2: $i > $i > $o ).

thf(k7_subset_1_type,type,
    k7_subset_1: $i > $i > $i > $i ).

thf(k7_relset_1_type,type,
    k7_relset_1: $i > $i > $i > $i > $i > $i > $i ).

thf(k2_realset1_type,type,
    k2_realset1: $i > $i > $i > $i ).

thf(k8_setfam_1_type,type,
    k8_setfam_1: $i > $i > $i ).

thf(k5_relset_2_type,type,
    k5_relset_2: $i > $i > $i ).

thf(k1_toler_1_type,type,
    k1_toler_1: $i > $i > $i ).

thf(u1_cat_1_type,type,
    u1_cat_1: $i > $i ).

thf(k2_functor0_type,type,
    k2_functor0: $i > $i > $i > $i > $i > $i > $i ).

thf(a_6_0_functor0_type,type,
    a_6_0_functor0: $i > $i > $i > $i > $i > $i > $i ).

thf(a_4_0_domain_1_type,type,
    a_4_0_domain_1: $i > $i > $i > $i > $i ).

thf(k15_classes2_type,type,
    k15_classes2: $i > $i ).

thf(k10_funcop_1_type,type,
    k10_funcop_1: $i > $i > $i > $i > $i ).

thf(r1_lattice2_type,type,
    r1_lattice2: $i > $i > $i > $o ).

thf(k7_domain_1_type,type,
    k7_domain_1: $i > $i > $i > $i ).

thf(a_3_0_domain_1_type,type,
    a_3_0_domain_1: $i > $i > $i > $i ).

thf(k1_nattra_1_type,type,
    k1_nattra_1: $i > $i > $i > $i > $i ).

thf(k1_oppcat_1_type,type,
    k1_oppcat_1: $i > $i > $i > $i > $i ).

thf(a_1_1_ens_1_type,type,
    a_1_1_ens_1: $i > $i ).

thf(r7_binop_1_type,type,
    r7_binop_1: $i > $i > $i > $o ).

thf(k34_binop_2_type,type,
    k34_binop_2: $i ).

thf(v1_yellow18_type,type,
    v1_yellow18: $i > $i > $i > $i > $o ).

thf(m1_orders_1_type,type,
    m1_orders_1: $i > $i > $o ).

thf(m2_realset1_type,type,
    m2_realset1: $i > $i > $i > $o ).

thf(k3_realset1_type,type,
    k3_realset1: $i > $i > $i > $i ).

thf(k2_funct_3_type,type,
    k2_funct_3: $i > $i > $i > $i ).

thf(k1_cantor_1_type,type,
    k1_cantor_1: $i > $i > $i ).

thf(k1_funct_7_type,type,
    k1_funct_7: $i > $i > $i ).

thf(k1_qc_lang1_type,type,
    k1_qc_lang1: $i ).

thf(g1_group_1_type,type,
    g1_group_1: $i > $i > $i ).

thf(a_0_0_pre_circ_type,type,
    a_0_0_pre_circ: $i ).

thf(g2_vectsp_1_type,type,
    g2_vectsp_1: $i > $i > $i > $i > $i ).

thf(f2_s1_card_fil_type,type,
    f2_s1_card_fil: $i ).

thf(a_0_0_card_fil_type,type,
    a_0_0_card_fil: $i ).

thf(p1_s1_card_fil_type,type,
    p1_s1_card_fil: $i > $o ).

thf(k3_cat_5_type,type,
    k3_cat_5: $i > $i > $i > $i ).

thf(g3_lattices_type,type,
    g3_lattices: $i > $i > $i > $i ).

thf(k1_orders_1_type,type,
    k1_orders_1: $i > $i ).

thf(k3_relset_2_type,type,
    k3_relset_2: $i > $i > $i > $i > $i ).

thf(f1_s2_multop_1_type,type,
    f1_s2_multop_1: $i ).

thf(p1_s2_multop_1_type,type,
    p1_s2_multop_1: $i > $i > $i > $i > $o ).

thf(k2_multop_1_type,type,
    k2_multop_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(k1_ens_1_type,type,
    k1_ens_1: $i > $i ).

thf(f1_s1_setwiseo_type,type,
    f1_s1_setwiseo: $i ).

thf(f2_s1_setwiseo_type,type,
    f2_s1_setwiseo: $i ).

thf(p1_s1_setwiseo_type,type,
    p1_s1_setwiseo: $i > $i > $o ).

thf(k13_ens_1_type,type,
    k13_ens_1: $i > $i > $i ).

thf(r1_realset1_type,type,
    r1_realset1: $i > $i > $i > $o ).

thf(k7_setfam_1_type,type,
    k7_setfam_1: $i > $i > $i ).

thf(k5_funcsdom_type,type,
    k5_funcsdom: $i > $i > $i > $i > $i > $i ).

thf(k9_zf_lang_type,type,
    k9_zf_lang: $i ).

thf(r1_zfrefle1_type,type,
    r1_zfrefle1: $i > $i > $o ).

thf(r3_zfrefle1_type,type,
    r3_zfrefle1: $i > $i > $o ).

thf(r2_zfrefle1_type,type,
    r2_zfrefle1: $i > $i > $o ).

thf(v2_cat_5_type,type,
    v2_cat_5: $i > $o ).

thf(m1_cat_5_type,type,
    m1_cat_5: $i > $i > $o ).

thf(k3_classes2_type,type,
    k3_classes2: $i > $i > $i ).

thf(a_2_3_domain_1_type,type,
    a_2_3_domain_1: $i > $i > $i ).

thf(p1_s2_domain_1_type,type,
    p1_s2_domain_1: $i > $i > $o ).

thf(k8_classes2_type,type,
    k8_classes2: $i > $i > $i > $i ).

thf(v2_setfam_1_type,type,
    v2_setfam_1: $i > $o ).

thf(k9_relset_1_type,type,
    k9_relset_1: $i > $i > $i > $i > $i ).

thf(v1_zf_model_type,type,
    v1_zf_model: $i > $o ).

thf(k2_zfrefle1_type,type,
    k2_zfrefle1: $i ).

thf(k1_borsuk_1_type,type,
    k1_borsuk_1: $i > $i > $i > $i ).

thf(k15_ens_1_type,type,
    k15_ens_1: $i > $i > $i ).

thf(u2_cat_1_type,type,
    u2_cat_1: $i > $i ).

thf(k9_classes2_type,type,
    k9_classes2: $i > $i > $i > $i ).

thf(k4_classes2_type,type,
    k4_classes2: $i > $i > $i ).

thf(g1_lattices_type,type,
    g1_lattices: $i > $i > $i ).

thf(a_0_0_yellow_3_type,type,
    a_0_0_yellow_3: $i ).

thf(f1_s1_yellow_3_type,type,
    f1_s1_yellow_3: $i ).

thf(f2_s1_yellow_3_type,type,
    f2_s1_yellow_3: $i > $i > $i ).

thf(p1_s1_yellow_3_type,type,
    p1_s1_yellow_3: $i > $i > $o ).

thf(k5_metric_1_type,type,
    k5_metric_1: $i > $i ).

thf(m2_card_fil_type,type,
    m2_card_fil: $i > $i > $o ).

thf(k8_waybel_5_type,type,
    k8_waybel_5: $i > $i > $i > $i > $i ).

thf(v5_grcat_1_type,type,
    v5_grcat_1: $i > $o ).

thf(m3_grcat_1_type,type,
    m3_grcat_1: $i > $i > $o ).

thf(k2_subset_1_type,type,
    k2_subset_1: $i > $i ).

thf(k6_funct_3_type,type,
    k6_funct_3: $i > $i > $i ).

thf(a_1_2_ens_1_type,type,
    a_1_2_ens_1: $i > $i ).

thf(a_2_0_lattice5_type,type,
    a_2_0_lattice5: $i > $i > $i ).

thf(k11_classes2_type,type,
    k11_classes2: $i > $i > $i > $i ).

thf(g2_rlvect_1_type,type,
    g2_rlvect_1: $i > $i > $i > $i > $i ).

thf(k32_binop_2_type,type,
    k32_binop_2: $i ).

thf(k4_relset_2_type,type,
    k4_relset_2: $i > $i > $i > $i > $i ).

thf(f1_s1_binop_2_type,type,
    f1_s1_binop_2: $i ).

thf(f2_s1_binop_2_type,type,
    f2_s1_binop_2: $i ).

thf(f3_s1_binop_2_type,type,
    f3_s1_binop_2: $i > $i ).

thf(k3_qc_lang1_type,type,
    k3_qc_lang1: $i ).

thf(k5_urysohn1_type,type,
    k5_urysohn1: $i ).

thf(k6_relset_2_type,type,
    k6_relset_2: $i > $i > $i > $i ).

thf(g3_quantal1_type,type,
    g3_quantal1: $i > $i > $i > $i > $i > $i > $i ).

thf(k9_relset_2_type,type,
    k9_relset_2: $i > $i > $i > $i > $i > $i ).

thf(k1_subset_1_type,type,
    k1_subset_1: $i > $i ).

thf(k10_classes2_type,type,
    k10_classes2: $i > $i > $i > $i ).

thf(v1_tex_2_type,type,
    v1_tex_2: $i > $i > $o ).

thf(k3_card_fil_type,type,
    k3_card_fil: $i > $i > $i > $i ).

thf(v4_orders_3_type,type,
    v4_orders_3: $i > $o ).

thf(k2_yellow21_type,type,
    k2_yellow21: $i > $i ).

thf(k6_classes2_type,type,
    k6_classes2: $i > $i > $i > $i ).

thf(k4_finsub_1_type,type,
    k4_finsub_1: $i > $i > $i > $i ).

thf(k3_funcsdom_type,type,
    k3_funcsdom: $i > $i > $i > $i ).

thf(k31_binop_2_type,type,
    k31_binop_2: $i ).

thf(g1_vectsp_1_type,type,
    g1_vectsp_1: $i > $i > $i > $i ).

thf(k2_relset_2_type,type,
    k2_relset_2: $i > $i > $i > $i > $i ).

thf(a_3_0_ens_1_type,type,
    a_3_0_ens_1: $i > $i > $i > $i ).

thf(v2_pre_topc_type,type,
    v2_pre_topc: $i > $o ).

thf(g1_pre_topc_type,type,
    g1_pre_topc: $i > $i > $i ).

thf(k12_classes2_type,type,
    k12_classes2: $i > $i > $i > $i ).

thf(a_0_32_fraenkel_type,type,
    a_0_32_fraenkel: $i ).

thf(f2_s17_fraenkel_type,type,
    f2_s17_fraenkel: $i ).

thf(m1_orders_3_type,type,
    m1_orders_3: $i > $i > $o ).

thf(k19_pralg_1_type,type,
    k19_pralg_1: $i > $i > $i > $i ).

thf(a_2_0_borsuk_1_type,type,
    a_2_0_borsuk_1: $i > $i > $i ).

thf(g1_rlvect_1_type,type,
    g1_rlvect_1: $i > $i > $i > $i ).

thf(a_0_33_fraenkel_type,type,
    a_0_33_fraenkel: $i ).

thf(f2_s18_fraenkel_type,type,
    f2_s18_fraenkel: $i ).

thf(k2_yellow_3_type,type,
    k2_yellow_3: $i > $i > $i > $i > $i > $i > $i ).

thf(a_4_1_yellow_9_type,type,
    a_4_1_yellow_9: $i > $i > $i > $i > $i ).

thf(a_4_0_pua2mss1_type,type,
    a_4_0_pua2mss1: $i > $i > $i > $i > $i ).

thf(g3_vectsp_1_type,type,
    g3_vectsp_1: $i > $i > $i > $i > $i > $i ).

thf(k1_cqc_lang_type,type,
    k1_cqc_lang: $i > $i > $i > $i > $i ).

thf(k1_cat_5_type,type,
    k1_cat_5: $i > $i > $i > $i > $i ).

thf(f1_s4_funct_2_type,type,
    f1_s4_funct_2: $i ).

thf(f2_s4_funct_2_type,type,
    f2_s4_funct_2: $i ).

thf(f3_s4_funct_2_type,type,
    f3_s4_funct_2: $i > $i ).

thf(k1_urysohn1_type,type,
    k1_urysohn1: $i ).

thf(k2_urysohn1_type,type,
    k2_urysohn1: $i ).

thf(k17_domain_1_type,type,
    k17_domain_1: $i > $i > $i > $i > $i ).

thf(k7_classes2_type,type,
    k7_classes2: $i > $i > $i > $i ).

thf(a_3_1_card_fil_type,type,
    a_3_1_card_fil: $i > $i > $i > $i ).

thf(k6_lattice5_type,type,
    k6_lattice5: $i > $i ).

thf(g1_funcsdom_type,type,
    g1_funcsdom: $i > $i > $i > $i > $i > $i > $i ).

thf(k15_domain_1_type,type,
    k15_domain_1: $i > $i > $i > $i > $i ).

thf(m2_cantor_1_type,type,
    m2_cantor_1: $i > $i > $o ).

thf(f2_s21_fraenkel_type,type,
    f2_s21_fraenkel: $i ).

thf(a_0_38_fraenkel_type,type,
    a_0_38_fraenkel: $i ).

thf(g1_quantal1_type,type,
    g1_quantal1: $i > $i > $i > $i > $i ).

thf(a_1_0_pua2mss1_type,type,
    a_1_0_pua2mss1: $i > $i ).

thf(f1_s14_funct_2_type,type,
    f1_s14_funct_2: $i ).

thf(f2_s14_funct_2_type,type,
    f2_s14_funct_2: $i ).

thf(p1_s14_funct_2_type,type,
    p1_s14_funct_2: $i > $i > $o ).

thf(f1_s13_funct_2_type,type,
    f1_s13_funct_2: $i ).

thf(f3_s13_funct_2_type,type,
    f3_s13_funct_2: $i > $i ).

thf(f2_s13_funct_2_type,type,
    f2_s13_funct_2: $i ).

thf(f1_s12_funct_2_type,type,
    f1_s12_funct_2: $i ).

thf(f3_s12_funct_2_type,type,
    f3_s12_funct_2: $i > $i ).

thf(f2_s12_funct_2_type,type,
    f2_s12_funct_2: $i ).

thf(g2_quantal1_type,type,
    g2_quantal1: $i > $i > $i > $i > $i > $i ).

thf(k14_domain_1_type,type,
    k14_domain_1: $i > $i > $i > $i > $i ).

thf(k4_card_fil_type,type,
    k4_card_fil: $i > $i ).

thf(m1_cantor_1_type,type,
    m1_cantor_1: $i > $i > $o ).

thf(a_3_0_card_fil_type,type,
    a_3_0_card_fil: $i > $i > $i > $i ).

thf(k4_multop_1_type,type,
    k4_multop_1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(k17_monoid_0_type,type,
    k17_monoid_0: $i > $i ).

thf(a_0_18_fraenkel_type,type,
    a_0_18_fraenkel: $i ).

thf(f1_s10_fraenkel_type,type,
    f1_s10_fraenkel: $i ).

thf(g2_lattices_type,type,
    g2_lattices: $i > $i > $i ).

thf(k2_cat_5_type,type,
    k2_cat_5: $i > $i > $i > $i > $i ).

thf(a_2_0_cantor_1_type,type,
    a_2_0_cantor_1: $i > $i > $i ).

thf(g1_metric_1_type,type,
    g1_metric_1: $i > $i > $i ).

thf(k3_pre_circ_type,type,
    k3_pre_circ: $i > $i > $i > $i ).

thf(k23_qc_lang1_type,type,
    k23_qc_lang1: $i > $i ).

thf(k3_metric_1_type,type,
    k3_metric_1: $i ).

thf(k1_classes2_type,type,
    k1_classes2: $i > $i > $i ).

thf(f1_s3_funct_2_type,type,
    f1_s3_funct_2: $i ).

thf(f2_s3_funct_2_type,type,
    f2_s3_funct_2: $i ).

thf(p1_s3_funct_2_type,type,
    p1_s3_funct_2: $i > $i > $o ).

thf(k5_classes2_type,type,
    k5_classes2: $i > $i > $i > $i ).

thf(k2_finsub_1_type,type,
    k2_finsub_1: $i > $i > $i > $i ).

thf(f3_s22_fraenkel_type,type,
    f3_s22_fraenkel: $i ).

thf(f4_s22_fraenkel_type,type,
    f4_s22_fraenkel: $i ).

thf(a_0_39_fraenkel_type,type,
    a_0_39_fraenkel: $i ).

thf(k5_funct_4_type,type,
    k5_funct_4: $i > $i > $i > $i > $i > $i ).

thf(f1_s1_funct_7_type,type,
    f1_s1_funct_7: $i ).

thf(f2_s1_funct_7_type,type,
    f2_s1_funct_7: $i ).

thf(f4_s1_funct_7_type,type,
    f4_s1_funct_7: $i > $i > $i ).

thf(f3_s1_funct_7_type,type,
    f3_s1_funct_7: $i ).

thf(f1_s1_altcat_2_type,type,
    f1_s1_altcat_2: $i ).

thf(f2_s1_altcat_2_type,type,
    f2_s1_altcat_2: $i > $i ).

thf(p1_s1_altcat_2_type,type,
    p1_s1_altcat_2: $i > $o ).

thf(a_1_2_domain_1_type,type,
    a_1_2_domain_1: $i > $i ).

thf(p1_s1_domain_1_type,type,
    p1_s1_domain_1: $i > $o ).

thf(f1_s4_altcat_1_type,type,
    f1_s4_altcat_1: $i ).

thf(f2_s4_altcat_1_type,type,
    f2_s4_altcat_1: $i ).

thf(f3_s4_altcat_1_type,type,
    f3_s4_altcat_1: $i ).

thf(f4_s4_altcat_1_type,type,
    f4_s4_altcat_1: $i > $i > $i > $i ).

thf(m1_nat_lat_type,type,
    m1_nat_lat: $i > $i > $i > $i > $o ).

thf(k11_domain_1_type,type,
    k11_domain_1: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(k2_cqc_lang_type,type,
    k2_cqc_lang: $i > $i > $i > $i > $i > $i ).

thf(k13_mcart_1_type,type,
    k13_mcart_1: $i > $i > $i > $i > $i > $i > $i ).

thf(a_6_0_domain_1_type,type,
    a_6_0_domain_1: $i > $i > $i > $i > $i > $i > $i ).

thf(a_3_6_domain_1_type,type,
    a_3_6_domain_1: $i > $i > $i > $i ).

thf(a_2_1_domain_1_type,type,
    a_2_1_domain_1: $i > $i > $i ).

thf(a_0_2_domain_1_type,type,
    a_0_2_domain_1: $i ).

thf(f3_s9_domain_1_type,type,
    f3_s9_domain_1: $i ).

thf(k14_mcart_1_type,type,
    k14_mcart_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(a_0_0_domain_1_type,type,
    a_0_0_domain_1: $i ).

thf(f1_s7_domain_1_type,type,
    f1_s7_domain_1: $i ).

thf(f1_s4_multop_1_type,type,
    f1_s4_multop_1: $i ).

thf(f2_s4_multop_1_type,type,
    f2_s4_multop_1: $i ).

thf(f3_s4_multop_1_type,type,
    f3_s4_multop_1: $i ).

thf(f4_s4_multop_1_type,type,
    f4_s4_multop_1: $i ).

thf(f5_s4_multop_1_type,type,
    f5_s4_multop_1: $i > $i > $i > $i ).

thf(f3_s11_funct_2_type,type,
    f3_s11_funct_2: $i ).

thf(f4_s11_funct_2_type,type,
    f4_s11_funct_2: $i ).

thf(f1_s11_funct_2_type,type,
    f1_s11_funct_2: $i ).

thf(f2_s11_funct_2_type,type,
    f2_s11_funct_2: $i ).

thf(f5_s11_funct_2_type,type,
    f5_s11_funct_2: $i ).

thf(f6_s11_funct_2_type,type,
    f6_s11_funct_2: $i ).

thf(f7_s11_funct_2_type,type,
    f7_s11_funct_2: $i > $i ).

thf(m1_pua2mss1_type,type,
    m1_pua2mss1: $i > $i > $i > $i > $o ).

thf(k16_domain_1_type,type,
    k16_domain_1: $i > $i > $i > $i > $i ).

thf(p1_s7_domain_1_type,type,
    p1_s7_domain_1: $i > $o ).

thf(f1_s6_filter_1_type,type,
    f1_s6_filter_1: $i ).

thf(f2_s6_filter_1_type,type,
    f2_s6_filter_1: $i ).

thf(p1_s6_filter_1_type,type,
    p1_s6_filter_1: $i > $i > $i > $o ).

thf(r1_filter_2_type,type,
    r1_filter_2: $i > $i > $i > $o ).

thf(m1_triang_1_type,type,
    m1_triang_1: $i > $i > $i > $o ).

thf(p1_s6_domain_1_type,type,
    p1_s6_domain_1: $i > $o ).

thf(p2_s6_domain_1_type,type,
    p2_s6_domain_1: $i > $o ).

thf(a_1_5_domain_1_type,type,
    a_1_5_domain_1: $i > $i ).

thf(a_1_6_domain_1_type,type,
    a_1_6_domain_1: $i > $i ).

thf(k10_domain_1_type,type,
    k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).

thf(f1_s3_subset_1_type,type,
    f1_s3_subset_1: $i ).

thf(p1_s3_subset_1_type,type,
    p1_s3_subset_1: $i > $o ).

thf(f1_s17_fraenkel_type,type,
    f1_s17_fraenkel: $i ).

thf(f3_s17_fraenkel_type,type,
    f3_s17_fraenkel: $i > $i ).

thf(p1_s17_fraenkel_type,type,
    p1_s17_fraenkel: $i > $o ).

thf(f1_s1_pre_circ_type,type,
    f1_s1_pre_circ: $i ).

thf(f2_s1_pre_circ_type,type,
    f2_s1_pre_circ: $i > $i ).

thf(p1_s1_pre_circ_type,type,
    p1_s1_pre_circ: $i > $o ).

thf(a_2_0_card_fil_type,type,
    a_2_0_card_fil: $i > $i > $i ).

thf(k5_trees_3_type,type,
    k5_trees_3: $i > $i ).

thf(a_1_3_domain_1_type,type,
    a_1_3_domain_1: $i > $i ).

thf(p1_s5_domain_1_type,type,
    p1_s5_domain_1: $i > $o ).

thf(a_3_5_domain_1_type,type,
    a_3_5_domain_1: $i > $i > $i > $i ).

thf(a_3_2_domain_1_type,type,
    a_3_2_domain_1: $i > $i > $i > $i ).

thf(f1_s23_fraenkel_type,type,
    f1_s23_fraenkel: $i ).

thf(p1_s23_fraenkel_type,type,
    p1_s23_fraenkel: $i > $i > $o ).

thf(f2_s23_fraenkel_type,type,
    f2_s23_fraenkel: $i ).

thf(a_2_2_domain_1_type,type,
    a_2_2_domain_1: $i > $i > $i ).

thf(k13_domain_1_type,type,
    k13_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(k8_subset_1_type,type,
    k8_subset_1: $i > $i ).

thf(f1_s22_fraenkel_type,type,
    f1_s22_fraenkel: $i ).

thf(f2_s22_fraenkel_type,type,
    f2_s22_fraenkel: $i ).

thf(f5_s22_fraenkel_type,type,
    f5_s22_fraenkel: $i > $i > $i ).

thf(a_0_1_domain_1_type,type,
    a_0_1_domain_1: $i ).

thf(f2_s8_domain_1_type,type,
    f2_s8_domain_1: $i ).

thf(k12_domain_1_type,type,
    k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(k8_domain_1_type,type,
    k8_domain_1: $i > $i > $i > $i > $i ).

thf(a_1_4_domain_1_type,type,
    a_1_4_domain_1: $i > $i ).

thf(p2_s5_domain_1_type,type,
    p2_s5_domain_1: $i > $o ).

thf(g2_struct_0_type,type,
    g2_struct_0: $i > $i > $i ).

thf(f1_s1_card_fil_type,type,
    f1_s1_card_fil: $i ).

thf(f1_s1_relset_1_type,type,
    f1_s1_relset_1: $i ).

thf(f2_s1_relset_1_type,type,
    f2_s1_relset_1: $i ).

thf(p1_s1_relset_1_type,type,
    p1_s1_relset_1: $i > $i > $o ).

thf(f1_s3_filter_1_type,type,
    f1_s3_filter_1: $i ).

thf(p1_s3_filter_1_type,type,
    p1_s3_filter_1: $i > $i > $i > $o ).

thf(k2_filter_1_type,type,
    k2_filter_1: $i > $i > $i > $i ).

thf(f2_s3_filter_1_type,type,
    f2_s3_filter_1: $i ).

thf(k8_eqrel_1_type,type,
    k8_eqrel_1: $i > $i > $i ).

thf(a_3_4_domain_1_type,type,
    a_3_4_domain_1: $i > $i > $i > $i ).

thf(a_8_0_domain_1_type,type,
    a_8_0_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(a_1_0_domain_1_type,type,
    a_1_0_domain_1: $i > $i ).

thf(f1_s8_domain_1_type,type,
    f1_s8_domain_1: $i ).

thf(f3_s8_domain_1_type,type,
    f3_s8_domain_1: $i > $i ).

thf(p1_s8_domain_1_type,type,
    p1_s8_domain_1: $i > $o ).

thf(a_3_1_domain_1_type,type,
    a_3_1_domain_1: $i > $i > $i > $i ).

thf(f1_s1_subset_1_type,type,
    f1_s1_subset_1: $i ).

thf(p1_s1_subset_1_type,type,
    p1_s1_subset_1: $i > $o ).

thf(f1_s9_domain_1_type,type,
    f1_s9_domain_1: $i ).

thf(f2_s9_domain_1_type,type,
    f2_s9_domain_1: $i ).

thf(f4_s9_domain_1_type,type,
    f4_s9_domain_1: $i > $i > $i ).

thf(p1_s9_domain_1_type,type,
    p1_s9_domain_1: $i > $i > $o ).

thf(a_4_1_domain_1_type,type,
    a_4_1_domain_1: $i > $i > $i > $i > $i ).

thf(k8_relset_2_type,type,
    k8_relset_2: $i > $i > $i > $i > $i ).

thf(k7_relset_2_type,type,
    k7_relset_2: $i > $i > $i > $i > $i ).

thf(a_0_0_group_5_type,type,
    a_0_0_group_5: $i ).

thf(f1_s1_group_5_type,type,
    f1_s1_group_5: $i ).

thf(f2_s1_group_5_type,type,
    f2_s1_group_5: $i ).

thf(f3_s1_group_5_type,type,
    f3_s1_group_5: $i ).

thf(f4_s1_group_5_type,type,
    f4_s1_group_5: $i > $i > $i > $i ).

thf(p1_s1_group_5_type,type,
    p1_s1_group_5: $i > $i > $i > $o ).

thf(f1_s4_filter_1_type,type,
    f1_s4_filter_1: $i ).

thf(f2_s4_filter_1_type,type,
    f2_s4_filter_1: $i ).

thf(p1_s4_filter_1_type,type,
    p1_s4_filter_1: $i > $o ).

thf(f1_s1_filter_1_type,type,
    f1_s1_filter_1: $i ).

thf(p1_s1_filter_1_type,type,
    p1_s1_filter_1: $i > $o ).

thf(f2_s1_filter_1_type,type,
    f2_s1_filter_1: $i ).

thf(k9_domain_1_type,type,
    k9_domain_1: $i > $i > $i > $i > $i > $i ).

thf(a_4_2_domain_1_type,type,
    a_4_2_domain_1: $i > $i > $i > $i > $i ).

thf(p1_s4_domain_1_type,type,
    p1_s4_domain_1: $i > $i > $i > $i > $o ).

thf(f1_s18_fraenkel_type,type,
    f1_s18_fraenkel: $i ).

thf(f3_s18_fraenkel_type,type,
    f3_s18_fraenkel: $i > $i ).

thf(p1_s18_fraenkel_type,type,
    p1_s18_fraenkel: $i > $o ).

thf(f1_s21_fraenkel_type,type,
    f1_s21_fraenkel: $i ).

thf(f3_s21_fraenkel_type,type,
    f3_s21_fraenkel: $i > $i ).

thf(f1_s2_filter_1_type,type,
    f1_s2_filter_1: $i ).

thf(p1_s2_filter_1_type,type,
    p1_s2_filter_1: $i > $i > $o ).

thf(f2_s2_filter_1_type,type,
    f2_s2_filter_1: $i ).

thf(f1_s2_subset_1_type,type,
    f1_s2_subset_1: $i ).

thf(p1_s2_subset_1_type,type,
    p1_s2_subset_1: $i > $o ).

thf(f1_s4_subset_1_type,type,
    f1_s4_subset_1: $i ).

thf(f2_s4_subset_1_type,type,
    f2_s4_subset_1: $i ).

thf(p1_s4_subset_1_type,type,
    p1_s4_subset_1: $i > $o ).

thf(f3_s4_subset_1_type,type,
    f3_s4_subset_1: $i ).

thf(a_3_3_domain_1_type,type,
    a_3_3_domain_1: $i > $i > $i > $i ).

thf(f1_s2_relset_1_type,type,
    f1_s2_relset_1: $i ).

thf(f2_s2_relset_1_type,type,
    f2_s2_relset_1: $i ).

thf(p1_s2_relset_1_type,type,
    p1_s2_relset_1: $i > $i > $o ).

thf(k2_classes2_type,type,
    k2_classes2: $i > $i > $i ).

thf(a_1_0_card_fil_type,type,
    a_1_0_card_fil: $i > $i ).

thf(a_3_8_domain_1_type,type,
    a_3_8_domain_1: $i > $i > $i > $i ).

thf(a_3_7_domain_1_type,type,
    a_3_7_domain_1: $i > $i > $i > $i ).

thf(a_2_1_card_fil_type,type,
    a_2_1_card_fil: $i > $i > $i ).

thf(a_2_0_relset_2_type,type,
    a_2_0_relset_2: $i > $i > $i ).

thf(f1_s10_funct_2_type,type,
    f1_s10_funct_2: $i ).

thf(f2_s10_funct_2_type,type,
    f2_s10_funct_2: $i ).

thf(f3_s10_funct_2_type,type,
    f3_s10_funct_2: $i ).

thf(f4_s10_funct_2_type,type,
    f4_s10_funct_2: $i ).

thf(f5_s10_funct_2_type,type,
    f5_s10_funct_2: $i > $i ).

thf(p1_s3_domain_1_type,type,
    p1_s3_domain_1: $i > $i > $i > $o ).

thf(f1_s5_filter_1_type,type,
    f1_s5_filter_1: $i ).

thf(f2_s5_filter_1_type,type,
    f2_s5_filter_1: $i ).

thf(p1_s5_filter_1_type,type,
    p1_s5_filter_1: $i > $i > $o ).

thf(f1_s2_pua2mss1_type,type,
    f1_s2_pua2mss1: $i ).

thf(f2_s2_pua2mss1_type,type,
    f2_s2_pua2mss1: $i ).

thf(p1_s2_pua2mss1_type,type,
    p1_s2_pua2mss1: $i > $i > $o ).

thf(p1_s10_fraenkel_type,type,
    p1_s10_fraenkel: $i > $o ).

thf(r1_cat_2_type,type,
    r1_cat_2: $i > $i > $o ).

thf(f1_s24_fraenkel_type,type,
    f1_s24_fraenkel: $i ).

thf(f2_s24_fraenkel_type,type,
    f2_s24_fraenkel: $i ).

thf(f3_s24_fraenkel_type,type,
    f3_s24_fraenkel: $i ).

thf(f4_s24_fraenkel_type,type,
    f4_s24_fraenkel: $i > $i ).

thf(p1_s24_fraenkel_type,type,
    p1_s24_fraenkel: $i > $i > $o ).

thf(1350,axiom,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ C ) @ D )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ C ) @ D ) )
                         => ! [G: $i] :
                              ( ( m2_finseq_2 @ G @ C @ ( k4_finseq_2 @ A @ C ) )
                             => ( m2_finseq_2 @ ( k5_funcop_1 @ F @ E @ G ) @ D @ ( k4_finseq_2 @ A @ D ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_finseq_2) ).

thf(8960,plain,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ C ) @ D )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ C ) @ D ) )
                         => ! [G: $i] :
                              ( ( m2_finseq_2 @ G @ C @ ( k4_finseq_2 @ A @ C ) )
                             => ( m2_finseq_2 @ ( k5_funcop_1 @ F @ E @ G ) @ D @ ( k4_finseq_2 @ A @ D ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).

thf(877,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ~ ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ( ( E
                      = ( k5_mcart_1 @ A @ B @ C @ D ) )
                  <=> ! [F: $i,G: $i,H: $i] :
                        ( ( D
                          = ( k3_mcart_1 @ F @ G @ H ) )
                       => ( E = F ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_mcart_1) ).

thf(6836,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ~ ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ( ( ( E
                        = ( k5_mcart_1 @ A @ B @ C @ D ) )
                     => ! [F: $i,G: $i,H: $i] :
                          ( ( D
                            = ( k3_mcart_1 @ F @ G @ H ) )
                         => ( E = F ) ) )
                    & ( ! [F: $i,G: $i,H: $i] :
                          ( ( D
                            = ( k3_mcart_1 @ F @ G @ H ) )
                         => ( E = F ) )
                     => ( E
                        = ( k5_mcart_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(1829,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ? [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_ens_1 @ A ) )
              & ? [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                  & ? [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                      & ( B
                        = ( k1_domain_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_ens_1 @ A ) @ ( k1_domain_1 @ A @ A @ D @ E ) @ C ) )
                      & ( ( E = k1_xboole_0 )
                       => ( D = k1_xboole_0 ) )
                      & ( v1_funct_1 @ C )
                      & ( v1_funct_2 @ C @ D @ E )
                      & ( m2_relset_1 @ C @ D @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_ens_1) ).

thf(11313,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ? [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_ens_1 @ A ) )
              & ? [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                  & ? [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                      & ( B
                        = ( k1_domain_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_ens_1 @ A ) @ ( k1_domain_1 @ A @ A @ D @ E ) @ C ) )
                      & ( ( E = k1_xboole_0 )
                       => ( D = k1_xboole_0 ) )
                      & ( v1_funct_1 @ C )
                      & ( v1_funct_2 @ C @ D @ E )
                      & ( m2_relset_1 @ C @ D @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1829]) ).

thf(177,axiom,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k5_numbers )
     => ( m1_subset_1 @ ( k3_urysohn1 @ A ) @ ( k1_zfmisc_1 @ k1_numbers ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_urysohn1) ).

thf(3581,plain,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k5_numbers )
     => ( m1_subset_1 @ ( k3_urysohn1 @ A ) @ ( k1_zfmisc_1 @ k1_numbers ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(693,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( r1_tarski @ A @ ( k1_funct_4 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_funct_4) ).

thf(5999,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( r1_tarski @ A @ ( k1_funct_4 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(853,axiom,
    ! [A: $i] :
      ( ( k1_funct_2 @ k1_xboole_0 @ A )
      = ( k1_tarski @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_5) ).

thf(6690,plain,
    ! [A: $i] :
      ( ( k1_funct_2 @ k1_xboole_0 @ A )
      = ( k1_tarski @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(2438,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( m1_subset_1 @ ( a_1_2_domain_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_domain_1) ).

thf(14221,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( m1_subset_1 @ ( a_1_2_domain_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2438]) ).

thf(1268,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
        & ( v1_funct_1 @ ( k7_relat_1 @ A @ B ) )
        & ( v1_finset_1 @ ( k7_relat_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_rfinseq) ).

thf(8607,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
        & ( v1_funct_1 @ ( k7_relat_1 @ A @ B ) )
        & ( v1_finset_1 @ ( k7_relat_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).

thf(1740,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_classes2 @ B ) )
     => ( ( r2_hidden @ A @ B )
       => ( r2_hidden @ ( k1_tarski @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_classes2) ).

thf(10822,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_classes2 @ B ) )
     => ( ( r2_hidden @ A @ B )
       => ( r2_hidden @ ( k1_tarski @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1740]) ).

thf(659,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r1_tarski @ B @ A )
              & ( v6_ordinal1 @ B )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ! [D: $i] :
                        ( ( r2_hidden @ D @ B )
                       => ( r1_tarski @ D @ C ) ) ) )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ( C != B )
                    & ( r1_tarski @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t175_orders_1) ).

thf(5810,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r1_tarski @ B @ A )
              & ( v6_ordinal1 @ B )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ! [D: $i] :
                        ( ( r2_hidden @ D @ B )
                       => ( r1_tarski @ D @ C ) ) ) )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ( C != B )
                    & ( r1_tarski @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(624,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ~ ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
             => ( ( ( k8_mcart_1 @ A @ B @ C @ D @ E )
                  = ( k1_mcart_1 @ ( k1_mcart_1 @ ( k1_mcart_1 @ E ) ) ) )
                & ( ( k9_mcart_1 @ A @ B @ C @ D @ E )
                  = ( k2_mcart_1 @ ( k1_mcart_1 @ ( k1_mcart_1 @ E ) ) ) )
                & ( ( k10_mcart_1 @ A @ B @ C @ D @ E )
                  = ( k2_mcart_1 @ ( k1_mcart_1 @ E ) ) )
                & ( ( k11_mcart_1 @ A @ B @ C @ D @ E )
                  = ( k2_mcart_1 @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_mcart_1) ).

thf(5659,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ~ ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
             => ( ( ( k8_mcart_1 @ A @ B @ C @ D @ E )
                  = ( k1_mcart_1 @ ( k1_mcart_1 @ ( k1_mcart_1 @ E ) ) ) )
                & ( ( k9_mcart_1 @ A @ B @ C @ D @ E )
                  = ( k2_mcart_1 @ ( k1_mcart_1 @ ( k1_mcart_1 @ E ) ) ) )
                & ( ( k10_mcart_1 @ A @ B @ C @ D @ E )
                  = ( k2_mcart_1 @ ( k1_mcart_1 @ E ) ) )
                & ( ( k11_mcart_1 @ A @ B @ C @ D @ E )
                  = ( k2_mcart_1 @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(1553,axiom,
    m1_subset_1 @ k2_qc_lang1 @ ( k1_zfmisc_1 @ k1_qc_lang1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_qc_lang1) ).

thf(9929,plain,
    m1_subset_1 @ k2_qc_lang1 @ ( k1_zfmisc_1 @ k1_qc_lang1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1553]) ).

thf(1253,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_xboole_0 @ ( k15_funct_3 @ A @ B ) )
        & ( v1_relat_1 @ ( k15_funct_3 @ A @ B ) )
        & ( v1_funct_1 @ ( k15_funct_3 @ A @ B ) )
        & ( v2_funct_1 @ ( k15_funct_3 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_functor0) ).

thf(8536,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_xboole_0 @ ( k15_funct_3 @ A @ B ) )
        & ( v1_relat_1 @ ( k15_funct_3 @ A @ B ) )
        & ( v1_funct_1 @ ( k15_funct_3 @ A @ B ) )
        & ( v2_funct_1 @ ( k15_funct_3 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).

thf(582,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ B ) )
     => ( r1_tarski @ ( k5_xboole_0 @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_xboole_1) ).

thf(5509,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ B ) )
     => ( r1_tarski @ ( k5_xboole_0 @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(1564,axiom,
    ! [A: $i] :
      ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_zfmisc_1) ).

thf(9982,plain,
    ! [A: $i] :
      ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1564]) ).

thf(974,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( ( B
                = ( k2_xboole_0 @ C @ ( k1_tarski @ A ) ) )
              | ( C
                = ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) ) )
           => ( ( k8_setfam_1 @ A @ B )
              = ( k8_setfam_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_yellow_9) ).

thf(7304,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( ( B
                = ( k2_xboole_0 @ C @ ( k1_tarski @ A ) ) )
              | ( C
                = ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) ) )
           => ( ( k8_setfam_1 @ A @ B )
              = ( k8_setfam_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).

thf(1571,axiom,
    ! [A: $i] :
      ( ( ( k1_funct_5 @ A )
        = k1_xboole_0 )
    <=> ( ( k2_funct_5 @ A )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_5) ).

thf(10007,plain,
    ! [A: $i] :
      ( ( ( ( k1_funct_5 @ A )
          = k1_xboole_0 )
       => ( ( k2_funct_5 @ A )
          = k1_xboole_0 ) )
      & ( ( ( k2_funct_5 @ A )
          = k1_xboole_0 )
       => ( ( k1_funct_5 @ A )
          = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1571]) ).

thf(2185,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ( ( v2_funct_1 @ C )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
                       => ( ( r2_hidden @ ( k8_funct_2 @ A @ B @ C @ D ) @ ( k2_funct_2 @ A @ B @ C @ E ) )
                         => ( r2_hidden @ D @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_funct_7) ).

thf(13266,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ( ( v2_funct_1 @ C )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
                       => ( ( r2_hidden @ ( k8_funct_2 @ A @ B @ C @ D ) @ ( k2_funct_2 @ A @ B @ C @ E ) )
                         => ( r2_hidden @ D @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2185]) ).

thf(1174,axiom,
    ! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k5_xboole_0 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_xboole_1) ).

thf(8186,plain,
    ! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k5_xboole_0 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).

thf(1465,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
         => ( ( ( ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D )
                = ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ E ) )
              & ! [F: $i,G: $i] :
                  ( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D ) )
                 => ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
                    = ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
           => ( D = E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_partfun1) ).

thf(9458,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
         => ( ( ( ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D )
                = ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ E ) )
              & ! [F: $i,G: $i] :
                  ( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k4_relset_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D ) )
                 => ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
                    = ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
           => ( D = E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1465]) ).

thf(282,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_funct_1 @ ( k1_funct_3 @ A ) )
        & ( v1_funct_2 @ ( k1_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) )
        & ( m2_relset_1 @ ( k1_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_3) ).

thf(4094,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_funct_1 @ ( k1_funct_3 @ A ) )
        & ( v1_funct_2 @ ( k1_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) )
        & ( m2_relset_1 @ ( k1_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(970,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ~ ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ C )
                 => ( ( E
                      = ( k7_mcart_1 @ A @ B @ C @ D ) )
                  <=> ! [F: $i,G: $i,H: $i] :
                        ( ( D
                          = ( k3_mcart_1 @ F @ G @ H ) )
                       => ( E = H ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_mcart_1) ).

thf(7272,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ~ ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ C )
                 => ( ( ( E
                        = ( k7_mcart_1 @ A @ B @ C @ D ) )
                     => ! [F: $i,G: $i,H: $i] :
                          ( ( D
                            = ( k3_mcart_1 @ F @ G @ H ) )
                         => ( E = H ) ) )
                    & ( ! [F: $i,G: $i,H: $i] :
                          ( ( D
                            = ( k3_mcart_1 @ F @ G @ H ) )
                         => ( E = H ) )
                     => ( E
                        = ( k7_mcart_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(1964,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ A )
                        & ( m2_relset_1 @ E @ B @ A ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ( ( k8_funct_2 @ B @ A @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ F )
                            = ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_funcop_1) ).

thf(12055,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ A )
                        & ( m2_relset_1 @ E @ B @ A ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ( ( k8_funct_2 @ B @ A @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ F )
                            = ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1964]) ).

thf(769,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
        & ( A != B )
        & ( A != C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_zfmisc_1) ).

thf(6355,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
        & ( A != B )
        & ( A != C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(133,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
          & ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
       => ( m2_relset_1 @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_relset_1) ).

thf(3345,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
          & ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
       => ( m2_relset_1 @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(362,axiom,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k1_numbers )
        & ( m1_subset_1 @ B @ k1_numbers ) )
     => ( m1_subset_1 @ ( k12_binop_2 @ A @ B ) @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_binop_2) ).

thf(4571,plain,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k1_numbers )
        & ( m1_subset_1 @ B @ k1_numbers ) )
     => ( m1_subset_1 @ ( k12_binop_2 @ A @ B ) @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(284,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( k2_relat_1 @ A )
            = ( k1_tarski @ B ) )
         => ( A
            = ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funcop_1) ).

thf(4101,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( k2_relat_1 @ A )
            = ( k1_tarski @ B ) )
         => ( A
            = ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(669,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( ( B
                = ( k2_xboole_0 @ C @ ( k1_tarski @ A ) ) )
              | ( C
                = ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) ) )
           => ( ( k2_cantor_1 @ A @ B )
              = ( k2_cantor_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_yellow_9) ).

thf(5857,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( ( B
                = ( k2_xboole_0 @ C @ ( k1_tarski @ A ) ) )
              | ( C
                = ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) ) )
           => ( ( k2_cantor_1 @ A @ B )
              = ( k2_cantor_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(345,axiom,
    ! [A: $i,B: $i] :
      ( ( m2_finseq_1 @ B @ A )
     => ( ( v1_funct_1 @ B )
        & ( v1_finseq_1 @ B )
        & ( m2_relset_1 @ B @ k5_numbers @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_finseq_1) ).

thf(4464,plain,
    ! [A: $i,B: $i] :
      ( ( m2_finseq_1 @ B @ A )
     => ( ( v1_funct_1 @ B )
        & ( v1_finseq_1 @ B )
        & ( m2_relset_1 @ B @ k5_numbers @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(417,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( r2_hidden @ C @ ( k1_relat_1 @ ( k5_funcop_1 @ B @ D @ A ) ) )
             => ( ( k1_funct_1 @ ( k5_funcop_1 @ B @ D @ A ) @ C )
                = ( k1_binop_1 @ B @ D @ ( k1_funct_1 @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_funcop_1) ).

thf(4824,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( r2_hidden @ C @ ( k1_relat_1 @ ( k5_funcop_1 @ B @ D @ A ) ) )
             => ( ( k1_funct_1 @ ( k5_funcop_1 @ B @ D @ A ) @ C )
                = ( k1_binop_1 @ B @ D @ ( k1_funct_1 @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(1101,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v2_funct_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).

thf(7854,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v2_funct_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).

thf(1811,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_finset_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_lopclset) ).

thf(11211,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_finset_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1811]) ).

thf(1031,axiom,
    ! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) @ ( k2_xboole_0 @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_xboole_1) ).

thf(7569,plain,
    ! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) @ ( k2_xboole_0 @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).

thf(748,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ B @ C )
            & ( m2_relset_1 @ E @ B @ C ) )
         => ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
           => ( ( ( C = k1_xboole_0 )
                & ( B != k1_xboole_0 ) )
              | ( ( B = k1_xboole_0 )
                & ( A != k1_xboole_0 ) )
              | ( v2_funct_1 @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_funct_2) ).

thf(6231,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ B @ C )
            & ( m2_relset_1 @ E @ B @ C ) )
         => ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
           => ( ( ( C = k1_xboole_0 )
                & ( B != k1_xboole_0 ) )
              | ( ( B = k1_xboole_0 )
                & ( A != k1_xboole_0 ) )
              | ( v2_funct_1 @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(519,axiom,
    ! [A: $i,B: $i] :
      ( ( k3_tarski @ ( k2_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) )
      = ( k2_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_zfmisc_1) ).

thf(5260,plain,
    ! [A: $i,B: $i] :
      ( ( k3_tarski @ ( k2_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) )
      = ( k2_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(2571,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ( k2_classes2 @ A @ B )
        = ( k1_zfmisc_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_classes2) ).

thf(14801,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ( k2_classes2 @ A @ B )
        = ( k1_zfmisc_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2571]) ).

thf(909,axiom,
    ! [A: $i] :
      ( ( v1_fraenkel @ A )
    <=> ! [B: $i] :
          ( ( r2_hidden @ B @ A )
         => ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_fraenkel) ).

thf(6976,plain,
    ! [A: $i] :
      ( ( ( v1_fraenkel @ A )
       => ! [B: $i] :
            ( ( r2_hidden @ B @ A )
           => ( ( v1_relat_1 @ B )
              & ( v1_funct_1 @ B ) ) ) )
      & ( ! [B: $i] :
            ( ( r2_hidden @ B @ A )
           => ( ( v1_relat_1 @ B )
              & ( v1_funct_1 @ B ) ) )
       => ( v1_fraenkel @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(433,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A )
      & ( v1_xboole_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_partfun1) ).

thf(4899,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A )
      & ( v1_xboole_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(1631,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_realset1 @ C @ A @ B )
         => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_realset1) ).

thf(10267,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_realset1 @ C @ A @ B )
         => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1631]) ).

thf(263,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( C
                  = ( k13_funct_3 @ A @ B ) )
              <=> ( ( ( k1_relat_1 @ C )
                    = ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                  & ! [D: $i] :
                      ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
                     => ( ( k1_funct_1 @ C @ D )
                        = ( k4_tarski @ ( k1_funct_1 @ A @ D ) @ ( k1_funct_1 @ B @ D ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_3) ).

thf(4022,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( C
                    = ( k13_funct_3 @ A @ B ) )
                 => ( ( ( k1_relat_1 @ C )
                      = ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                    & ! [D: $i] :
                        ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
                       => ( ( k1_funct_1 @ C @ D )
                          = ( k4_tarski @ ( k1_funct_1 @ A @ D ) @ ( k1_funct_1 @ B @ D ) ) ) ) ) )
                & ( ( ( ( k1_relat_1 @ C )
                      = ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                    & ! [D: $i] :
                        ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
                       => ( ( k1_funct_1 @ C @ D )
                          = ( k4_tarski @ ( k1_funct_1 @ A @ D ) @ ( k1_funct_1 @ B @ D ) ) ) ) )
                 => ( C
                    = ( k13_funct_3 @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(2126,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H )
      = ( k2_xboole_0 @ ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G ) @ ( k1_tarski @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_enumset1) ).

thf(12975,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H )
      = ( k2_xboole_0 @ ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G ) @ ( k1_tarski @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2126]) ).

thf(2507,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( m1_subset_1 @ ( k1_cat_5 @ A @ B @ C @ D ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_cat_5) ).

thf(14574,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( m1_subset_1 @ ( k1_cat_5 @ A @ B @ C @ D ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2507]) ).

thf(684,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( r1_partfun1 @ C @ D )
           => ( ( ( B = k1_xboole_0 )
                & ( A != k1_xboole_0 ) )
              | ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t155_funct_2) ).

thf(5950,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( r1_partfun1 @ C @ D )
           => ( ( ( B = k1_xboole_0 )
                & ( A != k1_xboole_0 ) )
              | ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(2476,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k6_funct_3 @ A @ B )
        = ( k6_relat_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_funct_3) ).

thf(14404,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k6_funct_3 @ A @ B )
        = ( k6_relat_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2476]) ).

thf(2321,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_setfam_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_setfam_1) ).

thf(13783,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_setfam_1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2321]) ).

thf(1155,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( r1_xboole_0 @ A @ C ) )
     => ( r1_xboole_0 @ ( k1_setfam_1 @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_setfam_1) ).

thf(8114,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( r1_xboole_0 @ A @ C ) )
     => ( r1_xboole_0 @ ( k1_setfam_1 @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).

thf(1058,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( ( v1_funct_1 @ H )
                                    & ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ A @ B ) @ C )
                                    & ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                                 => ! [I: $i] :
                                      ( ( m2_finseq_1 @ I @ B )
                                     => ( ( I
                                          = ( k11_finseq_1 @ E @ F @ G ) )
                                       => ( ( k5_funcop_1 @ H @ D @ I )
                                          = ( k11_finseq_1 @ ( k2_binop_1 @ A @ B @ C @ H @ D @ E ) @ ( k2_binop_1 @ A @ B @ C @ H @ D @ F ) @ ( k2_binop_1 @ A @ B @ C @ H @ D @ G ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_finseq_2) ).

thf(7673,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( ( v1_funct_1 @ H )
                                    & ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ A @ B ) @ C )
                                    & ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                                 => ! [I: $i] :
                                      ( ( m2_finseq_1 @ I @ B )
                                     => ( ( I
                                          = ( k11_finseq_1 @ E @ F @ G ) )
                                       => ( ( k5_funcop_1 @ H @ D @ I )
                                          = ( k11_finseq_1 @ ( k2_binop_1 @ A @ B @ C @ H @ D @ E ) @ ( k2_binop_1 @ A @ B @ C @ H @ D @ F ) @ ( k2_binop_1 @ A @ B @ C @ H @ D @ G ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

thf(1537,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C ) )
     => ( ( r2_hidden @ A @ ( a_2_0_domain_1 @ B @ C ) )
      <=> ? [D: $i,E: $i] :
            ( ( m1_subset_1 @ D @ B )
            & ( m1_subset_1 @ E @ C )
            & ( A
              = ( k1_domain_1 @ B @ C @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_domain_1) ).

thf(9833,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C ) )
     => ( ( ( r2_hidden @ A @ ( a_2_0_domain_1 @ B @ C ) )
         => ? [D: $i,E: $i] :
              ( ( m1_subset_1 @ D @ B )
              & ( m1_subset_1 @ E @ C )
              & ( A
                = ( k1_domain_1 @ B @ C @ D @ E ) ) ) )
        & ( ? [D: $i,E: $i] :
              ( ( m1_subset_1 @ D @ B )
              & ( m1_subset_1 @ E @ C )
              & ( A
                = ( k1_domain_1 @ B @ C @ D @ E ) ) )
         => ( r2_hidden @ A @ ( a_2_0_domain_1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537]) ).

thf(936,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
            & ( r2_hidden @ D @ ( k2_xboole_0 @ A @ B ) ) )
         => ( ( C = D )
            | ( r1_xboole_0 @ C @ D ) ) )
     => ( ( k3_tarski @ ( k3_xboole_0 @ A @ B ) )
        = ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t101_zfmisc_1) ).

thf(7100,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
            & ( r2_hidden @ D @ ( k2_xboole_0 @ A @ B ) ) )
         => ( ( C = D )
            | ( r1_xboole_0 @ C @ D ) ) )
     => ( ( k3_tarski @ ( k3_xboole_0 @ A @ B ) )
        = ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).

thf(1201,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( ( k2_relat_1 @ C )
            = B )
          & ( v2_funct_1 @ C ) )
       => ( ( B = k1_xboole_0 )
          | ( ( ( k5_relat_1 @ C @ ( k2_funct_1 @ C ) )
              = ( k6_partfun1 @ A ) )
            & ( ( k5_relat_1 @ ( k2_funct_1 @ C ) @ C )
              = ( k6_partfun1 @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_2) ).

thf(8283,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( ( k2_relat_1 @ C )
            = B )
          & ( v2_funct_1 @ C ) )
       => ( ( B = k1_xboole_0 )
          | ( ( ( k5_relat_1 @ C @ ( k2_funct_1 @ C ) )
              = ( k6_partfun1 @ A ) )
            & ( ( k5_relat_1 @ ( k2_funct_1 @ C ) @ C )
              = ( k6_partfun1 @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).

thf(2086,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ B @ A )
        & ( m1_relset_1 @ D @ B @ A )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ B @ A )
        & ( m1_relset_1 @ E @ B @ A ) )
     => ( ( v1_funct_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) )
        & ( v1_funct_2 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
        & ( m2_relset_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_funcop_1) ).

thf(12753,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ B @ A )
        & ( m1_relset_1 @ D @ B @ A )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ B @ A )
        & ( m1_relset_1 @ E @ B @ A ) )
     => ( ( v1_funct_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) )
        & ( v1_funct_2 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
        & ( m2_relset_1 @ ( k6_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2086]) ).

thf(2078,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k4_card_fil @ A ) ) ) )
         => ( ( v6_ordinal1 @ B )
           => ( m1_card_fil @ ( k3_tarski @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_card_fil) ).

thf(12731,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k4_card_fil @ A ) ) ) )
         => ( ( v6_ordinal1 @ B )
           => ( m1_card_fil @ ( k3_tarski @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2078]) ).

thf(792,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ D ) )
      = ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).

thf(6431,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ D ) )
      = ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(623,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ B @ A )
     => ( ( ( k10_relset_1 @ B @ A @ C @ ( k11_relset_1 @ B @ A @ C @ A ) )
          = ( k5_relset_1 @ B @ A @ C ) )
        & ( ( k11_relset_1 @ B @ A @ C @ ( k10_relset_1 @ B @ A @ C @ B ) )
          = ( k4_relset_1 @ B @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_relset_1) ).

thf(5654,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ B @ A )
     => ( ( ( k10_relset_1 @ B @ A @ C @ ( k11_relset_1 @ B @ A @ C @ A ) )
          = ( k5_relset_1 @ B @ A @ C ) )
        & ( ( k11_relset_1 @ B @ A @ C @ ( k10_relset_1 @ B @ A @ C @ B ) )
          = ( k4_relset_1 @ B @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(249,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ B ) )
     => ( ( k2_binop_1 @ A @ B @ C @ D @ E @ F )
        = ( k1_binop_1 @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).

thf(3969,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ B ) )
     => ( ( k2_binop_1 @ A @ B @ C @ D @ E @ F )
        = ( k1_binop_1 @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(1385,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ ( k2_funct_4 @ A ) )
        & ( v1_funct_1 @ ( k2_funct_4 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_4) ).

thf(9076,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ ( k2_funct_4 @ A ) )
        & ( v1_funct_1 @ ( k2_funct_4 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385]) ).

thf(878,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k3_enumset1 @ A @ B @ C @ D @ E )
      = ( k2_xboole_0 @ ( k2_enumset1 @ A @ B @ C @ D ) @ ( k1_tarski @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_enumset1) ).

thf(6845,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k3_enumset1 @ A @ B @ C @ D @ E )
      = ( k2_xboole_0 @ ( k2_enumset1 @ A @ B @ C @ D ) @ ( k1_tarski @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(1277,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( ( k7_relset_1 @ A @ A @ A @ B @ ( k6_partfun1 @ A ) @ C )
          = C )
        & ( ( k7_relset_1 @ A @ B @ B @ B @ C @ ( k6_partfun1 @ B ) )
          = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_2) ).

thf(8646,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( ( k7_relset_1 @ A @ A @ A @ B @ ( k6_partfun1 @ A ) @ C )
          = C )
        & ( ( k7_relset_1 @ A @ B @ B @ B @ C @ ( k6_partfun1 @ B ) )
          = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).

thf(174,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ ( k11_finseq_1 @ A @ B @ C ) )
      & ( v1_funct_1 @ ( k11_finseq_1 @ A @ B @ C ) )
      & ( v1_finset_1 @ ( k11_finseq_1 @ A @ B @ C ) )
      & ( v1_finseq_1 @ ( k11_finseq_1 @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_finseq_1) ).

thf(3566,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ ( k11_finseq_1 @ A @ B @ C ) )
      & ( v1_funct_1 @ ( k11_finseq_1 @ A @ B @ C ) )
      & ( v1_finset_1 @ ( k11_finseq_1 @ A @ B @ C ) )
      & ( v1_finseq_1 @ ( k11_finseq_1 @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(1843,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( ( A = k1_xboole_0 )
          & ( ( k2_zfmisc_1 @ B @ A )
            = k1_xboole_0 )
          & ( ( k2_zfmisc_1 @ A @ B )
            = k1_xboole_0 ) )
     => ( ( ( k1_funct_5 @ ( k2_zfmisc_1 @ B @ A ) )
          = B )
        & ( ( k2_funct_5 @ ( k2_zfmisc_1 @ A @ B ) )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funct_5) ).

thf(11394,plain,
    ! [A: $i,B: $i] :
      ( ~ ( ( A = k1_xboole_0 )
          & ( ( k2_zfmisc_1 @ B @ A )
            = k1_xboole_0 )
          & ( ( k2_zfmisc_1 @ A @ B )
            = k1_xboole_0 ) )
     => ( ( ( k1_funct_5 @ ( k2_zfmisc_1 @ B @ A ) )
          = B )
        & ( ( k2_funct_5 @ ( k2_zfmisc_1 @ A @ B ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1843]) ).

thf(822,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_eqrel_1 @ C @ B )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ C )
                    & ( m2_relset_1 @ D @ A @ C ) )
                 => ( ( ( r1_tarski @ C @ ( k2_relat_1 @ D ) )
                      & ( v2_funct_1 @ D ) )
                   => ( m2_pua2mss1 @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_pua2mss1) ).

thf(6566,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_eqrel_1 @ C @ B )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ C )
                    & ( m2_relset_1 @ D @ A @ C ) )
                 => ( ( ( r1_tarski @ C @ ( k2_relat_1 @ D ) )
                      & ( v2_funct_1 @ D ) )
                   => ( m2_pua2mss1 @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(972,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v8_monoid_0 @ B @ A )
          <=> ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ( ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
                              = ( k2_binop_1 @ A @ A @ A @ B @ C @ E ) )
                            | ( ( k2_binop_1 @ A @ A @ A @ B @ D @ C )
                              = ( k2_binop_1 @ A @ A @ A @ B @ E @ C ) ) )
                         => ( D = E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_monoid_0) ).

thf(7285,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( v8_monoid_0 @ B @ A )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
                                = ( k2_binop_1 @ A @ A @ A @ B @ C @ E ) )
                              | ( ( k2_binop_1 @ A @ A @ A @ B @ D @ C )
                                = ( k2_binop_1 @ A @ A @ A @ B @ E @ C ) ) )
                           => ( D = E ) ) ) ) ) )
            & ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
                                = ( k2_binop_1 @ A @ A @ A @ B @ C @ E ) )
                              | ( ( k2_binop_1 @ A @ A @ A @ B @ D @ C )
                                = ( k2_binop_1 @ A @ A @ A @ B @ E @ C ) ) )
                           => ( D = E ) ) ) ) )
             => ( v8_monoid_0 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).

thf(1389,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( B
        = ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).

thf(9091,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( B
        = ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389]) ).

thf(996,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ ( k5_finsub_1 @ A ) )
        & ( m2_relset_1 @ B @ A @ ( k5_finsub_1 @ A ) ) )
     => ( ( B
          = ( k11_setwiseo @ A ) )
      <=> ! [C: $i] :
            ( ( r2_hidden @ C @ A )
           => ( ( k1_funct_1 @ B @ C )
              = ( k1_tarski @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_setwiseo) ).

thf(7396,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ ( k5_finsub_1 @ A ) )
        & ( m2_relset_1 @ B @ A @ ( k5_finsub_1 @ A ) ) )
     => ( ( ( B
            = ( k11_setwiseo @ A ) )
         => ! [C: $i] :
              ( ( r2_hidden @ C @ A )
             => ( ( k1_funct_1 @ B @ C )
                = ( k1_tarski @ C ) ) ) )
        & ( ! [C: $i] :
              ( ( r2_hidden @ C @ A )
             => ( ( k1_funct_1 @ B @ C )
                = ( k1_tarski @ C ) ) )
         => ( B
            = ( k11_setwiseo @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).

thf(696,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( r1_tarski @ ( k2_relat_1 @ A ) @ B )
         => ( ( k5_relat_1 @ A @ ( k6_partfun1 @ B ) )
            = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funct_7) ).

thf(6014,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( r1_tarski @ ( k2_relat_1 @ A ) @ B )
         => ( ( k5_relat_1 @ A @ ( k6_partfun1 @ B ) )
            = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(2077,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D
        = ( k1_enumset1 @ A @ B @ C ) )
    <=> ! [E: $i] :
          ( ( r2_hidden @ E @ D )
        <=> ~ ( ( E != A )
              & ( E != B )
              & ( E != C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_enumset1) ).

thf(12699,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D
          = ( k1_enumset1 @ A @ B @ C ) )
       => ! [E: $i] :
            ( ( ( r2_hidden @ E @ D )
             => ~ ( ( E != A )
                  & ( E != B )
                  & ( E != C ) ) )
            & ( ~ ( ( E != A )
                  & ( E != B )
                  & ( E != C ) )
             => ( r2_hidden @ E @ D ) ) ) )
      & ( ! [E: $i] :
            ( ( ( r2_hidden @ E @ D )
             => ~ ( ( E != A )
                  & ( E != B )
                  & ( E != C ) ) )
            & ( ~ ( ( E != A )
                  & ( E != B )
                  & ( E != C ) )
             => ( r2_hidden @ E @ D ) ) )
       => ( D
          = ( k1_enumset1 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2077]) ).

thf(607,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k4_enumset1 @ A @ B @ C @ D @ E @ F )
      = ( k2_xboole_0 @ ( k1_enumset1 @ A @ B @ C ) @ ( k1_enumset1 @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_enumset1) ).

thf(5582,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k4_enumset1 @ A @ B @ C @ D @ E @ F )
      = ( k2_xboole_0 @ ( k1_enumset1 @ A @ B @ C ) @ ( k1_enumset1 @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(774,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( v2_funct_1 @ B ) )
           => ( v2_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_1) ).

thf(6374,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( v2_funct_1 @ B ) )
           => ( v2_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(1892,axiom,
    ! [A: $i,B: $i] :
      ( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ B ) )
        | ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ A ) ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t135_zfmisc_1) ).

thf(11659,plain,
    ! [A: $i,B: $i] :
      ( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ B ) )
        | ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ A ) ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1892]) ).

thf(2081,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) )
             => ( m1_subset_1 @ ( k4_subset_1 @ ( k1_closure2 @ A @ B ) @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_closure2) ).

thf(12738,plain,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) )
             => ( m1_subset_1 @ ( k4_subset_1 @ ( k1_closure2 @ A @ B ) @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2081]) ).

thf(434,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( ( B = k1_xboole_0 )
             => ( A = k1_xboole_0 ) )
           => ( ( r1_partfun1 @ C @ D )
            <=> ! [E: $i] :
                  ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
                 => ( ( k1_funct_1 @ C @ E )
                    = ( k1_funct_1 @ D @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_2) ).

thf(4904,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( ( B = k1_xboole_0 )
             => ( A = k1_xboole_0 ) )
           => ( ( ( r1_partfun1 @ C @ D )
               => ! [E: $i] :
                    ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
                   => ( ( k1_funct_1 @ C @ E )
                      = ( k1_funct_1 @ D @ E ) ) ) )
              & ( ! [E: $i] :
                    ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
                   => ( ( k1_funct_1 @ C @ E )
                      = ( k1_funct_1 @ D @ E ) ) )
               => ( r1_partfun1 @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(1179,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ( ( ( ( k4_funct_2 @ A @ C @ B )
                = B )
              & ( v2_funct_1 @ B ) )
           => ( C
              = ( k6_partfun1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funct_2) ).

thf(8200,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ( ( ( ( k4_funct_2 @ A @ C @ B )
                = B )
              & ( v2_funct_1 @ B ) )
           => ( C
              = ( k6_partfun1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).

thf(1459,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_relset_1 @ C @ A @ B )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ~ ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
                      & ! [E: $i] :
                          ( ( m1_subset_1 @ E @ B )
                         => ~ ( r2_hidden @ E @ ( k5_relset_1 @ A @ B @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_relset_1) ).

thf(9437,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_relset_1 @ C @ A @ B )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ~ ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
                      & ! [E: $i] :
                          ( ( m1_subset_1 @ E @ B )
                         => ~ ( r2_hidden @ E @ ( k5_relset_1 @ A @ B @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459]) ).

thf(2055,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m2_relset_1 @ D @ A @ C )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ( ( r2_hidden @ E @ ( k11_relset_1 @ A @ C @ D @ B ) )
                      <=> ? [F: $i] :
                            ( ( m1_subset_1 @ F @ C )
                            & ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
                            & ( r2_hidden @ F @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_relset_1) ).

thf(12549,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m2_relset_1 @ D @ A @ C )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ( ( ( r2_hidden @ E @ ( k11_relset_1 @ A @ C @ D @ B ) )
                         => ? [F: $i] :
                              ( ( m1_subset_1 @ F @ C )
                              & ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
                              & ( r2_hidden @ F @ B ) ) )
                        & ( ? [F: $i] :
                              ( ( m1_subset_1 @ F @ C )
                              & ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
                              & ( r2_hidden @ F @ B ) )
                         => ( r2_hidden @ E @ ( k11_relset_1 @ A @ C @ D @ B ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2055]) ).

thf(295,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v1_finseq_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finseq_1) ).

thf(4166,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v1_finseq_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(872,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( v2_funct_1 @ C )
       => ( ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
          = ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_funct_1) ).

thf(6808,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( v2_funct_1 @ C )
       => ( ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
          = ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(266,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).

thf(4043,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(665,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ C @ B ) )
     => ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
        = ( k2_tarski @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_zfmisc_1) ).

thf(5842,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ C @ B ) )
     => ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
        = ( k2_tarski @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(2143,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ~ ( v1_xboole_0 @ E ) )
     => ( ( r2_hidden @ A @ ( a_4_0_domain_1 @ B @ C @ D @ E ) )
      <=> ? [F: $i,G: $i,H: $i,I: $i] :
            ( ( m1_subset_1 @ F @ B )
            & ( m1_subset_1 @ G @ C )
            & ( m1_subset_1 @ H @ D )
            & ( m1_subset_1 @ I @ E )
            & ( A
              = ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_0_domain_1) ).

thf(13062,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ~ ( v1_xboole_0 @ E ) )
     => ( ( ( r2_hidden @ A @ ( a_4_0_domain_1 @ B @ C @ D @ E ) )
         => ? [F: $i,G: $i,H: $i,I: $i] :
              ( ( m1_subset_1 @ F @ B )
              & ( m1_subset_1 @ G @ C )
              & ( m1_subset_1 @ H @ D )
              & ( m1_subset_1 @ I @ E )
              & ( A
                = ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) ) ) )
        & ( ? [F: $i,G: $i,H: $i,I: $i] :
              ( ( m1_subset_1 @ F @ B )
              & ( m1_subset_1 @ G @ C )
              & ( m1_subset_1 @ H @ D )
              & ( m1_subset_1 @ I @ E )
              & ( A
                = ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) ) )
         => ( r2_hidden @ A @ ( a_4_0_domain_1 @ B @ C @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2143]) ).

thf(625,axiom,
    ! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_xboole_1) ).

thf(5669,plain,
    ! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(1597,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( r1_tarski @ ( k7_ens_1 @ A @ B @ C ) @ ( k2_ens_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_ens_1) ).

thf(10125,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( r1_tarski @ ( k7_ens_1 @ A @ B @ C ) @ ( k2_ens_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1597]) ).

thf(697,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k2_ens_1 @ A ) )
                 => ( ( r2_hidden @ D @ ( k7_ens_1 @ A @ B @ C ) )
                   => ( r2_hidden @ ( k2_mcart_1 @ D ) @ ( k1_funct_2 @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_ens_1) ).

thf(6017,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k2_ens_1 @ A ) )
                 => ( ( r2_hidden @ D @ ( k7_ens_1 @ A @ B @ C ) )
                   => ( r2_hidden @ ( k2_mcart_1 @ D ) @ ( k1_funct_2 @ B @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(705,axiom,
    ! [A: $i] :
      ( ~ ( v1_finset_1 @ A )
     => ! [B: $i] :
          ( ( ( v3_card_fil @ B @ A )
            & ( m1_card_fil @ B @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( r2_hidden @ C @ B )
              <=> ~ ( r2_hidden @ C @ ( k2_card_fil @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_card_fil) ).

thf(6057,plain,
    ! [A: $i] :
      ( ~ ( v1_finset_1 @ A )
     => ! [B: $i] :
          ( ( ( v3_card_fil @ B @ A )
            & ( m1_card_fil @ B @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( ( r2_hidden @ C @ B )
                 => ~ ( r2_hidden @ C @ ( k2_card_fil @ A @ B ) ) )
                & ( ~ ( r2_hidden @ C @ ( k2_card_fil @ A @ B ) )
                 => ( r2_hidden @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(1901,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
     => ! [D: $i] :
          ( ( ~ ( v1_xboole_0 @ D )
            & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
         => ! [E: $i] :
              ( ( ~ ( v1_xboole_0 @ E )
                & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) )
             => ( ( C
                  = ( a_4_1_yellow_9 @ A @ B @ D @ E ) )
               => ( ( k8_setfam_1 @ ( k2_zfmisc_1 @ A @ B ) @ C )
                  = ( k12_mcart_1 @ A @ B @ ( k8_setfam_1 @ A @ D ) @ ( k8_setfam_1 @ B @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_yellow_9) ).

thf(11688,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
     => ! [D: $i] :
          ( ( ~ ( v1_xboole_0 @ D )
            & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
         => ! [E: $i] :
              ( ( ~ ( v1_xboole_0 @ E )
                & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) )
             => ( ( C
                  = ( a_4_1_yellow_9 @ A @ B @ D @ E ) )
               => ( ( k8_setfam_1 @ ( k2_zfmisc_1 @ A @ B ) @ C )
                  = ( k12_mcart_1 @ A @ B @ ( k8_setfam_1 @ A @ D ) @ ( k8_setfam_1 @ B @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1901]) ).

thf(699,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ C @ D )
                            & ( m2_relset_1 @ F @ C @ D ) )
                         => ( ( r4_nattra_1 @ A @ B @ C @ D @ E @ F )
                          <=> ( ( A = C )
                              & ! [G: $i] :
                                  ( ( m1_subset_1 @ G @ A )
                                 => ( ( k8_funct_2 @ A @ B @ E @ G )
                                    = ( k1_funct_1 @ F @ G ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_nattra_1) ).

thf(6022,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ C @ D )
                            & ( m2_relset_1 @ F @ C @ D ) )
                         => ( ( ( r4_nattra_1 @ A @ B @ C @ D @ E @ F )
                             => ( ( A = C )
                                & ! [G: $i] :
                                    ( ( m1_subset_1 @ G @ A )
                                   => ( ( k8_funct_2 @ A @ B @ E @ G )
                                      = ( k1_funct_1 @ F @ G ) ) ) ) )
                            & ( ( ( A = C )
                                & ! [G: $i] :
                                    ( ( m1_subset_1 @ G @ A )
                                   => ( ( k8_funct_2 @ A @ B @ E @ G )
                                      = ( k1_funct_1 @ F @ G ) ) ) )
                             => ( r4_nattra_1 @ A @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(1828,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
        & ( v1_finset_1 @ ( k1_tarski @ A ) )
        & ( v1_fraenkel @ ( k1_tarski @ A ) )
        & ( v1_realset1 @ ( k1_tarski @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_altcat_1) ).

thf(11308,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
        & ( v1_finset_1 @ ( k1_tarski @ A ) )
        & ( v1_fraenkel @ ( k1_tarski @ A ) )
        & ( v1_realset1 @ ( k1_tarski @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1828]) ).

thf(868,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
    <=> ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C )
        & ( ( k1_funct_5 @ C )
          = A )
        & ( r1_tarski @ ( k2_funct_5 @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_yellow18) ).

thf(6791,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
       => ( ( v1_relat_1 @ C )
          & ( v1_funct_1 @ C )
          & ( ( k1_funct_5 @ C )
            = A )
          & ( r1_tarski @ ( k2_funct_5 @ C ) @ B ) ) )
      & ( ( ( v1_relat_1 @ C )
          & ( v1_funct_1 @ C )
          & ( ( k1_funct_5 @ C )
            = A )
          & ( r1_tarski @ ( k2_funct_5 @ C ) @ B ) )
       => ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(2067,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( v1_funct_1 @ ( k5_funcop_1 @ C @ E @ D ) )
                        & ( v1_funct_2 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B )
                        & ( m2_relset_1 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funcop_1) ).

thf(12634,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( v1_funct_1 @ ( k5_funcop_1 @ C @ E @ D ) )
                        & ( v1_funct_2 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B )
                        & ( m2_relset_1 @ ( k5_funcop_1 @ C @ E @ D ) @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2067]) ).

thf(255,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_binop_1 @ ( k9_funct_2 @ A @ B @ C ) @ A @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_altcat_1) ).

thf(3990,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_binop_1 @ ( k9_funct_2 @ A @ B @ C ) @ A @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(71,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
          & ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( ( ( k1_relat_1 @ C )
                        = A )
                      & ( ( k1_relat_1 @ D )
                        = A )
                      & ( ( k5_relat_1 @ B @ C )
                        = ( k5_relat_1 @ B @ D ) ) )
                   => ( C = D ) ) ) ) )
       => ( A
          = ( k2_relat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_funct_1) ).

thf(3072,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
          & ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( ( ( k1_relat_1 @ C )
                        = A )
                      & ( ( k1_relat_1 @ D )
                        = A )
                      & ( ( k5_relat_1 @ B @ C )
                        = ( k5_relat_1 @ B @ D ) ) )
                   => ( C = D ) ) ) ) )
       => ( A
          = ( k2_relat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(1492,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( m1_subset_1 @ ( k12_mcart_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_mcart_1) ).

thf(9573,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( m1_subset_1 @ ( k12_mcart_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1492]) ).

thf(1036,axiom,
    ! [A: $i,B: $i] :
      ( ( k5_xboole_0 @ A @ B )
      = ( k5_xboole_0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).

thf(7596,plain,
    ! [A: $i,B: $i] :
      ( ( k5_xboole_0 @ A @ B )
      = ( k5_xboole_0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).

thf(2144,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( B
              = ( k1_tarski @ C ) )
           => ( ( k8_setfam_1 @ A @ B )
              = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_mssubfam) ).

thf(13073,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( B
              = ( k1_tarski @ C ) )
           => ( ( k8_setfam_1 @ A @ B )
              = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2144]) ).

thf(989,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_pboole @ D @ B ) )
     => ( ( k7_pboole @ A @ B @ C @ D )
        = ( k5_relat_1 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_pboole) ).

thf(7358,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_pboole @ D @ B ) )
     => ( ( k7_pboole @ A @ B @ C @ D )
        = ( k5_relat_1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).

thf(956,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
            & ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ ( k1_tarski @ A ) @ B )
                & ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
             => ( ( ( k1_funct_1 @ C @ A )
                  = ( k1_funct_1 @ D @ A ) )
               => ( r4_nattra_1 @ ( k1_tarski @ A ) @ B @ ( k1_tarski @ A ) @ B @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_isocat_2) ).

thf(7164,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
            & ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ ( k1_tarski @ A ) @ B )
                & ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
             => ( ( ( k1_funct_1 @ C @ A )
                  = ( k1_funct_1 @ D @ A ) )
               => ( r4_nattra_1 @ ( k1_tarski @ A ) @ B @ ( k1_tarski @ A ) @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).

thf(2251,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v2_setfam_1 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) ) )
     => ? [C: $i] :
          ( ( m1_subset_1 @ C @ B )
          & ~ ( v1_xboole_0 @ C )
          & ( v1_finset_1 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_triang_1) ).

thf(13520,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v2_setfam_1 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) ) )
     => ? [C: $i] :
          ( ( m1_subset_1 @ C @ B )
          & ~ ( v1_xboole_0 @ C )
          & ( v1_finset_1 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2251]) ).

thf(1661,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k5_enumset1 @ A @ A @ A @ A @ A @ B @ C )
      = ( k1_enumset1 @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_enumset1) ).

thf(10431,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k5_enumset1 @ A @ A @ A @ A @ A @ B @ C )
      = ( k1_enumset1 @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1661]) ).

thf(328,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k1_relat_1 @ ( k2_xboole_0 @ A @ B ) )
            = ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_relat_1) ).

thf(4339,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k1_relat_1 @ ( k2_xboole_0 @ A @ B ) )
            = ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(635,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D ) )
     => ( ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ C ) )
        = ( k2_zfmisc_1 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_zfmisc_1) ).

thf(5718,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D ) )
     => ( ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ C ) )
        = ( k2_zfmisc_1 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(2151,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( v1_xboole_0 @ ( k2_ens_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ens_1) ).

thf(13110,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( v1_xboole_0 @ ( k2_ens_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2151]) ).

thf(2480,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v5_grcat_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_grcat_1) ).

thf(14414,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v5_grcat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2480]) ).

thf(2443,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
                                 => ( ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H )
                                    = ( a_8_0_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_domain_1) ).

thf(14235,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
                                 => ( ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H )
                                    = ( a_8_0_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2443]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( B
              = ( k7_relat_1 @ C @ A ) )
          <=> ( ( ( k1_relat_1 @ B )
                = ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
              & ! [D: $i] :
                  ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
                 => ( ( k1_funct_1 @ B @ D )
                    = ( k1_funct_1 @ C @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).

thf(2622,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( B
                = ( k7_relat_1 @ C @ A ) )
             => ( ( ( k1_relat_1 @ B )
                  = ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
                & ! [D: $i] :
                    ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
                   => ( ( k1_funct_1 @ B @ D )
                      = ( k1_funct_1 @ C @ D ) ) ) ) )
            & ( ( ( ( k1_relat_1 @ B )
                  = ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
                & ! [D: $i] :
                    ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
                   => ( ( k1_funct_1 @ B @ D )
                      = ( k1_funct_1 @ C @ D ) ) ) )
             => ( B
                = ( k7_relat_1 @ C @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(1790,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m1_relset_1 @ B @ A @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ A )
        & ( m1_relset_1 @ C @ A @ A ) )
     => ( ( v1_funct_1 @ ( k4_funct_2 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A )
        & ( m2_relset_1 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_funct_2) ).

thf(11107,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m1_relset_1 @ B @ A @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ A )
        & ( m1_relset_1 @ C @ A @ A ) )
     => ( ( v1_funct_1 @ ( k4_funct_2 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A )
        & ( m2_relset_1 @ ( k4_funct_2 @ A @ B @ C ) @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1790]) ).

thf(1413,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ ( k1_tarski @ C ) ) )
        & ~ ( r2_hidden @ C @ A )
        & ~ ( r1_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_setwiseo) ).

thf(9251,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ ( k1_tarski @ C ) ) )
        & ~ ( r2_hidden @ C @ A )
        & ~ ( r1_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413]) ).

thf(321,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
                = ( k2_relat_1 @ A ) )
              & ( v2_funct_1 @ A ) )
           => ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funct_1) ).

thf(4311,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
                = ( k2_relat_1 @ A ) )
              & ( v2_funct_1 @ A ) )
           => ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v5_monoid_0 @ B @ A )
          <=> ( ( v3_monoid_0 @ B @ A )
              & ( v4_monoid_0 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_monoid_0) ).

thf(2808,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( v5_monoid_0 @ B @ A )
             => ( ( v3_monoid_0 @ B @ A )
                & ( v4_monoid_0 @ B @ A ) ) )
            & ( ( ( v3_monoid_0 @ B @ A )
                & ( v4_monoid_0 @ B @ A ) )
             => ( v5_monoid_0 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(718,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ B ) )
     => ? [C: $i] : ( m1_filter_1 @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_filter_1) ).

thf(6106,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ B ) )
     => ? [C: $i] : ( m1_filter_1 @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(107,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( r2_hidden @ C @ ( k1_relat_1 @ ( k4_funcop_1 @ B @ A @ D ) ) )
             => ( ( k1_funct_1 @ ( k4_funcop_1 @ B @ A @ D ) @ C )
                = ( k1_binop_1 @ B @ ( k1_funct_1 @ A @ C ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funcop_1) ).

thf(3230,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( r2_hidden @ C @ ( k1_relat_1 @ ( k4_funcop_1 @ B @ A @ D ) ) )
             => ( ( k1_funct_1 @ ( k4_funcop_1 @ B @ A @ D ) @ C )
                = ( k1_binop_1 @ B @ ( k1_funct_1 @ A @ C ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(2205,axiom,
    ! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_enumset1 @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_setwiseo) ).

thf(13351,plain,
    ! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_enumset1 @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2205]) ).

thf(528,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( k5_relat_1 @ B @ ( k4_funcop_1 @ C @ A @ D ) )
                  = ( k4_funcop_1 @ C @ ( k5_relat_1 @ B @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funcop_1) ).

thf(5292,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( k5_relat_1 @ B @ ( k4_funcop_1 @ C @ A @ D ) )
                  = ( k4_funcop_1 @ C @ ( k5_relat_1 @ B @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(863,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) @ ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t155_relat_1) ).

thf(6744,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( r1_tarski @ ( k4_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) @ ( k9_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(2020,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ B )
        & ( m1_subset_1 @ F @ C ) )
     => ( m1_subset_1 @ ( k4_domain_1 @ A @ B @ C @ D @ E @ F ) @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_domain_1) ).

thf(12376,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ B )
        & ( m1_subset_1 @ F @ C ) )
     => ( m1_subset_1 @ ( k4_domain_1 @ A @ B @ C @ D @ E @ F ) @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2020]) ).

thf(744,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ A @ B )
     => ( ( r1_tarski @ ( k6_relat_1 @ C ) @ D )
       => ( ( r1_tarski @ C @ ( k4_relset_1 @ A @ B @ D ) )
          & ( r1_tarski @ C @ ( k5_relset_1 @ A @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relset_1) ).

thf(6219,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ A @ B )
     => ( ( r1_tarski @ ( k6_relat_1 @ C ) @ D )
       => ( ( r1_tarski @ C @ ( k4_relset_1 @ A @ B @ D ) )
          & ( r1_tarski @ C @ ( k5_relset_1 @ A @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(1464,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( ( r1_tarski @ A @ B )
               => ( r1_tarski @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_relat_1) ).

thf(9456,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( ( r1_tarski @ A @ B )
               => ( r1_tarski @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).

thf(1819,axiom,
    ~ ( v1_xboole_0 @ k2_qc_lang1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_qc_lang1) ).

thf(11277,plain,
    ~ ( v1_xboole_0 @ k2_qc_lang1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1819]) ).

thf(1228,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ! [B: $i,C: $i] :
            ( ( k9_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) )
            = ( k3_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
       => ( v2_funct_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_funct_1) ).

thf(8402,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ! [B: $i,C: $i] :
            ( ( k9_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) )
            = ( k3_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
       => ( v2_funct_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).

thf(1700,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( v1_funct_1 @ ( k1_funct_3 @ C ) )
          & ( v1_funct_2 @ ( k1_funct_3 @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) )
          & ( m2_relset_1 @ ( k1_funct_3 @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_3) ).

thf(10567,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( v1_funct_1 @ ( k1_funct_3 @ C ) )
          & ( v1_funct_2 @ ( k1_funct_3 @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) )
          & ( m2_relset_1 @ ( k1_funct_3 @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700]) ).

thf(1969,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ B @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_enumset1) ).

thf(12089,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ B @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1969]) ).

thf(1377,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
     => ! [F: $i] :
          ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
         => ! [G: $i] :
              ( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
             => ! [H: $i] :
                  ( ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
                 => ! [I: $i] :
                      ( ( m1_subset_1 @ I @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
                     => ( ( r2_hidden @ I @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
                       => ( ( r2_hidden @ ( k8_mcart_1 @ A @ B @ C @ D @ I ) @ E )
                          & ( r2_hidden @ ( k9_mcart_1 @ A @ B @ C @ D @ I ) @ F )
                          & ( r2_hidden @ ( k10_mcart_1 @ A @ B @ C @ D @ I ) @ G )
                          & ( r2_hidden @ ( k11_mcart_1 @ A @ B @ C @ D @ I ) @ H ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_mcart_1) ).

thf(9045,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
     => ! [F: $i] :
          ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
         => ! [G: $i] :
              ( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
             => ! [H: $i] :
                  ( ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
                 => ! [I: $i] :
                      ( ( m1_subset_1 @ I @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
                     => ( ( r2_hidden @ I @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
                       => ( ( r2_hidden @ ( k8_mcart_1 @ A @ B @ C @ D @ I ) @ E )
                          & ( r2_hidden @ ( k9_mcart_1 @ A @ B @ C @ D @ I ) @ F )
                          & ( r2_hidden @ ( k10_mcart_1 @ A @ B @ C @ D @ I ) @ G )
                          & ( r2_hidden @ ( k11_mcart_1 @ A @ B @ C @ D @ I ) @ H ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377]) ).

thf(530,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ( ( v2_funct_1 @ C )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ B )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
                           => ( ( r2_hidden @ D @ ( k6_subset_1 @ B @ ( k2_funct_2 @ A @ B @ C @ E ) @ F ) )
                             => ( r2_hidden @ ( k1_funct_1 @ ( k2_funct_1 @ C ) @ D ) @ ( k6_subset_1 @ A @ E @ ( k3_funct_2 @ A @ B @ C @ F ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_funct_7) ).

thf(5297,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ( ( v2_funct_1 @ C )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ B )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
                           => ( ( r2_hidden @ D @ ( k6_subset_1 @ B @ ( k2_funct_2 @ A @ B @ C @ E ) @ F ) )
                             => ( r2_hidden @ ( k1_funct_1 @ ( k2_funct_1 @ C ) @ D ) @ ( k6_subset_1 @ A @ E @ ( k3_funct_2 @ A @ B @ C @ F ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(2567,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( ( k7_setfam_1 @ A @ B )
              = ( k7_setfam_1 @ A @ C ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_setfam_1) ).

thf(14786,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( ( k7_setfam_1 @ A @ B )
              = ( k7_setfam_1 @ A @ C ) )
           => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2567]) ).

thf(389,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ C ) ) @ ( k1_relat_1 @ A ) )
               => ( ( k1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
                  = ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_funcop_1) ).

thf(4697,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ C ) ) @ ( k1_relat_1 @ A ) )
               => ( ( k1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
                  = ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(2293,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( r2_hidden @ A @ ( a_1_2_domain_1 @ B ) )
      <=> ? [C: $i] :
            ( ( m1_subset_1 @ C @ B )
            & ( A = C )
            & ( p1_s1_domain_1 @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_2_domain_1) ).

thf(13672,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( ( r2_hidden @ A @ ( a_1_2_domain_1 @ B ) )
         => ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A = C )
              & ( p1_s1_domain_1 @ C ) ) )
        & ( ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A = C )
              & ( p1_s1_domain_1 @ C ) )
         => ( r2_hidden @ A @ ( a_1_2_domain_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2293]) ).

thf(75,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
       => ( r1_tarski @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_sysrel) ).

thf(3098,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
       => ( r1_tarski @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(1549,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r2_hidden @ C @ A )
        & ( r2_hidden @ D @ B ) )
     => ( m2_relset_1 @ ( k1_tarski @ ( k4_tarski @ C @ D ) ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_relset_1) ).

thf(9918,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r2_hidden @ C @ A )
        & ( r2_hidden @ D @ B ) )
     => ( m2_relset_1 @ ( k1_tarski @ ( k4_tarski @ C @ D ) ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1549]) ).

thf(1288,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ( ( ( r1_tarski @ B @ A )
              & ( v6_ordinal1 @ B ) )
           => ( ( B = k1_xboole_0 )
              | ( r2_hidden @ ( k1_setfam_1 @ B ) @ A ) ) )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ( C != B )
                    & ( r1_tarski @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_orders_1) ).

thf(8695,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ( ( ( r1_tarski @ B @ A )
              & ( v6_ordinal1 @ B ) )
           => ( ( B = k1_xboole_0 )
              | ( r2_hidden @ ( k1_setfam_1 @ B ) @ A ) ) )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ( C != B )
                    & ( r1_tarski @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).

thf(1698,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( m1_card_fil @ ( k1_tarski @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_card_fil) ).

thf(10562,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( m1_card_fil @ ( k1_tarski @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1698]) ).

thf(654,axiom,
    ! [A: $i,B: $i] :
      ( ( k1_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) )
      = ( k3_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_zfmisc_1) ).

thf(5793,plain,
    ! [A: $i,B: $i] :
      ( ( k1_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) )
      = ( k3_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(2551,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k2_cantor_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_cantor_1) ).

thf(14729,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k2_cantor_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2551]) ).

thf(2091,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
     => ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_funct_2) ).

thf(12774,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
     => ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2091]) ).

thf(79,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ ( k9_finseq_1 @ A ) )
      & ( v1_funct_1 @ ( k9_finseq_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_finseq_1) ).

thf(3108,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ ( k9_finseq_1 @ A ) )
      & ( v1_funct_1 @ ( k9_finseq_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(767,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( v1_xboole_0 @ ( k4_funct_4 @ A @ B @ C @ D ) )
      & ( v1_relat_1 @ ( k4_funct_4 @ A @ B @ C @ D ) )
      & ( v1_funct_1 @ ( k4_funct_4 @ A @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_7) ).

thf(6338,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( v1_xboole_0 @ ( k4_funct_4 @ A @ B @ C @ D ) )
      & ( v1_relat_1 @ ( k4_funct_4 @ A @ B @ C @ D ) )
      & ( v1_funct_1 @ ( k4_funct_4 @ A @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(1642,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ~ ( v1_xboole_0 @ E )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
                     => ( ( A
                          = ( k8_mcart_1 @ B @ C @ D @ E @ F ) )
                      <=> ! [G: $i] :
                            ( ( m1_subset_1 @ G @ B )
                           => ! [H: $i] :
                                ( ( m1_subset_1 @ H @ C )
                               => ! [I: $i] :
                                    ( ( m1_subset_1 @ I @ D )
                                   => ! [J: $i] :
                                        ( ( m1_subset_1 @ J @ E )
                                       => ( ( F
                                            = ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
                                         => ( A = G ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_domain_1) ).

thf(10314,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ~ ( v1_xboole_0 @ E )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
                     => ( ( ( A
                            = ( k8_mcart_1 @ B @ C @ D @ E @ F ) )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ C )
                                 => ! [I: $i] :
                                      ( ( m1_subset_1 @ I @ D )
                                     => ! [J: $i] :
                                          ( ( m1_subset_1 @ J @ E )
                                         => ( ( F
                                              = ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
                                           => ( A = G ) ) ) ) ) ) )
                        & ( ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ C )
                                 => ! [I: $i] :
                                      ( ( m1_subset_1 @ I @ D )
                                     => ! [J: $i] :
                                          ( ( m1_subset_1 @ J @ E )
                                         => ( ( F
                                              = ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
                                           => ( A = G ) ) ) ) ) )
                         => ( A
                            = ( k8_mcart_1 @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1642]) ).

thf(64,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( m1_pboole @ D @ B )
             => ! [E: $i] :
                  ( ( m1_pboole @ E @ B )
                 => ! [F: $i] :
                      ( ( m3_pboole @ F @ B @ D @ E )
                     => ( m3_pboole @ ( k7_pboole @ A @ B @ C @ F ) @ A @ ( k7_pboole @ A @ B @ C @ D ) @ ( k7_pboole @ A @ B @ C @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_altcat_2) ).

thf(3012,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( m1_pboole @ D @ B )
             => ! [E: $i] :
                  ( ( m1_pboole @ E @ B )
                 => ! [F: $i] :
                      ( ( m3_pboole @ F @ B @ D @ E )
                     => ( m3_pboole @ ( k7_pboole @ A @ B @ C @ F ) @ A @ ( k7_pboole @ A @ B @ C @ D ) @ ( k7_pboole @ A @ B @ C @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(1994,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ( ( v1_funct_1 @ ( k3_funcop_1 @ C @ D @ E ) )
                        & ( v1_funct_2 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B )
                        & ( m2_relset_1 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_funcop_1) ).

thf(12261,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ( ( v1_funct_1 @ ( k3_funcop_1 @ C @ D @ E ) )
                        & ( v1_funct_2 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B )
                        & ( m2_relset_1 @ ( k3_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1994]) ).

thf(2472,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k3_setwiseo @ A @ B @ C )
        = ( k3_setwiseo @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_setwiseo) ).

thf(14377,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k3_setwiseo @ A @ B @ C )
        = ( k3_setwiseo @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2472]) ).

thf(2328,axiom,
    ! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset_1) ).

thf(13796,plain,
    ! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2328]) ).

thf(2118,axiom,
    ! [A: $i] :
      ( ( k3_enumset1 @ A @ A @ A @ A @ A )
      = ( k1_tarski @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_enumset1) ).

thf(12896,plain,
    ! [A: $i] :
      ( ( k3_enumset1 @ A @ A @ A @ A @ A )
      = ( k1_tarski @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2118]) ).

thf(324,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
        & ( r2_hidden @ ( k2_mcart_1 @ A ) @ C ) )
     => ( ! [D: $i,E: $i] :
            ( A
           != ( k4_tarski @ D @ E ) )
        | ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_mcart_1) ).

thf(4326,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
        & ( r2_hidden @ ( k2_mcart_1 @ A ) @ C ) )
     => ( ! [D: $i,E: $i] :
            ( A
           != ( k4_tarski @ D @ E ) )
        | ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(164,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
        & ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_relat_1) ).

thf(3498,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
        & ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(1870,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i,F: $i] :
          ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) )
        <=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ C @ D ) ) )
     => ( ( k2_zfmisc_1 @ A @ B )
        = ( k2_zfmisc_1 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_zfmisc_1) ).

thf(11556,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i,F: $i] :
          ( ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) )
           => ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ C @ D ) ) )
          & ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ C @ D ) )
           => ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) ) ) )
     => ( ( k2_zfmisc_1 @ A @ B )
        = ( k2_zfmisc_1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1870]) ).

thf(1750,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
     => ( ( v1_funct_1 @ ( k6_relset_2 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) )
        & ( m2_relset_1 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relset_2) ).

thf(10886,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
     => ( ( v1_funct_1 @ ( k6_relset_2 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) )
        & ( m2_relset_1 @ ( k6_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1750]) ).

thf(1932,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ( r2_hidden @ B @ ( k1_funct_2 @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_2) ).

thf(11881,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ( r2_hidden @ B @ ( k1_funct_2 @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1932]) ).

thf(1443,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( k5_relat_1 @ C @ ( k3_funcop_1 @ D @ A @ B ) )
                    = ( k3_funcop_1 @ D @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_funcop_1) ).

thf(9364,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( k5_relat_1 @ C @ ( k3_funcop_1 @ D @ A @ B ) )
                    = ( k3_funcop_1 @ D @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443]) ).

thf(1533,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ C )
                    & ( m2_relset_1 @ D @ B @ C ) )
                 => ( ( ( C = k1_xboole_0 )
                     => ( B = k1_xboole_0 ) )
                   => ( r2_hidden @ ( k1_domain_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k1_domain_1 @ A @ A @ B @ C ) @ D ) @ ( k7_ens_1 @ A @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_ens_1) ).

thf(9818,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ C )
                    & ( m2_relset_1 @ D @ B @ C ) )
                 => ( ( ( C = k1_xboole_0 )
                     => ( B = k1_xboole_0 ) )
                   => ( r2_hidden @ ( k1_domain_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k1_domain_1 @ A @ A @ B @ C ) @ D ) @ ( k7_ens_1 @ A @ B @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1533]) ).

thf(402,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( ! [B: $i] :
              ~ ( ( r2_hidden @ B @ A )
                & ( B = k1_xboole_0 ) )
          & ! [B: $i] :
              ( ( ( v1_relat_1 @ B )
                & ( v1_funct_1 @ B ) )
             => ~ ( ( ( k1_relat_1 @ B )
                    = A )
                  & ! [C: $i] :
                      ( ( r2_hidden @ C @ A )
                     => ( r2_hidden @ ( k1_funct_1 @ B @ C ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_wellord2) ).

thf(4747,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( ! [B: $i] :
              ~ ( ( r2_hidden @ B @ A )
                & ( B = k1_xboole_0 ) )
          & ! [B: $i] :
              ( ( ( v1_relat_1 @ B )
                & ( v1_funct_1 @ B ) )
             => ~ ( ( ( k1_relat_1 @ B )
                    = A )
                  & ! [C: $i] :
                      ( ( r2_hidden @ C @ A )
                     => ( r2_hidden @ ( k1_funct_1 @ B @ C ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(1952,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_relset_1 @ C @ A @ B )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
                  <=> ? [E: $i] :
                        ( ( m1_subset_1 @ E @ B )
                        & ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relset_1) ).

thf(12013,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_relset_1 @ C @ A @ B )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
                     => ? [E: $i] :
                          ( ( m1_subset_1 @ E @ B )
                          & ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
                    & ( ? [E: $i] :
                          ( ( m1_subset_1 @ E @ B )
                          & ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) )
                     => ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1952]) ).

thf(743,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
      & ( v1_relat_1 @ C )
      & ( v1_funct_1 @ C )
      & ( v1_funct_2 @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_2) ).

thf(6214,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
      & ( v1_relat_1 @ C )
      & ( v1_funct_1 @ C )
      & ( v1_funct_2 @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(1364,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C )
      = ( k3_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_xboole_1) ).

thf(9003,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C )
      = ( k3_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).

thf(1784,axiom,
    ( ( k5_finsub_1 @ k1_xboole_0 )
    = ( k1_tarski @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finsub_1) ).

thf(11080,plain,
    ( ( k5_finsub_1 @ k1_xboole_0 )
    = ( k1_tarski @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1784]) ).

thf(146,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( r2_binop_1 @ A @ B @ C )
          <=> ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ( k1_binop_1 @ C @ D @ B )
                  = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_binop_1) ).

thf(3382,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( r2_binop_1 @ A @ B @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( k1_binop_1 @ C @ D @ B )
                    = D ) ) )
            & ( ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( k1_binop_1 @ C @ D @ B )
                    = D ) )
             => ( r2_binop_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(2422,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) )
      & ~ ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_triang_1) ).

thf(14156,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) )
      & ~ ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2422]) ).

thf(2434,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k4_subset_1 @ A @ B @ C )
        = ( k4_subset_1 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).

thf(14200,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k4_subset_1 @ A @ B @ C )
        = ( k4_subset_1 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2434]) ).

thf(2170,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_pboole @ D @ A )
        & ( m1_pboole @ E @ B ) )
     => ! [F: $i] :
          ( ( m1_functor0 @ F @ A @ B @ C @ D @ E )
         => ( m1_pboole @ F @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_functor0) ).

thf(13187,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_pboole @ D @ A )
        & ( m1_pboole @ E @ B ) )
     => ! [F: $i] :
          ( ( m1_functor0 @ F @ A @ B @ C @ D @ E )
         => ( m1_pboole @ F @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2170]) ).

thf(1855,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k2_funcop_1 @ A @ C ) @ ( k2_funcop_1 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_funct_4) ).

thf(11468,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k2_funcop_1 @ A @ C ) @ ( k2_funcop_1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1855]) ).

thf(1304,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( r1_tarski @ ( k2_relat_1 @ ( k1_funct_3 @ A ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_funct_3) ).

thf(8765,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( r1_tarski @ ( k2_relat_1 @ ( k1_funct_3 @ A ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).

thf(1260,axiom,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
      = ( k4_xboole_0 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).

thf(8568,plain,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
      = ( k4_xboole_0 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).

thf(423,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                 => ( ( D
                      = ( k1_realset1 @ C @ B ) )
                   => ( ( ( v1_binop_1 @ C @ A )
                       => ( v1_binop_1 @ D @ B ) )
                      & ( ( v3_binop_1 @ C @ A )
                       => ( v3_binop_1 @ D @ B ) )
                      & ( ( v2_binop_1 @ C @ A )
                       => ( v2_binop_1 @ D @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_filter_2) ).

thf(4856,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                 => ( ( D
                      = ( k1_realset1 @ C @ B ) )
                   => ( ( ( v1_binop_1 @ C @ A )
                       => ( v1_binop_1 @ D @ B ) )
                      & ( ( v3_binop_1 @ C @ A )
                       => ( v3_binop_1 @ D @ B ) )
                      & ( ( v2_binop_1 @ C @ A )
                       => ( v2_binop_1 @ D @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(867,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A != k1_xboole_0 )
       => ( ( B
            = ( k1_setfam_1 @ A ) )
        <=> ! [C: $i] :
              ( ( r2_hidden @ C @ B )
            <=> ! [D: $i] :
                  ( ( r2_hidden @ D @ A )
                 => ( r2_hidden @ C @ D ) ) ) ) )
      & ( ( A = k1_xboole_0 )
       => ( ( B
            = ( k1_setfam_1 @ A ) )
        <=> ( B = k1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).

thf(6759,plain,
    ! [A: $i,B: $i] :
      ( ( ( A != k1_xboole_0 )
       => ( ( ( B
              = ( k1_setfam_1 @ A ) )
           => ! [C: $i] :
                ( ( ( r2_hidden @ C @ B )
                 => ! [D: $i] :
                      ( ( r2_hidden @ D @ A )
                     => ( r2_hidden @ C @ D ) ) )
                & ( ! [D: $i] :
                      ( ( r2_hidden @ D @ A )
                     => ( r2_hidden @ C @ D ) )
                 => ( r2_hidden @ C @ B ) ) ) )
          & ( ! [C: $i] :
                ( ( ( r2_hidden @ C @ B )
                 => ! [D: $i] :
                      ( ( r2_hidden @ D @ A )
                     => ( r2_hidden @ C @ D ) ) )
                & ( ! [D: $i] :
                      ( ( r2_hidden @ D @ A )
                     => ( r2_hidden @ C @ D ) )
                 => ( r2_hidden @ C @ B ) ) )
           => ( B
              = ( k1_setfam_1 @ A ) ) ) ) )
      & ( ( A = k1_xboole_0 )
       => ( ( ( B
              = ( k1_setfam_1 @ A ) )
           => ( B = k1_xboole_0 ) )
          & ( ( B = k1_xboole_0 )
           => ( B
              = ( k1_setfam_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(1610,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( v1_zf_model @ A )
       => ( r1_zfrefle1 @ A @ k2_zfrefle1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_zfrefle1) ).

thf(10170,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( v1_zf_model @ A )
       => ( r1_zfrefle1 @ A @ k2_zfrefle1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1610]) ).

thf(2160,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u2_cat_1 @ ( k12_ens_1 @ A ) ) )
         => ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_ens_1) ).

thf(13152,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u2_cat_1 @ ( k12_ens_1 @ A ) ) )
         => ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2160]) ).

thf(66,axiom,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ~ ( v1_xboole_0 @ C )
                & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
             => ! [D: $i] :
                  ( ( m2_finseq_2 @ D @ C @ ( k4_finseq_2 @ A @ C ) )
                 => ( m2_finseq_2 @ D @ B @ ( k4_finseq_2 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_finseq_2) ).

thf(3017,plain,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ~ ( v1_xboole_0 @ C )
                & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
             => ! [D: $i] :
                  ( ( m2_finseq_2 @ D @ C @ ( k4_finseq_2 @ A @ C ) )
                 => ( m2_finseq_2 @ D @ B @ ( k4_finseq_2 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(597,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ B )
        & ( m1_subset_1 @ G @ C )
        & ( m1_subset_1 @ H @ D ) )
     => ( ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H )
        = ( k4_mcart_1 @ E @ F @ G @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_domain_1) ).

thf(5550,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ B )
        & ( m1_subset_1 @ G @ C )
        & ( m1_subset_1 @ H @ D ) )
     => ( ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H )
        = ( k4_mcart_1 @ E @ F @ G @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(1088,axiom,
    ! [A: $i,B: $i] :
      ( ( k1_funct_4 @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ B ) )
      = ( k6_partfun1 @ ( k2_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_4) ).

thf(7793,plain,
    ! [A: $i,B: $i] :
      ( ( k1_funct_4 @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ B ) )
      = ( k6_partfun1 @ ( k2_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).

thf(222,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( k5_funcop_1 @ B @ C @ A )
              = ( k3_funcop_1 @ B @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_funcop_1) ).

thf(3848,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( k5_funcop_1 @ B @ C @ A )
              = ( k3_funcop_1 @ B @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(2485,axiom,
    ! [A: $i] :
      ( ( v1_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( v1_membered @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).

thf(14441,plain,
    ! [A: $i] :
      ( ( v1_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( v1_membered @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2485]) ).

thf(1560,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ~ ( v1_xboole_0 @ E )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
                     => ( ( A
                          = ( k11_mcart_1 @ B @ C @ D @ E @ F ) )
                      <=> ! [G: $i] :
                            ( ( m1_subset_1 @ G @ B )
                           => ! [H: $i] :
                                ( ( m1_subset_1 @ H @ C )
                               => ! [I: $i] :
                                    ( ( m1_subset_1 @ I @ D )
                                   => ! [J: $i] :
                                        ( ( m1_subset_1 @ J @ E )
                                       => ( ( F
                                            = ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
                                         => ( A = J ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_domain_1) ).

thf(9956,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ~ ( v1_xboole_0 @ E )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
                     => ( ( ( A
                            = ( k11_mcart_1 @ B @ C @ D @ E @ F ) )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ C )
                                 => ! [I: $i] :
                                      ( ( m1_subset_1 @ I @ D )
                                     => ! [J: $i] :
                                          ( ( m1_subset_1 @ J @ E )
                                         => ( ( F
                                              = ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
                                           => ( A = J ) ) ) ) ) ) )
                        & ( ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ C )
                                 => ! [I: $i] :
                                      ( ( m1_subset_1 @ I @ D )
                                     => ! [J: $i] :
                                          ( ( m1_subset_1 @ J @ E )
                                         => ( ( F
                                              = ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
                                           => ( A = J ) ) ) ) ) )
                         => ( A
                            = ( k11_mcart_1 @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1560]) ).

thf(2556,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( r2_hidden @ A @ ( a_2_2_domain_1 @ B @ C ) )
      <=> ? [D: $i] :
            ( ( m1_subset_1 @ D @ B )
            & ( A = D )
            & ~ ( r2_hidden @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_2_domain_1) ).

thf(14741,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( ( r2_hidden @ A @ ( a_2_2_domain_1 @ B @ C ) )
         => ? [D: $i] :
              ( ( m1_subset_1 @ D @ B )
              & ( A = D )
              & ~ ( r2_hidden @ D @ C ) ) )
        & ( ? [D: $i] :
              ( ( m1_subset_1 @ D @ B )
              & ( A = D )
              & ~ ( r2_hidden @ D @ C ) )
         => ( r2_hidden @ A @ ( a_2_2_domain_1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2556]) ).

thf(106,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( B
          = ( k6_relat_1 @ A ) )
      <=> ( ( ( k1_relat_1 @ B )
            = A )
          & ! [C: $i] :
              ( ( r2_hidden @ C @ A )
             => ( ( k1_funct_1 @ B @ C )
                = C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).

thf(3217,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( ( B
            = ( k6_relat_1 @ A ) )
         => ( ( ( k1_relat_1 @ B )
              = A )
            & ! [C: $i] :
                ( ( r2_hidden @ C @ A )
               => ( ( k1_funct_1 @ B @ C )
                  = C ) ) ) )
        & ( ( ( ( k1_relat_1 @ B )
              = A )
            & ! [C: $i] :
                ( ( r2_hidden @ C @ A )
               => ( ( k1_funct_1 @ B @ C )
                  = C ) ) )
         => ( B
            = ( k6_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(167,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
      <=> ! [B: $i] :
            ( ( ( v1_relat_1 @ B )
              & ( v1_funct_1 @ B ) )
           => ! [C: $i] :
                ( ( ( v1_relat_1 @ C )
                  & ( v1_funct_1 @ C ) )
               => ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
                    & ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
                    & ( ( k1_relat_1 @ B )
                      = ( k1_relat_1 @ C ) )
                    & ( ( k5_relat_1 @ B @ A )
                      = ( k5_relat_1 @ C @ A ) ) )
                 => ( B = C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funct_1) ).

thf(3530,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( ( v2_funct_1 @ A )
         => ! [B: $i] :
              ( ( ( v1_relat_1 @ B )
                & ( v1_funct_1 @ B ) )
             => ! [C: $i] :
                  ( ( ( v1_relat_1 @ C )
                    & ( v1_funct_1 @ C ) )
                 => ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
                      & ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
                      & ( ( k1_relat_1 @ B )
                        = ( k1_relat_1 @ C ) )
                      & ( ( k5_relat_1 @ B @ A )
                        = ( k5_relat_1 @ C @ A ) ) )
                   => ( B = C ) ) ) ) )
        & ( ! [B: $i] :
              ( ( ( v1_relat_1 @ B )
                & ( v1_funct_1 @ B ) )
             => ! [C: $i] :
                  ( ( ( v1_relat_1 @ C )
                    & ( v1_funct_1 @ C ) )
                 => ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
                      & ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
                      & ( ( k1_relat_1 @ B )
                        = ( k1_relat_1 @ C ) )
                      & ( ( k5_relat_1 @ B @ A )
                        = ( k5_relat_1 @ C @ A ) ) )
                   => ( B = C ) ) ) )
         => ( v2_funct_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(1483,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ C )
           => ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_subset_1) ).

thf(9526,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ C )
           => ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483]) ).

thf(810,axiom,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k1_numbers )
     => ( ( k7_binop_2 @ ( k7_binop_2 @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_binop_2) ).

thf(6505,plain,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k1_numbers )
     => ( ( k7_binop_2 @ ( k7_binop_2 @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(2512,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v2_cat_5 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_cat_5) ).

thf(14602,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v2_cat_5 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2512]) ).

thf(2063,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( r2_hidden @ ( k3_subset_1 @ A @ C ) @ ( k7_setfam_1 @ A @ B ) )
          <=> ( r2_hidden @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_setfam_1) ).

thf(12590,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( ( r2_hidden @ ( k3_subset_1 @ A @ C ) @ ( k7_setfam_1 @ A @ B ) )
             => ( r2_hidden @ C @ B ) )
            & ( ( r2_hidden @ C @ B )
             => ( r2_hidden @ ( k3_subset_1 @ A @ C ) @ ( k7_setfam_1 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2063]) ).

thf(2225,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( r1_tarski @ B @ C )
           => ( r1_tarski @ ( k1_cantor_1 @ A @ B ) @ ( k1_cantor_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_cantor_1) ).

thf(13442,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( r1_tarski @ B @ C )
           => ( r1_tarski @ ( k1_cantor_1 @ A @ B ) @ ( k1_cantor_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2225]) ).

thf(1783,axiom,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ! [B: $i] :
          ( ( m4_realset1 @ B @ A )
        <=> ? [C: $i] :
              ( ( m1_subset_1 @ C @ A )
              & ( B
                = ( k1_tarski @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_realset1) ).

thf(11072,plain,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ! [B: $i] :
          ( ( ( m4_realset1 @ B @ A )
           => ? [C: $i] :
                ( ( m1_subset_1 @ C @ A )
                & ( B
                  = ( k1_tarski @ C ) ) ) )
          & ( ? [C: $i] :
                ( ( m1_subset_1 @ C @ A )
                & ( B
                  = ( k1_tarski @ C ) ) )
           => ( m4_realset1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1783]) ).

thf(1395,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k7_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
      = ( k2_funcop_1 @ ( k3_xboole_0 @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funcop_1) ).

thf(9127,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k7_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
      = ( k2_funcop_1 @ ( k3_xboole_0 @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).

thf(16,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
       => ( ( k7_relat_1 @ B @ A )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_relat_1) ).

thf(2686,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
       => ( ( k7_relat_1 @ B @ A )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(364,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( ( ( k2_relat_1 @ A )
            = ( k1_relat_1 @ ( k2_funct_1 @ A ) ) )
          & ( ( k1_relat_1 @ A )
            = ( k2_relat_1 @ ( k2_funct_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).

thf(4575,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( ( ( k2_relat_1 @ A )
            = ( k1_relat_1 @ ( k2_funct_1 @ A ) ) )
          & ( ( k1_relat_1 @ A )
            = ( k2_relat_1 @ ( k2_funct_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(1233,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ~ ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
           => ( r1_partfun1 @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t185_partfun1) ).

thf(8430,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ~ ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
           => ( r1_partfun1 @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).

thf(2280,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( r1_tarski @ C @ ( k2_zfmisc_1 @ ( k1_funct_5 @ C ) @ ( k2_funct_5 @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_yellow_3) ).

thf(13623,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( r1_tarski @ C @ ( k2_zfmisc_1 @ ( k1_funct_5 @ C ) @ ( k2_funct_5 @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2280]) ).

thf(130,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k4_finseq_1 @ A ) @ ( k4_finseq_1 @ A ) )
            & ( m2_relset_1 @ B @ ( k4_finseq_1 @ A ) @ ( k4_finseq_1 @ A ) ) )
         => ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) )
            & ( v1_funct_1 @ ( k5_relat_1 @ B @ A ) )
            & ( v1_finseq_1 @ ( k5_relat_1 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_finseq_2) ).

thf(3332,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k4_finseq_1 @ A ) @ ( k4_finseq_1 @ A ) )
            & ( m2_relset_1 @ B @ ( k4_finseq_1 @ A ) @ ( k4_finseq_1 @ A ) ) )
         => ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) )
            & ( v1_funct_1 @ ( k5_relat_1 @ B @ A ) )
            & ( v1_finseq_1 @ ( k5_relat_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(750,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
     => ( ( ( k4_relset_1 @ A @ k1_xboole_0 @ B )
          = k1_xboole_0 )
        & ( ( k2_relat_1 @ B )
          = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_partfun1) ).

thf(6246,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
     => ( ( ( k4_relset_1 @ A @ k1_xboole_0 @ B )
          = k1_xboole_0 )
        & ( ( k2_relat_1 @ B )
          = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(141,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_funct_4 @ B @ C ) ) )
          <=> ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
              | ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_funct_4) ).

thf(3367,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_funct_4 @ B @ C ) ) )
             => ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
                | ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) ) )
            & ( ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
                | ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) )
             => ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_funct_4 @ B @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(643,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
                 => ( ( k10_setwiseo @ A @ B @ ( k5_setwiseo @ A @ D @ E ) @ C )
                    = ( k5_setwiseo @ B @ ( k10_setwiseo @ A @ B @ D @ C ) @ ( k10_setwiseo @ A @ B @ E @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_setwiseo) ).

thf(5755,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
                 => ( ( k10_setwiseo @ A @ B @ ( k5_setwiseo @ A @ D @ E ) @ C )
                    = ( k5_setwiseo @ B @ ( k10_setwiseo @ A @ B @ D @ C ) @ ( k10_setwiseo @ A @ B @ E @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(770,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_realset1) ).

thf(6359,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(1648,axiom,
    ! [A: $i] :
      ( ( r2_hidden @ A @ a_0_0_yellow_3 )
    <=> ? [B: $i,C: $i] :
          ( ( m1_subset_1 @ B @ f1_s1_yellow_3 )
          & ( m1_subset_1 @ C @ f1_s1_yellow_3 )
          & ( A
            = ( f2_s1_yellow_3 @ B @ C ) )
          & ( p1_s1_yellow_3 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_0_yellow_3) ).

thf(10358,plain,
    ! [A: $i] :
      ( ( ( r2_hidden @ A @ a_0_0_yellow_3 )
       => ? [B: $i,C: $i] :
            ( ( m1_subset_1 @ B @ f1_s1_yellow_3 )
            & ( m1_subset_1 @ C @ f1_s1_yellow_3 )
            & ( A
              = ( f2_s1_yellow_3 @ B @ C ) )
            & ( p1_s1_yellow_3 @ B @ C ) ) )
      & ( ? [B: $i,C: $i] :
            ( ( m1_subset_1 @ B @ f1_s1_yellow_3 )
            & ( m1_subset_1 @ C @ f1_s1_yellow_3 )
            & ( A
              = ( f2_s1_yellow_3 @ B @ C ) )
            & ( p1_s1_yellow_3 @ B @ C ) )
       => ( r2_hidden @ A @ a_0_0_yellow_3 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1648]) ).

thf(1272,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k1_funct_5 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k1_funct_5 @ A ) @ ( k1_funct_5 @ B ) ) )
      & ( r1_tarski @ ( k2_funct_5 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k2_funct_5 @ A ) @ ( k2_funct_5 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_funct_5) ).

thf(8622,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k1_funct_5 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k1_funct_5 @ A ) @ ( k1_funct_5 @ B ) ) )
      & ( r1_tarski @ ( k2_funct_5 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k2_funct_5 @ A ) @ ( k2_funct_5 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).

thf(1357,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).

thf(8981,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).

thf(939,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
         => ( ! [E: $i] :
                ( ( r2_hidden @ E @ D )
               => ( ( r1_tarski @ E @ C )
                  & ? [F: $i] :
                      ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ A ) )
                      & ? [G: $i] :
                          ( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ B ) )
                          & ( E
                            = ( k12_mcart_1 @ A @ B @ F @ G ) ) ) ) ) )
           => ( r1_tarski @ ( k2_zfmisc_1 @ ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ ( k9_funct_3 @ A @ B ) ) @ D ) ) @ ( k1_setfam_1 @ ( k9_relat_1 @ ( k1_funct_3 @ ( k10_funct_3 @ A @ B ) ) @ D ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_borsuk_1) ).

thf(7115,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
         => ( ! [E: $i] :
                ( ( r2_hidden @ E @ D )
               => ( ( r1_tarski @ E @ C )
                  & ? [F: $i] :
                      ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ A ) )
                      & ? [G: $i] :
                          ( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ B ) )
                          & ( E
                            = ( k12_mcart_1 @ A @ B @ F @ G ) ) ) ) ) )
           => ( r1_tarski @ ( k2_zfmisc_1 @ ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ ( k9_funct_3 @ A @ B ) ) @ D ) ) @ ( k1_setfam_1 @ ( k9_relat_1 @ ( k1_funct_3 @ ( k10_funct_3 @ A @ B ) ) @ D ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(2532,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ A )
        & ( m1_subset_1 @ H @ A )
        & ( m1_subset_1 @ I @ A ) )
     => ( m1_subset_1 @ ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_domain_1) ).

thf(14665,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ A )
        & ( m1_subset_1 @ H @ A )
        & ( m1_subset_1 @ I @ A ) )
     => ( m1_subset_1 @ ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2532]) ).

thf(1810,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ C )
        & ( m1_relset_1 @ E @ A @ C )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ B @ D )
        & ( m1_relset_1 @ F @ B @ D ) )
     => ( ( v1_funct_1 @ ( k9_cat_2 @ A @ B @ C @ D @ E @ F ) )
        & ( v1_funct_2 @ ( k9_cat_2 @ A @ B @ C @ D @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
        & ( m2_relset_1 @ ( k9_cat_2 @ A @ B @ C @ D @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_cat_2) ).

thf(11207,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ C )
        & ( m1_relset_1 @ E @ A @ C )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ B @ D )
        & ( m1_relset_1 @ F @ B @ D ) )
     => ( ( v1_funct_1 @ ( k9_cat_2 @ A @ B @ C @ D @ E @ F ) )
        & ( v1_funct_2 @ ( k9_cat_2 @ A @ B @ C @ D @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
        & ( m2_relset_1 @ ( k9_cat_2 @ A @ B @ C @ D @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1810]) ).

thf(1297,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
     => ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_xboole_1) ).

thf(8747,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
     => ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297]) ).

thf(2573,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).

thf(14829,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2573]) ).

thf(935,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_pboole @ C @ B )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_closure2 @ B @ C ) ) )
             => ( ( ( r2_hidden @ A @ B )
                  & ( E
                    = ( k1_tarski @ D ) ) )
               => ( ( k1_funct_1 @ ( k4_closure2 @ B @ C @ E ) @ A )
                  = ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_closure2) ).

thf(7096,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_pboole @ C @ B )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_closure2 @ B @ C ) ) )
             => ( ( ( r2_hidden @ A @ B )
                  & ( E
                    = ( k1_tarski @ D ) ) )
               => ( ( k1_funct_1 @ ( k4_closure2 @ B @ C @ E ) @ A )
                  = ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).

thf(1826,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( v1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_orders_1) ).

thf(11303,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( v1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1826]) ).

thf(158,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( v1_binop_1 @ B @ A )
           => ( ( r3_binop_1 @ A @ C @ B )
            <=> ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( k1_binop_1 @ B @ C @ D )
                    = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_binop_1) ).

thf(3446,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( v1_binop_1 @ B @ A )
           => ( ( ( r3_binop_1 @ A @ C @ B )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ( ( k1_binop_1 @ B @ C @ D )
                      = D ) ) )
              & ( ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ( ( k1_binop_1 @ B @ C @ D )
                      = D ) )
               => ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(1056,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).

thf(7669,plain,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).

thf(1822,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( v2_pre_topc @ ( g1_pre_topc @ A @ ( k1_cantor_1 @ A @ ( k2_cantor_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_waybel18) ).

thf(11288,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( v2_pre_topc @ ( g1_pre_topc @ A @ ( k1_cantor_1 @ A @ ( k2_cantor_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1822]) ).

thf(377,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_relat_1 @ E )
        & ( v1_funct_1 @ E ) )
     => ! [F: $i] :
          ( ( ( v1_relat_1 @ F )
            & ( v1_funct_1 @ F ) )
         => ( ( ( ( k1_relat_1 @ E )
                = ( k2_zfmisc_1 @ A @ B ) )
              & ( ( k1_relat_1 @ F )
                = ( k2_zfmisc_1 @ C @ D ) ) )
           => ( ( k1_relat_1 @ ( k3_funct_4 @ E @ F ) )
              = ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_4) ).

thf(4638,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_relat_1 @ E )
        & ( v1_funct_1 @ E ) )
     => ! [F: $i] :
          ( ( ( v1_relat_1 @ F )
            & ( v1_funct_1 @ F ) )
         => ( ( ( ( k1_relat_1 @ E )
                = ( k2_zfmisc_1 @ A @ B ) )
              & ( ( k1_relat_1 @ F )
                = ( k2_zfmisc_1 @ C @ D ) ) )
           => ( ( k1_relat_1 @ ( k3_funct_4 @ E @ F ) )
              = ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(787,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_partfun1) ).

thf(6416,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(2053,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( ( r2_hidden @ B @ D )
          & ( r1_xboole_0 @ B @ C ) )
       => ( r1_xboole_0 @ ( k8_setfam_1 @ A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_mssubfam) ).

thf(12545,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( ( r2_hidden @ B @ D )
          & ( r1_xboole_0 @ B @ C ) )
       => ( r1_xboole_0 @ ( k8_setfam_1 @ A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2053]) ).

thf(2110,axiom,
    ! [A: $i] :
      ( ( k4_partfun1 @ k1_xboole_0 @ A )
      = ( k1_tarski @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_partfun1) ).

thf(12865,plain,
    ! [A: $i] :
      ( ( k4_partfun1 @ k1_xboole_0 @ A )
      = ( k1_tarski @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2110]) ).

thf(2289,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ ( k1_tarski @ B ) )
        & ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
            & ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
         => ( C = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_2) ).

thf(13655,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ ( k1_tarski @ B ) )
        & ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
            & ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
         => ( C = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2289]) ).

thf(1363,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r2_hidden @ C @ A )
       => ( ( B = k1_xboole_0 )
          | ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ ( k2_relat_1 @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_2) ).

thf(9000,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r2_hidden @ C @ A )
       => ( ( B = k1_xboole_0 )
          | ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ ( k2_relat_1 @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).

thf(497,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( A = k1_xboole_0 )
        | ( r1_tarski @ ( k1_setfam_1 @ B ) @ ( k1_setfam_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_setfam_1) ).

thf(5163,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( A = k1_xboole_0 )
        | ( r1_tarski @ ( k1_setfam_1 @ B ) @ ( k1_setfam_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(1757,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k2_ens_1 @ A ) )
                 => ( ( r2_hidden @ D @ ( k7_ens_1 @ A @ B @ C ) )
                   => ( D
                      = ( k4_tarski @ ( k1_domain_1 @ A @ A @ B @ C ) @ ( k2_mcart_1 @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_ens_1) ).

thf(10940,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k2_ens_1 @ A ) )
                 => ( ( r2_hidden @ D @ ( k7_ens_1 @ A @ B @ C ) )
                   => ( D
                      = ( k4_tarski @ ( k1_domain_1 @ A @ A @ B @ C ) @ ( k2_mcart_1 @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1757]) ).

thf(1220,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
        = ( k1_tarski @ A ) )
    <=> ~ ( r2_hidden @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_zfmisc_1) ).

thf(8370,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
          = ( k1_tarski @ A ) )
       => ~ ( r2_hidden @ A @ B ) )
      & ( ~ ( r2_hidden @ A @ B )
       => ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
          = ( k1_tarski @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).

thf(2024,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ~ ( ~ ( v1_realset1 @ B )
            & ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ~ ( ( r2_hidden @ C @ B )
                        & ( r2_hidden @ D @ B )
                        & ( C != D ) ) ) ) )
        & ~ ( ? [C: $i] :
                ( ( m1_subset_1 @ C @ A )
                & ? [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                    & ( r2_hidden @ C @ B )
                    & ( r2_hidden @ D @ B )
                    & ( C != D ) ) )
            & ( v1_realset1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_realset1) ).

thf(12398,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ~ ( ~ ( v1_realset1 @ B )
            & ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ~ ( ( r2_hidden @ C @ B )
                        & ( r2_hidden @ D @ B )
                        & ( C != D ) ) ) ) )
        & ~ ( ? [C: $i] :
                ( ( m1_subset_1 @ C @ A )
                & ? [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                    & ( r2_hidden @ C @ B )
                    & ( r2_hidden @ D @ B )
                    & ( C != D ) ) )
            & ( v1_realset1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2024]) ).

thf(627,axiom,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) )
     => ( ( A = k4_urysohn1 )
      <=> ! [B: $i] :
            ( ( m1_subset_1 @ B @ k1_numbers )
           => ( ( r2_hidden @ B @ A )
            <=> ? [C: $i] :
                  ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
                  & ( r2_hidden @ B @ ( k3_urysohn1 @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_urysohn1) ).

thf(5674,plain,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) )
     => ( ( ( A = k4_urysohn1 )
         => ! [B: $i] :
              ( ( m1_subset_1 @ B @ k1_numbers )
             => ( ( ( r2_hidden @ B @ A )
                 => ? [C: $i] :
                      ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
                      & ( r2_hidden @ B @ ( k3_urysohn1 @ C ) ) ) )
                & ( ? [C: $i] :
                      ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
                      & ( r2_hidden @ B @ ( k3_urysohn1 @ C ) ) )
                 => ( r2_hidden @ B @ A ) ) ) ) )
        & ( ! [B: $i] :
              ( ( m1_subset_1 @ B @ k1_numbers )
             => ( ( ( r2_hidden @ B @ A )
                 => ? [C: $i] :
                      ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
                      & ( r2_hidden @ B @ ( k3_urysohn1 @ C ) ) ) )
                & ( ? [C: $i] :
                      ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
                      & ( r2_hidden @ B @ ( k3_urysohn1 @ C ) ) )
                 => ( r2_hidden @ B @ A ) ) ) )
         => ( A = k4_urysohn1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(1347,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ ( k1_tarski @ B ) ) )
      <=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_relset_2) ).

thf(8947,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ ( k1_tarski @ B ) ) )
         => ( r2_hidden @ ( k4_tarski @ B @ A ) @ C ) )
        & ( ( r2_hidden @ ( k4_tarski @ B @ A ) @ C )
         => ( r2_hidden @ A @ ( k9_relat_1 @ C @ ( k1_tarski @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347]) ).

thf(1001,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( D
            = ( k5_partfun1 @ A @ B @ C ) )
        <=> ! [E: $i] :
              ( ( r2_hidden @ E @ D )
            <=> ? [F: $i] :
                  ( ( v1_funct_1 @ F )
                  & ( m2_relset_1 @ F @ A @ B )
                  & ( F = E )
                  & ( v1_partfun1 @ F @ A @ B )
                  & ( r1_partfun1 @ C @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_partfun1) ).

thf(7422,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( D
              = ( k5_partfun1 @ A @ B @ C ) )
           => ! [E: $i] :
                ( ( ( r2_hidden @ E @ D )
                 => ? [F: $i] :
                      ( ( v1_funct_1 @ F )
                      & ( m2_relset_1 @ F @ A @ B )
                      & ( F = E )
                      & ( v1_partfun1 @ F @ A @ B )
                      & ( r1_partfun1 @ C @ F ) ) )
                & ( ? [F: $i] :
                      ( ( v1_funct_1 @ F )
                      & ( m2_relset_1 @ F @ A @ B )
                      & ( F = E )
                      & ( v1_partfun1 @ F @ A @ B )
                      & ( r1_partfun1 @ C @ F ) )
                 => ( r2_hidden @ E @ D ) ) ) )
          & ( ! [E: $i] :
                ( ( ( r2_hidden @ E @ D )
                 => ? [F: $i] :
                      ( ( v1_funct_1 @ F )
                      & ( m2_relset_1 @ F @ A @ B )
                      & ( F = E )
                      & ( v1_partfun1 @ F @ A @ B )
                      & ( r1_partfun1 @ C @ F ) ) )
                & ( ? [F: $i] :
                      ( ( v1_funct_1 @ F )
                      & ( m2_relset_1 @ F @ A @ B )
                      & ( F = E )
                      & ( v1_partfun1 @ F @ A @ B )
                      & ( r1_partfun1 @ C @ F ) )
                 => ( r2_hidden @ E @ D ) ) )
           => ( D
              = ( k5_partfun1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).

thf(1864,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ~ ( ( B != k1_xboole_0 )
            & ( ( k7_setfam_1 @ A @ B )
              = k1_xboole_0 ) )
        & ~ ( ( ( k7_setfam_1 @ A @ B )
             != k1_xboole_0 )
            & ( B = k1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_tops_2) ).

thf(11513,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ~ ( ( B != k1_xboole_0 )
            & ( ( k7_setfam_1 @ A @ B )
              = k1_xboole_0 ) )
        & ~ ( ( ( k7_setfam_1 @ A @ B )
             != k1_xboole_0 )
            & ( B = k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1864]) ).

thf(818,axiom,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_zfmisc_1) ).

thf(6551,plain,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(83,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) )
           => ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
              = ( k2_relat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).

thf(3121,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ B ) )
           => ( ( k2_relat_1 @ ( k5_relat_1 @ B @ A ) )
              = ( k2_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(958,axiom,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
     => ( ( k1_funct_2 @ A @ k1_xboole_0 )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_2) ).

thf(7188,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
     => ( ( k1_funct_2 @ A @ k1_xboole_0 )
        = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).

thf(1330,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k15_funct_3 @ ( k2_funcop_1 @ A @ C ) @ ( k2_funcop_1 @ B @ D ) )
      = ( k2_funcop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k4_tarski @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_altcat_2) ).

thf(8881,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k15_funct_3 @ ( k2_funcop_1 @ A @ C ) @ ( k2_funcop_1 @ B @ D ) )
      = ( k2_funcop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k4_tarski @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).

thf(1779,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ C @ A )
       => ( ( ( B = k1_xboole_0 )
            & ( A != k1_xboole_0 ) )
          | ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
            & ( v1_funct_2 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B )
            & ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_2) ).

thf(11055,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ C @ A )
       => ( ( ( B = k1_xboole_0 )
            & ( A != k1_xboole_0 ) )
          | ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
            & ( v1_funct_2 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B )
            & ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ D @ C ) @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1779]) ).

thf(2539,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( k4_card_fil @ A )
        = ( a_1_0_card_fil @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_card_fil) ).

thf(14689,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( k4_card_fil @ A )
        = ( a_1_0_card_fil @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2539]) ).

thf(1423,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
            & ! [F: $i] :
                ~ ( ( r2_hidden @ F @ A )
                  & ( r2_hidden @ F @ C )
                  & ( E
                    = ( k1_funct_1 @ D @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_funct_2) ).

thf(9278,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
            & ! [F: $i] :
                ~ ( ( r2_hidden @ F @ A )
                  & ( r2_hidden @ F @ C )
                  & ( E
                    = ( k1_funct_1 @ D @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1423]) ).

thf(2158,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ B )
         => ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
            & ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
            & ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_funcop_1) ).

thf(13145,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ B )
         => ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
            & ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
            & ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2158]) ).

thf(2355,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k1_cantor_1 @ A @ ( k1_cantor_1 @ A @ B ) )
        = ( k1_cantor_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_yellow_9) ).

thf(13901,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k1_cantor_1 @ A @ ( k1_cantor_1 @ A @ B ) )
        = ( k1_cantor_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2355]) ).

thf(1918,axiom,
    ! [A: $i] :
      ( ~ ( ? [B: $i] :
              ( ( B != k1_xboole_0 )
              & ( r2_hidden @ B @ A ) )
          & ( ( k3_tarski @ A )
            = k1_xboole_0 ) )
      & ~ ( ( ( k3_tarski @ A )
           != k1_xboole_0 )
          & ! [B: $i] :
              ~ ( ( B != k1_xboole_0 )
                & ( r2_hidden @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_orders_1) ).

thf(11756,plain,
    ! [A: $i] :
      ( ~ ( ? [B: $i] :
              ( ( B != k1_xboole_0 )
              & ( r2_hidden @ B @ A ) )
          & ( ( k3_tarski @ A )
            = k1_xboole_0 ) )
      & ~ ( ( ( k3_tarski @ A )
           != k1_xboole_0 )
          & ! [B: $i] :
              ~ ( ( B != k1_xboole_0 )
                & ( r2_hidden @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1918]) ).

thf(1074,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k9_relat_1 @ A @ k1_xboole_0 )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_relat_1) ).

thf(7748,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k9_relat_1 @ A @ k1_xboole_0 )
        = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).

thf(206,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k9_finseq_1 @ A )
     != ( k11_finseq_1 @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_finseq_3) ).

thf(3717,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k9_finseq_1 @ A )
     != ( k11_finseq_1 @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(2141,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ C )
                        & ( m2_relset_1 @ E @ A @ C ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ( ( k8_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ F )
                            = ( k4_tarski @ ( k8_funct_2 @ A @ B @ D @ F ) @ ( k8_funct_2 @ A @ C @ E @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funct_3) ).

thf(13056,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ C )
                        & ( m2_relset_1 @ E @ A @ C ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ( ( k8_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ F )
                            = ( k4_tarski @ ( k8_funct_2 @ A @ B @ D @ F ) @ ( k8_funct_2 @ A @ C @ E @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2141]) ).

thf(505,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ( ( k3_funct_2 @ A @ A @ B @ ( k2_funct_2 @ A @ A @ B @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funct_2) ).

thf(5192,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ( ( k3_funct_2 @ A @ A @ B @ ( k2_funct_2 @ A @ A @ B @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(2466,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
                 => ( ( k12_mcart_1 @ A @ B @ C @ D )
                    = ( a_4_1_domain_1 @ A @ B @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_domain_1) ).

thf(14354,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
                 => ( ( k12_mcart_1 @ A @ B @ C @ D )
                    = ( a_4_1_domain_1 @ A @ B @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2466]) ).

thf(1299,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_realset1 @ A )
        & ( m4_realset1 @ B @ A ) )
     => ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_realset1) ).

thf(8752,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_realset1 @ A )
        & ( m4_realset1 @ B @ A ) )
     => ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).

thf(2102,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
    <=> ! [C: $i] :
          ( ( r2_hidden @ C @ A )
         => ( r2_hidden @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

thf(12816,plain,
    ! [A: $i,B: $i] :
      ( ( ( r1_tarski @ A @ B )
       => ! [C: $i] :
            ( ( r2_hidden @ C @ A )
           => ( r2_hidden @ C @ B ) ) )
      & ( ! [C: $i] :
            ( ( r2_hidden @ C @ A )
           => ( r2_hidden @ C @ B ) )
       => ( r1_tarski @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2102]) ).

thf(2240,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_subset_1) ).

thf(13488,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2240]) ).

thf(556,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                         => ! [G: $i] :
                              ( ( m2_finseq_1 @ G @ B )
                             => ( ( G
                                  = ( k12_finseq_1 @ B @ E ) )
                               => ( ( k5_funcop_1 @ F @ D @ G )
                                  = ( k12_finseq_1 @ C @ ( k2_binop_1 @ A @ B @ C @ F @ D @ E ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_finseq_2) ).

thf(5412,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                         => ! [G: $i] :
                              ( ( m2_finseq_1 @ G @ B )
                             => ( ( G
                                  = ( k12_finseq_1 @ B @ E ) )
                               => ( ( k5_funcop_1 @ F @ D @ G )
                                  = ( k12_finseq_1 @ C @ ( k2_binop_1 @ A @ B @ C @ F @ D @ E ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(1510,axiom,
    ! [A: $i] :
      ( ( v1_realset1 @ A )
     => ( v1_finset_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_yellow13) ).

thf(9672,plain,
    ! [A: $i] :
      ( ( v1_realset1 @ A )
     => ( v1_finset_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1510]) ).

thf(517,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ C )
        & ( v4_finsub_1 @ C ) )
     => ( ( ( m1_subset_1 @ A @ C )
          & ( m1_subset_1 @ B @ C ) )
       => ( m1_subset_1 @ ( k5_xboole_0 @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finsub_1) ).

thf(5252,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ C )
        & ( v4_finsub_1 @ C ) )
     => ( ( ( m1_subset_1 @ A @ C )
          & ( m1_subset_1 @ B @ C ) )
       => ( m1_subset_1 @ ( k5_xboole_0 @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(751,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( v1_binop_1 @ C @ B )
                       => ( ( k8_funcop_1 @ B @ A @ C @ E @ D )
                          = ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funcop_1) ).

thf(6251,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( v1_binop_1 @ C @ B )
                       => ( ( k8_funcop_1 @ B @ A @ C @ E @ D )
                          = ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(1519,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_zfmisc_1) ).

thf(9746,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1519]) ).

thf(574,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ C )
                         => ( ( k3_funct_2 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) @ ( k16_funct_3 @ A @ C @ B @ C @ D @ ( k6_partfun1 @ C ) ) @ ( k6_domain_1 @ ( k2_zfmisc_1 @ B @ C ) @ ( k1_domain_1 @ B @ C @ E @ F ) ) )
                            = ( k12_mcart_1 @ A @ C @ ( k3_funct_2 @ A @ B @ D @ ( k6_domain_1 @ B @ E ) ) @ ( k6_domain_1 @ C @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_borsuk_1) ).

thf(5476,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ C )
                         => ( ( k3_funct_2 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) @ ( k16_funct_3 @ A @ C @ B @ C @ D @ ( k6_partfun1 @ C ) ) @ ( k6_domain_1 @ ( k2_zfmisc_1 @ B @ C ) @ ( k1_domain_1 @ B @ C @ E @ F ) ) )
                            = ( k12_mcart_1 @ A @ C @ ( k3_funct_2 @ A @ B @ D @ ( k6_domain_1 @ B @ E ) ) @ ( k6_domain_1 @ C @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(964,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
      = ( k3_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_xboole_1) ).

thf(7240,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
      = ( k3_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).

thf(1169,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
        & ( v1_funct_1 @ ( k7_relat_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).

thf(8165,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
        & ( v1_funct_1 @ ( k7_relat_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).

thf(371,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( r1_xboole_0 @ B @ ( k1_relat_1 @ A ) )
         => ( ( k7_relat_1 @ A @ B )
            = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t187_relat_1) ).

thf(4607,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( r1_xboole_0 @ B @ ( k1_relat_1 @ A ) )
         => ( ( k7_relat_1 @ A @ B )
            = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(2114,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_zfmisc_1) ).

thf(12879,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2114]) ).

thf(443,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v3_binop_1 @ B @ A )
          <=> ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ( ( k2_binop_1 @ A @ A @ A @ B @ C @ C )
                  = C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_binop_1) ).

thf(4941,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( v3_binop_1 @ B @ A )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ( ( k2_binop_1 @ A @ A @ A @ B @ C @ C )
                    = C ) ) )
            & ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ( ( k2_binop_1 @ A @ A @ A @ B @ C @ C )
                    = C ) )
             => ( v3_binop_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(1646,axiom,
    ! [A: $i] : ( m2_relset_1 @ ( k6_relat_1 @ A ) @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_relset_1) ).

thf(10351,plain,
    ! [A: $i] : ( m2_relset_1 @ ( k6_relat_1 @ A ) @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1646]) ).

thf(1102,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( r1_xboole_0 @ A @ ( k2_relat_1 @ ( k1_funct_4 @ ( k6_partfun1 @ B ) @ ( k2_funcop_1 @ A @ C ) ) ) )
     => ( r2_hidden @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_funct_7) ).

thf(7858,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( r1_xboole_0 @ A @ ( k2_relat_1 @ ( k1_funct_4 @ ( k6_partfun1 @ B ) @ ( k2_funcop_1 @ A @ C ) ) ) )
     => ( r2_hidden @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).

thf(1337,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( r1_lattice2 @ A @ B @ C )
              <=> ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
                          = D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattice2) ).

thf(8911,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( ( r1_lattice2 @ A @ B @ C )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
                            = D ) ) ) )
                & ( ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
                            = D ) ) )
                 => ( r1_lattice2 @ A @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).

thf(268,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
         => ( ( k7_relat_1 @ A @ ( k1_tarski @ B ) )
            = ( k3_cqc_lang @ B @ ( k1_funct_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_7) ).

thf(4047,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
         => ( ( k7_relat_1 @ A @ ( k1_tarski @ B ) )
            = ( k3_cqc_lang @ B @ ( k1_funct_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ A )
                        & ( m2_relset_1 @ E @ B @ A ) )
                     => ( ( ( v1_binop_1 @ C @ A )
                          & ( v2_binop_1 @ C @ A )
                          & ( v3_binop_1 @ C @ A ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                           => ( ( r2_hidden @ F @ D )
                             => ( ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ E @ F ) @ ( k7_setwiseo @ B @ A @ C @ D @ E ) )
                                = ( k7_setwiseo @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_setwiseo) ).

thf(3103,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ A )
                        & ( m2_relset_1 @ E @ B @ A ) )
                     => ( ( ( v1_binop_1 @ C @ A )
                          & ( v2_binop_1 @ C @ A )
                          & ( v3_binop_1 @ C @ A ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                           => ( ( r2_hidden @ F @ D )
                             => ( ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ E @ F ) @ ( k7_setwiseo @ B @ A @ C @ D @ E ) )
                                = ( k7_setwiseo @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(2302,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( m1_subset_1 @ ( k2_cqc_lang @ A @ B @ C @ D @ E ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_cqc_lang) ).

thf(13700,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( m1_subset_1 @ ( k2_cqc_lang @ A @ B @ C @ D @ E ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2302]) ).

thf(1649,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( r1_tarski @ A @ B )
          <=> ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_orders_1) ).

thf(10368,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( ( r1_tarski @ A @ B )
             => ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) )
            & ( ( r2_hidden @ A @ ( k1_orders_1 @ B ) )
             => ( r1_tarski @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1649]) ).

thf(2234,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( r1_tarski @ B @ C )
           => ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_setfam_1) ).

thf(13469,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( r1_tarski @ B @ C )
           => ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2234]) ).

thf(2435,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
    <=> ( r1_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

thf(14203,plain,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
       => ( r1_tarski @ A @ B ) )
      & ( ( r1_tarski @ A @ B )
       => ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2435]) ).

thf(1623,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ~ ( ( B != k1_xboole_0 )
          & ( ( k7_setfam_1 @ A @ B )
            = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).

thf(10230,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ~ ( ( B != k1_xboole_0 )
          & ( ( k7_setfam_1 @ A @ B )
            = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1623]) ).

thf(2229,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ C @ D @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_enumset1) ).

thf(13452,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ C @ D @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2229]) ).

thf(1660,axiom,
    ( ( v1_funct_1 @ k34_binop_2 )
    & ( v1_funct_2 @ k34_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( m2_relset_1 @ k34_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k34_binop_2) ).

thf(10427,plain,
    ( ( v1_funct_1 @ k34_binop_2 )
    & ( v1_funct_2 @ k34_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( m2_relset_1 @ k34_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1660]) ).

thf(109,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ ( k1_tarski @ C ) ) )
     => ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
        & ( ( k2_mcart_1 @ A )
          = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_mcart_1) ).

thf(3236,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ ( k1_tarski @ C ) ) )
     => ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
        & ( ( k2_mcart_1 @ A )
          = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(135,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) )
          & ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
          & ( v2_funct_1 @ C ) )
       => ( r1_tarski @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t157_funct_1) ).

thf(3350,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) )
          & ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
          & ( v2_funct_1 @ C ) )
       => ( r1_tarski @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(800,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ A ) ) @ C )
                = ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funcop_1) ).

thf(6466,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ A ) ) @ C )
                = ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(2282,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ C )
        & ( v1_classes2 @ C ) )
     => ( ( ( r2_hidden @ A @ C )
          & ( r2_hidden @ B @ C ) )
       => ( ( r2_hidden @ ( k2_zfmisc_1 @ A @ B ) @ C )
          & ( r2_hidden @ ( k1_funct_2 @ A @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_classes2) ).

thf(13628,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ C )
        & ( v1_classes2 @ C ) )
     => ( ( ( r2_hidden @ A @ C )
          & ( r2_hidden @ B @ C ) )
       => ( ( r2_hidden @ ( k2_zfmisc_1 @ A @ B ) @ C )
          & ( r2_hidden @ ( k1_funct_2 @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2282]) ).

thf(168,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( ( v1_xboole_0 @ ( k1_relat_1 @ A ) )
        & ( v1_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).

thf(3545,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( ( v1_xboole_0 @ ( k1_relat_1 @ A ) )
        & ( v1_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(1427,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) )
        & ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).

thf(9292,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) )
        & ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427]) ).

thf(1146,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
     => ! [E: $i] :
          ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
         => ! [F: $i] :
              ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
             => ! [G: $i] :
                  ( ( m1_subset_1 @ G @ ( k3_zfmisc_1 @ A @ B @ C ) )
                 => ( ( r2_hidden @ G @ ( k3_zfmisc_1 @ D @ E @ F ) )
                   => ( ( r2_hidden @ ( k5_mcart_1 @ A @ B @ C @ G ) @ D )
                      & ( r2_hidden @ ( k6_mcart_1 @ A @ B @ C @ G ) @ E )
                      & ( r2_hidden @ ( k7_mcart_1 @ A @ B @ C @ G ) @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_mcart_1) ).

thf(8086,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
     => ! [E: $i] :
          ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
         => ! [F: $i] :
              ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
             => ! [G: $i] :
                  ( ( m1_subset_1 @ G @ ( k3_zfmisc_1 @ A @ B @ C ) )
                 => ( ( r2_hidden @ G @ ( k3_zfmisc_1 @ D @ E @ F ) )
                   => ( ( r2_hidden @ ( k5_mcart_1 @ A @ B @ C @ G ) @ D )
                      & ( r2_hidden @ ( k6_mcart_1 @ A @ B @ C @ G ) @ E )
                      & ( r2_hidden @ ( k7_mcart_1 @ A @ B @ C @ G ) @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).

thf(1048,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( v1_binop_1 @ B @ A )
           => ( ( r1_binop_1 @ A @ C @ B )
            <=> ( r2_binop_1 @ A @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_binop_1) ).

thf(7637,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( v1_binop_1 @ B @ A )
           => ( ( ( r1_binop_1 @ A @ C @ B )
               => ( r2_binop_1 @ A @ C @ B ) )
              & ( ( r2_binop_1 @ A @ C @ B )
               => ( r1_binop_1 @ A @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).

thf(57,axiom,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k1_numbers )
        & ( m1_subset_1 @ B @ k1_numbers ) )
     => ( m1_subset_1 @ ( k11_binop_2 @ A @ B ) @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_binop_2) ).

thf(2985,plain,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k1_numbers )
        & ( m1_subset_1 @ B @ k1_numbers ) )
     => ( m1_subset_1 @ ( k11_binop_2 @ A @ B ) @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(1838,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_orders_3 @ A ) )
     => ? [B: $i] : ( m1_orders_3 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_orders_3) ).

thf(11382,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_orders_3 @ A ) )
     => ? [B: $i] : ( m1_orders_3 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1838]) ).

thf(1708,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
     => ( B = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_partfun1) ).

thf(10599,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
     => ( B = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1708]) ).

thf(2167,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ ( k5_finsub_1 @ B ) )
        & ( m1_relset_1 @ D @ A @ ( k5_finsub_1 @ B ) ) )
     => ( m1_subset_1 @ ( k10_setwiseo @ A @ B @ C @ D ) @ ( k5_finsub_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_setwiseo) ).

thf(13179,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ ( k5_finsub_1 @ B ) )
        & ( m1_relset_1 @ D @ A @ ( k5_finsub_1 @ B ) ) )
     => ( m1_subset_1 @ ( k10_setwiseo @ A @ B @ C @ D ) @ ( k5_finsub_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2167]) ).

thf(586,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) @ ( k5_finsub_1 @ ( k2_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finsub_1) ).

thf(5518,plain,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) @ ( k5_finsub_1 @ ( k2_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(2483,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k4_partfun1 @ A @ B ) ) ) )
     => ! [D: $i] :
          ( ( m1_pua2mss1 @ D @ A @ B @ C )
         => ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_pua2mss1) ).

thf(14436,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k4_partfun1 @ A @ B ) ) ) )
     => ! [D: $i] :
          ( ( m1_pua2mss1 @ D @ A @ B @ C )
         => ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2483]) ).

thf(883,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ( ( v2_binop_1 @ C @ B )
                           => ( ( k7_funcop_1 @ B @ A @ C @ D @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) )
                              = ( k7_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ E ) @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_funcop_1) ).

thf(6872,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ( ( v2_binop_1 @ C @ B )
                           => ( ( k7_funcop_1 @ B @ A @ C @ D @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) )
                              = ( k7_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ E ) @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(776,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_partfun1 @ A @ B )
          <=> ( ( k2_xboole_0 @ A @ B )
              = ( k1_funct_4 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_funct_4) ).

thf(6381,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( r1_partfun1 @ A @ B )
             => ( ( k2_xboole_0 @ A @ B )
                = ( k1_funct_4 @ A @ B ) ) )
            & ( ( ( k2_xboole_0 @ A @ B )
                = ( k1_funct_4 @ A @ B ) )
             => ( r1_partfun1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(2377,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k7_classes2 @ A @ B @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k7_classes2) ).

thf(13997,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k7_classes2 @ A @ B @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2377]) ).

thf(1883,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( r1_tarski @ ( k1_funct_2 @ B @ C ) @ ( k1_ens_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_ens_1) ).

thf(11613,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( r1_tarski @ ( k1_funct_2 @ B @ C ) @ ( k1_ens_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1883]) ).

thf(888,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ A )
                        & ( m2_relset_1 @ E @ B @ A ) )
                     => ( ( ( v3_binop_1 @ C @ A )
                          & ( v1_binop_1 @ C @ A )
                          & ( v2_binop_1 @ C @ A ) )
                       => ( ( D = k1_xboole_0 )
                          | ! [F: $i] :
                              ( ( m1_subset_1 @ F @ B )
                             => ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ D @ ( k2_setwiseo @ B @ F ) ) @ E )
                                = ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ D @ E ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_setwiseo) ).

thf(6887,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ A )
                        & ( m2_relset_1 @ E @ B @ A ) )
                     => ( ( ( v3_binop_1 @ C @ A )
                          & ( v1_binop_1 @ C @ A )
                          & ( v2_binop_1 @ C @ A ) )
                       => ( ( D = k1_xboole_0 )
                          | ! [F: $i] :
                              ( ( m1_subset_1 @ F @ B )
                             => ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ D @ ( k2_setwiseo @ B @ F ) ) @ E )
                                = ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ D @ E ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(1515,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( k6_subset_1 @ A @ B @ C )
            = ( k5_subset_1 @ A @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_subset_1) ).

thf(9735,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( k6_subset_1 @ A @ B @ C )
            = ( k5_subset_1 @ A @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1515]) ).

thf(835,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) @ ( k1_tarski @ E ) )
      = ( k2_enumset1 @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ B @ C @ E ) @ ( k3_mcart_1 @ A @ D @ E ) @ ( k3_mcart_1 @ B @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_mcart_1) ).

thf(6623,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) @ ( k1_tarski @ E ) )
      = ( k2_enumset1 @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ B @ C @ E ) @ ( k3_mcart_1 @ A @ D @ E ) @ ( k3_mcart_1 @ B @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(506,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( k2_tarski @ A @ B ) )
    <=> ! [D: $i] :
          ( ( r2_hidden @ D @ C )
        <=> ( ( D = A )
            | ( D = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

thf(5195,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C
          = ( k2_tarski @ A @ B ) )
       => ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ( ( D = A )
                | ( D = B ) ) )
            & ( ( ( D = A )
                | ( D = B ) )
             => ( r2_hidden @ D @ C ) ) ) )
      & ( ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ( ( D = A )
                | ( D = B ) ) )
            & ( ( ( D = A )
                | ( D = B ) )
             => ( r2_hidden @ D @ C ) ) )
       => ( C
          = ( k2_tarski @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(2004,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ! [E: $i,F: $i] :
            ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ A )
           => ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) ) )
     => ( r1_tarski @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_zfmisc_1) ).

thf(12303,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ! [E: $i,F: $i] :
            ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ A )
           => ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) ) )
     => ( r1_tarski @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2004]) ).

thf(2087,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B )
        & ( v1_finset_1 @ C )
        & ( v1_finset_1 @ D ) )
     => ( v1_finset_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_finset_1) ).

thf(12757,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B )
        & ( v1_finset_1 @ C )
        & ( v1_finset_1 @ D ) )
     => ( v1_finset_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2087]) ).

thf(2146,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k2_zfmisc_1 @ A @ B )
        = k1_xboole_0 )
    <=> ( ( A = k1_xboole_0 )
        | ( B = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).

thf(13083,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( k2_zfmisc_1 @ A @ B )
          = k1_xboole_0 )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 ) ) )
      & ( ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 ) )
       => ( ( k2_zfmisc_1 @ A @ B )
          = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2146]) ).

thf(981,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( v1_relat_1 @ ( k5_funcop_1 @ A @ B @ C ) )
        & ( v1_funct_1 @ ( k5_funcop_1 @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_funcop_1) ).

thf(7326,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( v1_relat_1 @ ( k5_funcop_1 @ A @ B @ C ) )
        & ( v1_funct_1 @ ( k5_funcop_1 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

thf(660,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( r1_tarski @ ( k2_funct_4 @ ( k2_funct_4 @ A ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_4) ).

thf(5825,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( r1_tarski @ ( k2_funct_4 @ ( k2_funct_4 @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(473,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( k9_relat_1 @ C @ ( k5_setfam_1 @ A @ B ) )
            = ( k3_tarski @ ( a_3_0_relset_2 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_2) ).

thf(5056,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( k9_relat_1 @ C @ ( k5_setfam_1 @ A @ B ) )
            = ( k3_tarski @ ( a_3_0_relset_2 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(2210,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k2_zfmisc_1 @ A @ B )
        = ( k2_zfmisc_1 @ B @ A ) )
     => ( ( A = k1_xboole_0 )
        | ( B = k1_xboole_0 )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_zfmisc_1) ).

thf(13378,plain,
    ! [A: $i,B: $i] :
      ( ( ( k2_zfmisc_1 @ A @ B )
        = ( k2_zfmisc_1 @ B @ A ) )
     => ( ( A = k1_xboole_0 )
        | ( B = k1_xboole_0 )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2210]) ).

thf(2123,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( r2_hidden @ B @ ( k4_card_fil @ A ) )
        <=> ( m1_card_fil @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_card_fil) ).

thf(12960,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( r2_hidden @ B @ ( k4_card_fil @ A ) )
           => ( m1_card_fil @ B @ A ) )
          & ( ( m1_card_fil @ B @ A )
           => ( r2_hidden @ B @ ( k4_card_fil @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2123]) ).

thf(1281,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ C )
        & ( m1_relset_1 @ E @ A @ C )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ B @ D )
        & ( m1_relset_1 @ F @ B @ D ) )
     => ( ( k16_funct_3 @ A @ B @ C @ D @ E @ F )
        = ( k15_funct_3 @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k16_funct_3) ).

thf(8671,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ C )
        & ( m1_relset_1 @ E @ A @ C )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ B @ D )
        & ( m1_relset_1 @ F @ B @ D ) )
     => ( ( k16_funct_3 @ A @ B @ C @ D @ E @ F )
        = ( k15_funct_3 @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).

thf(1196,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).

thf(8256,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( v1_xboole_0 @ ( k2_xboole_0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).

thf(2548,axiom,
    ? [A: $i] :
      ~ ( v1_xboole_0 @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(14716,plain,
    ? [A: $i] :
      ~ ( v1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2548]) ).

thf(1467,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( m1_relset_1 @ E @ A @ B )
        & ( v1_funct_1 @ F )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( ( k1_partfun1 @ A @ B @ C @ D @ E @ F )
        = ( k5_relat_1 @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_partfun1) ).

thf(9465,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( m1_relset_1 @ E @ A @ B )
        & ( v1_funct_1 @ F )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( ( k1_partfun1 @ A @ B @ C @ D @ E @ F )
        = ( k5_relat_1 @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467]) ).

thf(1697,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_zfmisc_1 @ A @ B @ C @ D )
      = ( k2_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_zfmisc_1) ).

thf(10559,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_zfmisc_1 @ A @ B @ C @ D )
      = ( k2_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1697]) ).

thf(2385,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( ~ ( v1_xboole_0 @ C )
                & ( m1_finseq_2 @ C @ B ) )
             => ( ~ ( v1_xboole_0 @ C )
                & ( m1_finseq_2 @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_finseq_2) ).

thf(14023,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( ~ ( v1_xboole_0 @ C )
                & ( m1_finseq_2 @ C @ B ) )
             => ( ~ ( v1_xboole_0 @ C )
                & ( m1_finseq_2 @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2385]) ).

thf(2535,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A ) )
     => ( m1_subset_1 @ ( k8_domain_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_domain_1) ).

thf(14677,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A ) )
     => ( m1_subset_1 @ ( k8_domain_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2535]) ).

thf(2524,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( m1_subset_1 @ ( k3_subset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).

thf(14644,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( m1_subset_1 @ ( k3_subset_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2524]) ).

thf(449,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_tarski @ A @ B )
           => ( ( ( k1_funct_4 @ A @ B )
                = B )
              & ( ( k1_funct_4 @ B @ A )
                = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funct_4) ).

thf(4963,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_tarski @ A @ B )
           => ( ( ( k1_funct_4 @ A @ B )
                = B )
              & ( ( k1_funct_4 @ B @ A )
                = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(2094,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_eqrel_1 @ B @ A )
         => ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_eqrel_1) ).

thf(12785,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_eqrel_1 @ B @ A )
         => ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2094]) ).

thf(293,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
            & ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
              = k1_xboole_0 ) )
         => ( r1_tarski @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) @ A ) )
        & ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
            & ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
              = k1_xboole_0 ) )
         => ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_sysrel) ).

thf(4156,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
            & ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
              = k1_xboole_0 ) )
         => ( r1_tarski @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) @ A ) )
        & ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
            & ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
              = k1_xboole_0 ) )
         => ( r1_tarski @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(522,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_xboole_0 @ A @ B )
    <=> ( ( k4_xboole_0 @ A @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).

thf(5269,plain,
    ! [A: $i,B: $i] :
      ( ( ( r1_xboole_0 @ A @ B )
       => ( ( k4_xboole_0 @ A @ B )
          = A ) )
      & ( ( ( k4_xboole_0 @ A @ B )
          = A )
       => ( r1_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(2011,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ k1_numbers @ A ) @ A )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ k1_numbers @ A ) @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A ) )
     => ! [G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
          ( ( ( g1_funcsdom @ A @ B @ C @ D @ E @ F )
            = ( g1_funcsdom @ G @ H @ I @ J @ K @ L ) )
         => ( ( A = G )
            & ( B = H )
            & ( C = I )
            & ( D = J )
            & ( E = K )
            & ( F = L ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_funcsdom) ).

thf(12324,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ k1_numbers @ A ) @ A )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ k1_numbers @ A ) @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A ) )
     => ! [G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
          ( ( ( g1_funcsdom @ A @ B @ C @ D @ E @ F )
            = ( g1_funcsdom @ G @ H @ I @ J @ K @ L ) )
         => ( ( A = G )
            & ( B = H )
            & ( C = I )
            & ( D = J )
            & ( E = K )
            & ( F = L ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2011]) ).

thf(1450,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( v1_funct_1 @ G )
        & ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ! [H: $i] :
          ( ( ( v1_funct_1 @ H )
            & ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ D @ E ) @ F ) )
         => ( ( v1_funct_1 @ ( k3_funct_4 @ G @ H ) )
            & ( m2_relset_1 @ ( k3_funct_4 @ G @ H ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ E ) ) @ ( k2_zfmisc_1 @ C @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_4) ).

thf(9394,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( v1_funct_1 @ G )
        & ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ! [H: $i] :
          ( ( ( v1_funct_1 @ H )
            & ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ D @ E ) @ F ) )
         => ( ( v1_funct_1 @ ( k3_funct_4 @ G @ H ) )
            & ( m2_relset_1 @ ( k3_funct_4 @ G @ H ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ E ) ) @ ( k2_zfmisc_1 @ C @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450]) ).

thf(372,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ( ( k4_ens_1 @ A @ B )
            = ( k2_mcart_1 @ ( k1_mcart_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_ens_1) ).

thf(4610,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ( ( k4_ens_1 @ A @ B )
            = ( k2_mcart_1 @ ( k1_mcart_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(1541,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k5_enumset1 @ A @ A @ A @ B @ C @ D @ E )
      = ( k3_enumset1 @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_enumset1) ).

thf(9850,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k5_enumset1 @ A @ A @ A @ B @ C @ D @ E )
      = ( k3_enumset1 @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1541]) ).

thf(1034,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_relat_1 @ B ) )
     => ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).

thf(7592,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_relat_1 @ B ) )
     => ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).

thf(1680,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ A )
                     => ! [G: $i] :
                          ( ( m1_subset_1 @ G @ A )
                         => ( ( A != k1_xboole_0 )
                           => ( m1_subset_1 @ ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_subset_1) ).

thf(10501,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ A )
                     => ! [G: $i] :
                          ( ( m1_subset_1 @ G @ A )
                         => ( ( A != k1_xboole_0 )
                           => ( m1_subset_1 @ ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1680]) ).

thf(1557,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
     => ( ( r2_hidden @ A @ ( k1_funct_5 @ C ) )
        & ( r2_hidden @ B @ ( k2_funct_5 @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_5) ).

thf(9946,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
     => ( ( r2_hidden @ A @ ( k1_funct_5 @ C ) )
        & ( r2_hidden @ B @ ( k2_funct_5 @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1557]) ).

thf(975,axiom,
    ( ( k2_relat_1 @ k1_xboole_0 )
    = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_partfun1) ).

thf(7311,plain,
    ( ( k2_relat_1 @ k1_xboole_0 )
    = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).

thf(1045,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
     => ( ( k9_funcop_1 @ A @ B @ C @ D )
        = ( k2_relat_1 @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_funcop_1) ).

thf(7628,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
     => ( ( k9_funcop_1 @ A @ B @ C @ D )
        = ( k2_relat_1 @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).

thf(1704,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( v1_funct_1 @ ( k11_ens_1 @ A ) )
        & ( v1_funct_2 @ ( k11_ens_1 @ A ) @ A @ ( k2_ens_1 @ A ) )
        & ( m2_relset_1 @ ( k11_ens_1 @ A ) @ A @ ( k2_ens_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_ens_1) ).

thf(10584,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( v1_funct_1 @ ( k11_ens_1 @ A ) )
        & ( v1_funct_2 @ ( k11_ens_1 @ A ) @ A @ ( k2_ens_1 @ A ) )
        & ( m2_relset_1 @ ( k11_ens_1 @ A ) @ A @ ( k2_ens_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1704]) ).

thf(545,axiom,
    ! [A: $i,B: $i] :
      ( ( k1_enumset1 @ A @ A @ B )
      = ( k2_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_enumset1) ).

thf(5352,plain,
    ! [A: $i,B: $i] :
      ( ( k1_enumset1 @ A @ A @ B )
      = ( k2_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(352,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
          = A )
        & ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_funct_1) ).

thf(4539,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
          = A )
        & ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(1382,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_xboole_0 @ A @ B )
     => ( ( k2_xboole_0 @ ( k4_xboole_0 @ C @ A ) @ B )
        = ( k4_xboole_0 @ ( k2_xboole_0 @ C @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_xboole_1) ).

thf(9067,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_xboole_0 @ A @ B )
     => ( ( k2_xboole_0 @ ( k4_xboole_0 @ C @ A ) @ B )
        = ( k4_xboole_0 @ ( k2_xboole_0 @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382]) ).

thf(525,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( r1_tarski @ D @ C )
           => ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t165_funct_2) ).

thf(5284,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( r1_tarski @ D @ C )
           => ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(90,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( ( k1_relat_1 @ A )
                = ( k2_relat_1 @ B ) )
              & ( ( k2_relat_1 @ A )
                = ( k1_relat_1 @ B ) )
              & ! [C: $i,D: $i] :
                  ( ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
                    & ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) )
                 => ( ( ( k1_funct_1 @ A @ C )
                      = D )
                  <=> ( ( k1_funct_1 @ B @ D )
                      = C ) ) ) )
           => ( B
              = ( k2_funct_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funct_1) ).

thf(3148,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( ( k1_relat_1 @ A )
                = ( k2_relat_1 @ B ) )
              & ( ( k2_relat_1 @ A )
                = ( k1_relat_1 @ B ) )
              & ! [C: $i,D: $i] :
                  ( ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
                    & ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) )
                 => ( ( ( ( k1_funct_1 @ A @ C )
                        = D )
                     => ( ( k1_funct_1 @ B @ D )
                        = C ) )
                    & ( ( ( k1_funct_1 @ B @ D )
                        = C )
                     => ( ( k1_funct_1 @ A @ C )
                        = D ) ) ) ) )
           => ( B
              = ( k2_funct_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(2023,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( r2_hidden @ B @ A )
       => ( ( r2_hidden @ B @ ( k8_setfam_1 @ A @ C ) )
        <=> ! [D: $i] :
              ( ( r2_hidden @ D @ C )
             => ( r2_hidden @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_setfam_1) ).

thf(12394,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( r2_hidden @ B @ A )
       => ( ( ( r2_hidden @ B @ ( k8_setfam_1 @ A @ C ) )
           => ! [D: $i] :
                ( ( r2_hidden @ D @ C )
               => ( r2_hidden @ B @ D ) ) )
          & ( ! [D: $i] :
                ( ( r2_hidden @ D @ C )
               => ( r2_hidden @ B @ D ) )
           => ( r2_hidden @ B @ ( k8_setfam_1 @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2023]) ).

thf(232,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( r1_xboole_0 @ C @ ( k1_relat_1 @ B ) )
             => ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ C )
                = ( k7_relat_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funct_4) ).

thf(3891,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( r1_xboole_0 @ C @ ( k1_relat_1 @ B ) )
             => ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ C )
                = ( k7_relat_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(598,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ B @ A )
     => ( ( r1_tarski @ ( k6_relat_1 @ B ) @ C )
       => ( ( B
            = ( k4_relset_1 @ B @ A @ C ) )
          & ( r1_tarski @ B @ ( k5_relset_1 @ B @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_relset_1) ).

thf(5553,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ B @ A )
     => ( ( r1_tarski @ ( k6_relat_1 @ B ) @ C )
       => ( ( B
            = ( k4_relset_1 @ B @ A @ C ) )
          & ( r1_tarski @ B @ ( k5_relset_1 @ B @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(1847,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ! [C: $i] :
            ~ ( ( r2_hidden @ C @ B )
              & ! [D: $i] :
                  ~ ( ( r2_hidden @ D @ B )
                    & ( r2_hidden @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).

thf(11426,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ! [C: $i] :
            ~ ( ( r2_hidden @ C @ B )
              & ! [D: $i] :
                  ~ ( ( r2_hidden @ D @ B )
                    & ( r2_hidden @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1847]) ).

thf(1430,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
        & ( r2_hidden @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_zfmisc_1) ).

thf(9300,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
        & ( r2_hidden @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430]) ).

thf(1380,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( r2_binop_1 @ A @ B @ C )
              <=> ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ( ( k2_binop_1 @ A @ A @ A @ C @ D @ B )
                      = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_binop_1) ).

thf(9056,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( ( r2_binop_1 @ A @ B @ C )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ( ( k2_binop_1 @ A @ A @ A @ C @ D @ B )
                        = D ) ) )
                & ( ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ( ( k2_binop_1 @ A @ A @ A @ C @ D @ B )
                        = D ) )
                 => ( r2_binop_1 @ A @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380]) ).

thf(1087,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k3_funct_2 @ A @ A @ ( k6_partfun1 @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_borsuk_1) ).

thf(7790,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k3_funct_2 @ A @ A @ ( k6_partfun1 @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).

thf(1943,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ B ) )
     => ( m1_subset_1 @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_domain_1) ).

thf(11949,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ B ) )
     => ( m1_subset_1 @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1943]) ).

thf(2290,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k7_classes2 @ A @ B @ C )
        = ( k7_classes2 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k7_classes2) ).

thf(13658,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k7_classes2 @ A @ B @ C )
        = ( k7_classes2 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2290]) ).

thf(561,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ( ( v2_funct_1 @ C )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
                           => ( ( r2_hidden @ ( k8_funct_2 @ A @ B @ C @ D ) @ ( k6_subset_1 @ B @ ( k2_funct_2 @ A @ B @ C @ E ) @ F ) )
                             => ( r2_hidden @ D @ ( k6_subset_1 @ A @ E @ ( k3_funct_2 @ A @ B @ C @ F ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_7) ).

thf(5429,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ( ( v2_funct_1 @ C )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
                           => ( ( r2_hidden @ ( k8_funct_2 @ A @ B @ C @ D ) @ ( k6_subset_1 @ B @ ( k2_funct_2 @ A @ B @ C @ E ) @ F ) )
                             => ( r2_hidden @ D @ ( k6_subset_1 @ A @ E @ ( k3_funct_2 @ A @ B @ C @ F ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(608,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k6_subset_1 @ A @ B @ C )
        = ( k4_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).

thf(5585,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k6_subset_1 @ A @ B @ C )
        = ( k4_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(251,axiom,
    ! [A: $i] :
      ( ? [B: $i,C: $i] :
          ( A
          = ( k4_tarski @ B @ C ) )
     => ( ( k4_tarski @ ( k1_mcart_1 @ A ) @ ( k2_mcart_1 @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_mcart_1) ).

thf(3976,plain,
    ! [A: $i] :
      ( ? [B: $i,C: $i] :
          ( A
          = ( k4_tarski @ B @ C ) )
     => ( ( k4_tarski @ ( k1_mcart_1 @ A ) @ ( k2_mcart_1 @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v9_monoid_0 @ B @ A )
          <=> ( ( v1_setwiseo @ B @ A )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
                          = ( k3_binop_1 @ A @ B ) )
                       => ( ( C = D )
                          & ( D
                            = ( k3_binop_1 @ A @ B ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_monoid_0) ).

thf(2603,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( v9_monoid_0 @ B @ A )
             => ( ( v1_setwiseo @ B @ A )
                & ! [C: $i] :
                    ( ( m1_subset_1 @ C @ A )
                   => ! [D: $i] :
                        ( ( m1_subset_1 @ D @ A )
                       => ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
                            = ( k3_binop_1 @ A @ B ) )
                         => ( ( C = D )
                            & ( D
                              = ( k3_binop_1 @ A @ B ) ) ) ) ) ) ) )
            & ( ( ( v1_setwiseo @ B @ A )
                & ! [C: $i] :
                    ( ( m1_subset_1 @ C @ A )
                   => ! [D: $i] :
                        ( ( m1_subset_1 @ D @ A )
                       => ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
                            = ( k3_binop_1 @ A @ B ) )
                         => ( ( C = D )
                            & ( D
                              = ( k3_binop_1 @ A @ B ) ) ) ) ) ) )
             => ( v9_monoid_0 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(1755,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
        & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) )
     => ( ( k9_relset_2 @ A @ B @ C @ D @ E )
        = ( k5_relat_1 @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_relset_2) ).

thf(10935,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
        & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) )
     => ( ( k9_relset_2 @ A @ B @ C @ D @ E )
        = ( k5_relat_1 @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1755]) ).

thf(100,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( k2_xboole_0 @ A @ B )
                  = C )
               => ! [D: $i] :
                    ( ( r2_hidden @ D @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                   => ( ( k1_funct_1 @ A @ D )
                      = ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_partfun1) ).

thf(3195,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( k2_xboole_0 @ A @ B )
                  = C )
               => ! [D: $i] :
                    ( ( r2_hidden @ D @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                   => ( ( k1_funct_1 @ A @ D )
                      = ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(1244,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( B != k1_xboole_0 )
              & ( r1_tarski @ B @ A )
              & ( v6_ordinal1 @ B )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ! [D: $i] :
                        ( ( r2_hidden @ D @ B )
                       => ( r1_tarski @ D @ C ) ) ) )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ( C != B )
                    & ( r1_tarski @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_lattice4) ).

thf(8500,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( B != k1_xboole_0 )
              & ( r1_tarski @ B @ A )
              & ( v6_ordinal1 @ B )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ! [D: $i] :
                        ( ( r2_hidden @ D @ B )
                       => ( r1_tarski @ D @ C ) ) ) )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ( C != B )
                    & ( r1_tarski @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).

thf(1425,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( r1_tarski @ ( k9_relat_1 @ ( k7_relat_1 @ C @ A ) @ B ) @ ( k9_relat_1 @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t161_relat_1) ).

thf(9287,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( r1_tarski @ ( k9_relat_1 @ ( k7_relat_1 @ C @ A ) @ B ) @ ( k9_relat_1 @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425]) ).

thf(155,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) )
     => ! [D: $i,E: $i] :
          ( ( ( r2_hidden @ D @ A )
            & ( r2_hidden @ E @ B ) )
         => ( ( k9_funct_2 @ D @ E @ ( k1_binop_1 @ C @ D @ E ) )
            = ( k7_relat_1 @ C @ ( k2_zfmisc_1 @ ( k1_tarski @ D ) @ ( k1_tarski @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_7) ).

thf(3425,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) )
     => ! [D: $i,E: $i] :
          ( ( ( r2_hidden @ D @ A )
            & ( r2_hidden @ E @ B ) )
         => ( ( k9_funct_2 @ D @ E @ ( k1_binop_1 @ C @ D @ E ) )
            = ( k7_relat_1 @ C @ ( k2_zfmisc_1 @ ( k1_tarski @ D ) @ ( k1_tarski @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(2543,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k6_subset_1 @ A @ B @ C )
                = ( a_3_3_domain_1 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_domain_1) ).

thf(14701,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k6_subset_1 @ A @ B @ C )
                = ( a_3_3_domain_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2543]) ).

thf(424,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) ) )
     => ( m1_subset_1 @ ( k6_ens_1 @ A @ B @ C ) @ ( k2_ens_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_ens_1) ).

thf(4866,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) ) )
     => ( m1_subset_1 @ ( k6_ens_1 @ A @ B @ C ) @ ( k2_ens_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(1926,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( k7_funct_2 @ A @ B @ B @ D @ ( k8_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
                        = ( k8_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_funcop_1) ).

thf(11844,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( k7_funct_2 @ A @ B @ B @ D @ ( k8_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
                        = ( k8_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1926]) ).

thf(30,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
       => ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_relset_1) ).

thf(2735,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
       => ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(2248,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_finset_1 @ ( k2_zfmisc_1 @ B @ A ) )
     => ( ( A = k1_xboole_0 )
        | ( v1_finset_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_finset_1) ).

thf(13511,plain,
    ! [A: $i,B: $i] :
      ( ( v1_finset_1 @ ( k2_zfmisc_1 @ B @ A ) )
     => ( ( A = k1_xboole_0 )
        | ( v1_finset_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2248]) ).

thf(1353,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) )
            = ( k9_relat_1 @ B @ ( k2_relat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_relat_1) ).

thf(8967,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) )
            = ( k9_relat_1 @ B @ ( k2_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).

thf(815,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k2_ens_1 @ A ) )
                 => ( ( r2_hidden @ D @ ( k7_ens_1 @ A @ B @ C ) )
                  <=> ( ( ( k3_ens_1 @ A @ D )
                        = B )
                      & ( ( k4_ens_1 @ A @ D )
                        = C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_ens_1) ).

thf(6538,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k2_ens_1 @ A ) )
                 => ( ( ( r2_hidden @ D @ ( k7_ens_1 @ A @ B @ C ) )
                     => ( ( ( k3_ens_1 @ A @ D )
                          = B )
                        & ( ( k4_ens_1 @ A @ D )
                          = C ) ) )
                    & ( ( ( ( k3_ens_1 @ A @ D )
                          = B )
                        & ( ( k4_ens_1 @ A @ D )
                          = C ) )
                     => ( r2_hidden @ D @ ( k7_ens_1 @ A @ B @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(1535,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_card_fil @ B @ A ) )
     => ( ( k2_card_fil @ A @ B )
        = ( k7_setfam_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_card_fil) ).

thf(9828,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_card_fil @ B @ A ) )
     => ( ( k2_card_fil @ A @ B )
        = ( k7_setfam_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1535]) ).

thf(19,axiom,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k1_numbers )
        & ( m1_subset_1 @ B @ k1_numbers ) )
     => ( ( k9_binop_2 @ A @ B )
        = ( k9_binop_2 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k9_binop_2) ).

thf(2698,plain,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k1_numbers )
        & ( m1_subset_1 @ B @ k1_numbers ) )
     => ( ( k9_binop_2 @ A @ B )
        = ( k9_binop_2 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(1328,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( r1_tarski @ ( k9_relat_1 @ ( k13_funct_3 @ B @ C ) @ A ) @ ( k2_zfmisc_1 @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funct_3) ).

thf(8875,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( r1_tarski @ ( k9_relat_1 @ ( k13_funct_3 @ B @ C ) @ A ) @ ( k2_zfmisc_1 @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).

thf(81,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ C )
             => ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ C )
                = ( k7_relat_1 @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_funct_4) ).

thf(3116,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ C )
             => ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ C )
                = ( k7_relat_1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(2105,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_ens_1 @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_ens_1 @ A ) @ A ) )
         => ( ( B
              = ( k8_ens_1 @ A ) )
          <=> ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
               => ( ( k8_funct_2 @ ( k2_ens_1 @ A ) @ A @ B @ C )
                  = ( k3_ens_1 @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_ens_1) ).

thf(12832,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_ens_1 @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_ens_1 @ A ) @ A ) )
         => ( ( ( B
                = ( k8_ens_1 @ A ) )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
                 => ( ( k8_funct_2 @ ( k2_ens_1 @ A ) @ A @ B @ C )
                    = ( k3_ens_1 @ A @ C ) ) ) )
            & ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
                 => ( ( k8_funct_2 @ ( k2_ens_1 @ A ) @ A @ B @ C )
                    = ( k3_ens_1 @ A @ C ) ) )
             => ( B
                = ( k8_ens_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2105]) ).

thf(1489,axiom,
    v1_finset_1 @ a_0_0_pre_circ,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_pre_circ) ).

thf(9561,plain,
    v1_finset_1 @ a_0_0_pre_circ,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489]) ).

thf(1941,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ C )
                        & ( m2_relset_1 @ E @ A @ C ) )
                     => ~ ( ! [F: $i] :
                              ( ( m1_subset_1 @ F @ A )
                             => ! [G: $i] :
                                  ( ( m1_subset_1 @ G @ A )
                                 => ( ( ( k8_funct_2 @ A @ B @ D @ F )
                                      = ( k8_funct_2 @ A @ B @ D @ G ) )
                                   => ( ( k8_funct_2 @ A @ C @ E @ F )
                                      = ( k8_funct_2 @ A @ C @ E @ G ) ) ) ) )
                          & ! [F: $i] :
                              ( ( ( v1_funct_1 @ F )
                                & ( v1_funct_2 @ F @ B @ C )
                                & ( m2_relset_1 @ F @ B @ C ) )
                             => ( ( k7_funct_2 @ A @ B @ C @ D @ F )
                               != E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_borsuk_1) ).

thf(11913,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ C )
                        & ( m2_relset_1 @ E @ A @ C ) )
                     => ~ ( ! [F: $i] :
                              ( ( m1_subset_1 @ F @ A )
                             => ! [G: $i] :
                                  ( ( m1_subset_1 @ G @ A )
                                 => ( ( ( k8_funct_2 @ A @ B @ D @ F )
                                      = ( k8_funct_2 @ A @ B @ D @ G ) )
                                   => ( ( k8_funct_2 @ A @ C @ E @ F )
                                      = ( k8_funct_2 @ A @ C @ E @ G ) ) ) ) )
                          & ! [F: $i] :
                              ( ( ( v1_funct_1 @ F )
                                & ( v1_funct_2 @ F @ B @ C )
                                & ( m2_relset_1 @ F @ B @ C ) )
                             => ( ( k7_funct_2 @ A @ B @ C @ D @ F )
                               != E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1941]) ).

thf(2121,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_xboole_0 @ ( k1_funct_5 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_yellow_3) ).

thf(12956,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_xboole_0 @ ( k1_funct_5 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2121]) ).

thf(1438,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( ( v1_funct_1 @ H )
                                    & ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ A @ B ) @ C )
                                    & ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                                 => ! [I: $i] :
                                      ( ( m2_finseq_1 @ I @ A )
                                     => ( ( I
                                          = ( k11_finseq_1 @ D @ E @ F ) )
                                       => ( ( k4_funcop_1 @ H @ I @ G )
                                          = ( k11_finseq_1 @ ( k2_binop_1 @ A @ B @ C @ H @ D @ G ) @ ( k2_binop_1 @ A @ B @ C @ H @ E @ G ) @ ( k2_binop_1 @ A @ B @ C @ H @ F @ G ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_finseq_2) ).

thf(9332,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( ( v1_funct_1 @ H )
                                    & ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ A @ B ) @ C )
                                    & ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                                 => ! [I: $i] :
                                      ( ( m2_finseq_1 @ I @ A )
                                     => ( ( I
                                          = ( k11_finseq_1 @ D @ E @ F ) )
                                       => ( ( k4_funcop_1 @ H @ I @ G )
                                          = ( k11_finseq_1 @ ( k2_binop_1 @ A @ B @ C @ H @ D @ G ) @ ( k2_binop_1 @ A @ B @ C @ H @ E @ G ) @ ( k2_binop_1 @ A @ B @ C @ H @ F @ G ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1438]) ).

thf(911,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k9_relat_1 @ ( k6_relat_1 @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t162_funct_1) ).

thf(6987,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k9_relat_1 @ ( k6_relat_1 @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).

thf(1216,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( k7_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
          = ( k1_funct_4 @ ( k7_relat_1 @ A @ B ) @ ( k7_relat_1 @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_funct_4) ).

thf(8357,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( k7_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
          = ( k1_funct_4 @ ( k7_relat_1 @ A @ B ) @ ( k7_relat_1 @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).

thf(163,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v2_funct_1 @ A )
            & ( ( k2_relat_1 @ A )
              = ( k1_tarski @ B ) ) )
         => ( A
            = ( k9_finseq_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_finseq_3) ).

thf(3495,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v2_funct_1 @ A )
            & ( ( k2_relat_1 @ A )
              = ( k1_tarski @ B ) ) )
         => ( A
            = ( k9_finseq_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(1246,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_enumset1 @ A @ B @ C )
      = ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_enumset1) ).

thf(8515,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_enumset1 @ A @ B @ C )
      = ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).

thf(885,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
        = k1_xboole_0 )
      | ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
        = ( k1_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_zfmisc_1) ).

thf(6878,plain,
    ! [A: $i,B: $i] :
      ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
        = k1_xboole_0 )
      | ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
        = ( k1_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(1311,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i,E: $i] :
                  ( ( ( r2_hidden @ C @ D )
                    & ( r2_hidden @ D @ E )
                    & ( r2_hidden @ E @ B ) )
                 => ( r1_xboole_0 @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_mcart_1) ).

thf(8806,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i,E: $i] :
                  ( ( ( r2_hidden @ C @ D )
                    & ( r2_hidden @ D @ E )
                    & ( r2_hidden @ E @ B ) )
                 => ( r1_xboole_0 @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ~ ( ( v1_finset_1 @ B )
            & ( r1_tarski @ B @ ( k2_relat_1 @ A ) )
            & ! [C: $i] :
                ~ ( ( r1_tarski @ C @ ( k1_relat_1 @ A ) )
                  & ( v1_finset_1 @ C )
                  & ( ( k9_relat_1 @ A @ C )
                    = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t195_orders_1) ).

thf(3061,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ~ ( ( v1_finset_1 @ B )
            & ( r1_tarski @ B @ ( k2_relat_1 @ A ) )
            & ! [C: $i] :
                ~ ( ( r1_tarski @ C @ ( k1_relat_1 @ A ) )
                  & ( v1_finset_1 @ C )
                  & ( ( k9_relat_1 @ A @ C )
                    = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(2279,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( ( k5_setfam_1 @ A @ B )
          = A )
       => ! [C: $i] :
            ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
           => ! [D: $i] :
                ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
               => ( ( D
                    = ( k3_tarski @ C ) )
                 => ( r1_tarski @ ( k3_subset_1 @ A @ D ) @ ( k3_tarski @ ( k3_subset_1 @ B @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_borsuk_1) ).

thf(13619,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( ( k5_setfam_1 @ A @ B )
          = A )
       => ! [C: $i] :
            ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
           => ! [D: $i] :
                ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
               => ( ( D
                    = ( k3_tarski @ C ) )
                 => ( r1_tarski @ ( k3_subset_1 @ A @ D ) @ ( k3_tarski @ ( k3_subset_1 @ B @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2279]) ).

thf(2288,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m1_relset_1 @ D @ A @ B )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ B @ C )
        & ( m1_relset_1 @ E @ B @ C ) )
     => ( ( v1_funct_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) )
        & ( v1_funct_2 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C )
        & ( m2_relset_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funct_2) ).

thf(13651,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m1_relset_1 @ D @ A @ B )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ B @ C )
        & ( m1_relset_1 @ E @ B @ C ) )
     => ( ( v1_funct_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) )
        & ( v1_funct_2 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C )
        & ( m2_relset_1 @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2288]) ).

thf(709,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                 => ( ( v2_funct_1 @ D )
                  <=> ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ A )
                           => ! [G: $i] :
                                ( ( m1_subset_1 @ G @ B )
                               => ! [H: $i] :
                                    ( ( m1_subset_1 @ H @ B )
                                   => ( ( ( k2_binop_1 @ A @ B @ C @ D @ E @ G )
                                        = ( k2_binop_1 @ A @ B @ C @ D @ F @ H ) )
                                     => ( ( E = F )
                                        & ( G = H ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yellow18) ).

thf(6066,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                 => ( ( ( v2_funct_1 @ D )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ! [F: $i] :
                              ( ( m1_subset_1 @ F @ A )
                             => ! [G: $i] :
                                  ( ( m1_subset_1 @ G @ B )
                                 => ! [H: $i] :
                                      ( ( m1_subset_1 @ H @ B )
                                     => ( ( ( k2_binop_1 @ A @ B @ C @ D @ E @ G )
                                          = ( k2_binop_1 @ A @ B @ C @ D @ F @ H ) )
                                       => ( ( E = F )
                                          & ( G = H ) ) ) ) ) ) ) )
                    & ( ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ! [F: $i] :
                              ( ( m1_subset_1 @ F @ A )
                             => ! [G: $i] :
                                  ( ( m1_subset_1 @ G @ B )
                                 => ! [H: $i] :
                                      ( ( m1_subset_1 @ H @ B )
                                     => ( ( ( k2_binop_1 @ A @ B @ C @ D @ E @ G )
                                          = ( k2_binop_1 @ A @ B @ C @ D @ F @ H ) )
                                       => ( ( E = F )
                                          & ( G = H ) ) ) ) ) ) )
                     => ( v2_funct_1 @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(188,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
                  & ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) ) )
               => ( ( k5_relat_1 @ ( k1_funct_4 @ B @ C ) @ A )
                  = ( k1_funct_4 @ ( k5_relat_1 @ B @ A ) @ ( k5_relat_1 @ C @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_funct_7) ).

thf(3617,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
                  & ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) ) )
               => ( ( k5_relat_1 @ ( k1_funct_4 @ B @ C ) @ A )
                  = ( k1_funct_4 @ ( k5_relat_1 @ B @ A ) @ ( k5_relat_1 @ C @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(2180,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 ) )
    <=> ( ( k3_zfmisc_1 @ A @ B @ C )
       != k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_mcart_1) ).

thf(13241,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( A != k1_xboole_0 )
          & ( B != k1_xboole_0 )
          & ( C != k1_xboole_0 ) )
       => ( ( k3_zfmisc_1 @ A @ B @ C )
         != k1_xboole_0 ) )
      & ( ( ( k3_zfmisc_1 @ A @ B @ C )
         != k1_xboole_0 )
       => ( ( A != k1_xboole_0 )
          & ( B != k1_xboole_0 )
          & ( C != k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2180]) ).

thf(2417,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( ( k1_relset_2 @ A @ B @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k1_relset_2) ).

thf(14141,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( ( k1_relset_2 @ A @ B @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2417]) ).

thf(161,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) )
                 => ( ( ( ( k1_mcart_1 @ C )
                        = ( k1_mcart_1 @ D ) )
                      & ( ( k2_mcart_1 @ C )
                        = ( k2_mcart_1 @ D ) ) )
                   => ( C = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_domain_1) ).

thf(3485,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) )
                 => ( ( ( ( k1_mcart_1 @ C )
                        = ( k1_mcart_1 @ D ) )
                      & ( ( k2_mcart_1 @ C )
                        = ( k2_mcart_1 @ D ) ) )
                   => ( C = D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(406,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k7_relat_1 @ A @ ( k1_relat_1 @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_relat_1) ).

thf(4778,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k7_relat_1 @ A @ ( k1_relat_1 @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(2025,axiom,
    ! [A: $i] :
      ( ( k6_enumset1 @ A @ A @ A @ A @ A @ A @ A @ A )
      = ( k1_tarski @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_enumset1) ).

thf(12407,plain,
    ! [A: $i] :
      ( ( k6_enumset1 @ A @ A @ A @ A @ A @ A @ A @ A )
      = ( k1_tarski @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2025]) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( ( k1_relat_1 @ B )
                = A )
              & ( ( k1_relat_1 @ C )
                = A ) )
           => ( ( k1_relat_1 @ ( k13_funct_3 @ B @ C ) )
              = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_3) ).

thf(2682,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( ( k1_relat_1 @ B )
                = A )
              & ( ( k1_relat_1 @ C )
                = A ) )
           => ( ( k1_relat_1 @ ( k13_funct_3 @ B @ C ) )
              = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(1967,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C ) )
     => ~ ( v1_xboole_0 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_subset_1) ).

thf(12065,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C ) )
     => ~ ( v1_xboole_0 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1967]) ).

thf(1791,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
     => ( ( v1_funct_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) )
        & ( v1_funct_2 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) )
        & ( m2_relset_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_funcop_1) ).

thf(11111,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
     => ( ( v1_funct_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) )
        & ( v1_funct_2 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) )
        & ( m2_relset_1 @ ( k10_funcop_1 @ A @ B @ C @ D ) @ A @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1791]) ).

thf(850,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_partfun1 @ A @ B )
          <=> ? [C: $i] :
                ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C )
                & ( ( k2_xboole_0 @ A @ B )
                  = C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_partfun1) ).

thf(6676,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( r1_partfun1 @ A @ B )
             => ? [C: $i] :
                  ( ( v1_relat_1 @ C )
                  & ( v1_funct_1 @ C )
                  & ( ( k2_xboole_0 @ A @ B )
                    = C ) ) )
            & ( ? [C: $i] :
                  ( ( v1_relat_1 @ C )
                  & ( v1_funct_1 @ C )
                  & ( ( k2_xboole_0 @ A @ B )
                    = C ) )
             => ( r1_partfun1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(2387,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
     => ( ( k6_relset_2 @ A @ B @ C )
        = ( k5_relset_2 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_relset_2) ).

thf(14029,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
     => ( ( k6_relset_2 @ A @ B @ C )
        = ( k5_relset_2 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2387]) ).

thf(496,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( k9_relat_1 @ C @ A )
        = ( k2_relat_1 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_partfun1) ).

thf(5160,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( k9_relat_1 @ C @ A )
        = ( k2_relat_1 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(119,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ( ( k1_relat_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
                = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_lattice2) ).

thf(3280,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ( ( k1_relat_1 @ ( k2_partfun1 @ A @ B @ D @ C ) )
                = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(2591,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
     => ( m1_subset_1 @ ( k4_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_2) ).

thf(14923,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
     => ( m1_subset_1 @ ( k4_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2591]) ).

thf(1710,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( m1_subset_1 @ B @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ k1_numbers @ A ) @ A )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ k1_numbers @ A ) @ A ) )
     => ! [E: $i,F: $i,G: $i,H: $i] :
          ( ( ( g2_rlvect_1 @ A @ B @ C @ D )
            = ( g2_rlvect_1 @ E @ F @ G @ H ) )
         => ( ( A = E )
            & ( B = F )
            & ( C = G )
            & ( D = H ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g2_rlvect_1) ).

thf(10606,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( m1_subset_1 @ B @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ k1_numbers @ A ) @ A )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ k1_numbers @ A ) @ A ) )
     => ! [E: $i,F: $i,G: $i,H: $i] :
          ( ( ( g2_rlvect_1 @ A @ B @ C @ D )
            = ( g2_rlvect_1 @ E @ F @ G @ H ) )
         => ( ( A = E )
            & ( B = F )
            & ( C = G )
            & ( D = H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1710]) ).

thf(622,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( v2_funct_1 @ C )
        <=> ! [D: $i,E: $i] :
              ( ( ( r2_hidden @ D @ A )
                & ( r2_hidden @ E @ A )
                & ( ( k1_funct_1 @ C @ D )
                  = ( k1_funct_1 @ C @ E ) ) )
             => ( D = E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_funct_2) ).

thf(5640,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( ( v2_funct_1 @ C )
           => ! [D: $i,E: $i] :
                ( ( ( r2_hidden @ D @ A )
                  & ( r2_hidden @ E @ A )
                  & ( ( k1_funct_1 @ C @ D )
                    = ( k1_funct_1 @ C @ E ) ) )
               => ( D = E ) ) )
          & ( ! [D: $i,E: $i] :
                ( ( ( r2_hidden @ D @ A )
                  & ( r2_hidden @ E @ A )
                  & ( ( k1_funct_1 @ C @ D )
                    = ( k1_funct_1 @ C @ E ) ) )
               => ( D = E ) )
           => ( v2_funct_1 @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(72,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
        & ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).

thf(3089,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
        & ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(1508,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] : ( v1_finset_1 @ ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_finset_1) ).

thf(9668,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] : ( v1_finset_1 @ ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1508]) ).

thf(793,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) )
    <=> ( ( r2_hidden @ A @ B )
        & ( A != C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_zfmisc_1) ).

thf(6434,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) )
       => ( ( r2_hidden @ A @ B )
          & ( A != C ) ) )
      & ( ( ( r2_hidden @ A @ B )
          & ( A != C ) )
       => ( r2_hidden @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(527,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_membered @ A )
     => ( v1_membered @ ( k4_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc37_membered) ).

thf(5289,plain,
    ! [A: $i,B: $i] :
      ( ( v1_membered @ A )
     => ( v1_membered @ ( k4_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(1777,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ~ ( ( v1_tex_2 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) )
              & ( v1_realset1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_tex_2) ).

thf(11051,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ~ ( ( v1_tex_2 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) )
              & ( v1_realset1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1777]) ).

thf(361,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( k1_binop_1 @ A @ B @ C )
          = ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_binop_1) ).

thf(4568,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( k1_binop_1 @ A @ B @ C )
          = ( k1_funct_1 @ A @ ( k4_tarski @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(1133,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).

thf(8022,plain,
    ! [A: $i,B: $i] : ( r1_tarski @ A @ ( k2_xboole_0 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).

thf(2188,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D )
        & ( r1_tarski @ E @ F )
        & ( r1_tarski @ G @ H ) )
     => ( r1_tarski @ ( k4_zfmisc_1 @ A @ C @ E @ G ) @ ( k4_zfmisc_1 @ B @ D @ F @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_mcart_1) ).

thf(13275,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D )
        & ( r1_tarski @ E @ F )
        & ( r1_tarski @ G @ H ) )
     => ( r1_tarski @ ( k4_zfmisc_1 @ A @ C @ E @ G ) @ ( k4_zfmisc_1 @ B @ D @ F @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2188]) ).

thf(487,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ B @ A )
     => ( ( k1_funct_1 @ ( k2_funcop_1 @ A @ C ) @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_funcop_1) ).

thf(5108,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ B @ A )
     => ( ( k1_funct_1 @ ( k2_funcop_1 @ A @ C ) @ B )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(2357,axiom,
    ! [A: $i] :
      ( ( v1_finset_1 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( v1_finset_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).

thf(13906,plain,
    ! [A: $i] :
      ( ( v1_finset_1 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( v1_finset_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2357]) ).

thf(663,axiom,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ( v1_membered @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_membered) ).

thf(5836,plain,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ( v1_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(2441,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ~ ( v1_xboole_0 @ ( k2_cantor_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_cantor_1) ).

thf(14228,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ~ ( v1_xboole_0 @ ( k2_cantor_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2441]) ).

thf(524,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( r2_hidden @ C @ A )
         => ( r1_tarski @ B @ C ) )
     => ( ( A = k1_xboole_0 )
        | ( r1_tarski @ B @ ( k1_setfam_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_setfam_1) ).

thf(5279,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( r2_hidden @ C @ A )
         => ( r1_tarski @ B @ C ) )
     => ( ( A = k1_xboole_0 )
        | ( r1_tarski @ B @ ( k1_setfam_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(1721,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( k3_tarski @ A ) )
    <=> ! [C: $i] :
          ( ( r2_hidden @ C @ B )
        <=> ? [D: $i] :
              ( ( r2_hidden @ C @ D )
              & ( r2_hidden @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).

thf(10655,plain,
    ! [A: $i,B: $i] :
      ( ( ( B
          = ( k3_tarski @ A ) )
       => ! [C: $i] :
            ( ( ( r2_hidden @ C @ B )
             => ? [D: $i] :
                  ( ( r2_hidden @ C @ D )
                  & ( r2_hidden @ D @ A ) ) )
            & ( ? [D: $i] :
                  ( ( r2_hidden @ C @ D )
                  & ( r2_hidden @ D @ A ) )
             => ( r2_hidden @ C @ B ) ) ) )
      & ( ! [C: $i] :
            ( ( ( r2_hidden @ C @ B )
             => ? [D: $i] :
                  ( ( r2_hidden @ C @ D )
                  & ( r2_hidden @ D @ A ) ) )
            & ( ? [D: $i] :
                  ( ( r2_hidden @ C @ D )
                  & ( r2_hidden @ D @ A ) )
             => ( r2_hidden @ C @ B ) ) )
       => ( B
          = ( k3_tarski @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1721]) ).

thf(511,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( k13_funct_3 @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) )
                = ( k5_relat_1 @ C @ ( k13_funct_3 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_funct_3) ).

thf(5231,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( k13_funct_3 @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ C @ B ) )
                = ( k5_relat_1 @ C @ ( k13_funct_3 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(1816,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ B )
        & ( m1_subset_1 @ D @ B ) )
     => ( ( r2_hidden @ A @ ( a_3_0_ens_1 @ B @ C @ D ) )
      <=> ? [E: $i] :
            ( ( m1_subset_1 @ E @ ( k1_ens_1 @ B ) )
            & ( A
              = ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) )
            & ( r2_hidden @ ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) @ ( k2_ens_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_ens_1) ).

thf(11232,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ B )
        & ( m1_subset_1 @ D @ B ) )
     => ( ( ( r2_hidden @ A @ ( a_3_0_ens_1 @ B @ C @ D ) )
         => ? [E: $i] :
              ( ( m1_subset_1 @ E @ ( k1_ens_1 @ B ) )
              & ( A
                = ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) )
              & ( r2_hidden @ ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) @ ( k2_ens_1 @ B ) ) ) )
        & ( ? [E: $i] :
              ( ( m1_subset_1 @ E @ ( k1_ens_1 @ B ) )
              & ( A
                = ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) )
              & ( r2_hidden @ ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) @ ( k2_ens_1 @ B ) ) )
         => ( r2_hidden @ A @ ( a_3_0_ens_1 @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1816]) ).

thf(334,axiom,
    ! [A: $i] : ( r3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k1_setwiseo @ A ) @ ( k9_setwiseo @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_setwiseo) ).

thf(4358,plain,
    ! [A: $i] : ( r3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k1_setwiseo @ A ) @ ( k9_setwiseo @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(376,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ! [D: $i] :
                      ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
                    <=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                        & ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ ( k1_relat_1 @ B ) ) ) )
                  & ! [D: $i] :
                      ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
                     => ( ( k1_funct_1 @ C @ D )
                        = ( k1_funct_1 @ B @ ( k1_funct_1 @ A @ D ) ) ) ) )
               => ( C
                  = ( k5_relat_1 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funct_1) ).

thf(4622,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ! [D: $i] :
                      ( ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
                       => ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                          & ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ ( k1_relat_1 @ B ) ) ) )
                      & ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                          & ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ ( k1_relat_1 @ B ) ) )
                       => ( r2_hidden @ D @ ( k1_relat_1 @ C ) ) ) )
                  & ! [D: $i] :
                      ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
                     => ( ( k1_funct_1 @ C @ D )
                        = ( k1_funct_1 @ B @ ( k1_funct_1 @ A @ D ) ) ) ) )
               => ( C
                  = ( k5_relat_1 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(1188,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ D @ A )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ B @ A )
        & ( m1_relset_1 @ E @ B @ A ) )
     => ( ( k8_funcop_1 @ A @ B @ C @ D @ E )
        = ( k5_funcop_1 @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_funcop_1) ).

thf(8235,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ D @ A )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ B @ A )
        & ( m1_relset_1 @ E @ B @ A ) )
     => ( ( k8_funcop_1 @ A @ B @ C @ D @ E )
        = ( k5_funcop_1 @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).

thf(1126,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
                 => ( ( ( k2_partfun1 @ A @ B @ C @ E )
                      = ( k2_partfun1 @ A @ B @ D @ E ) )
                   => ( ( k2_funct_2 @ A @ B @ C @ E )
                      = ( k2_funct_2 @ A @ B @ D @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_lattice2) ).

thf(7997,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
                 => ( ( ( k2_partfun1 @ A @ B @ C @ E )
                      = ( k2_partfun1 @ A @ B @ D @ E ) )
                   => ( ( k2_funct_2 @ A @ B @ C @ E )
                      = ( k2_funct_2 @ A @ B @ D @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).

thf(18,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k1_relat_1 @ ( k1_cat_1 @ A @ B @ C ) )
        = ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
      & ( ( k1_relat_1 @ ( k1_cat_1 @ A @ B @ C ) )
        = ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_cat_1) ).

thf(2691,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k1_relat_1 @ ( k1_cat_1 @ A @ B @ C ) )
        = ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
      & ( ( k1_relat_1 @ ( k1_cat_1 @ A @ B @ C ) )
        = ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(2074,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ~ ( v1_xboole_0 @ E )
                 => ( ( r2_hidden @ A @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
                  <=> ? [F: $i] :
                        ( ( m1_subset_1 @ F @ B )
                        & ? [G: $i] :
                            ( ( m1_subset_1 @ G @ C )
                            & ? [H: $i] :
                                ( ( m1_subset_1 @ H @ D )
                                & ? [I: $i] :
                                    ( ( m1_subset_1 @ I @ E )
                                    & ( A
                                      = ( k4_mcart_1 @ F @ G @ H @ I ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_domain_1) ).

thf(12682,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ~ ( v1_xboole_0 @ E )
                 => ( ( ( r2_hidden @ A @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
                     => ? [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                          & ? [G: $i] :
                              ( ( m1_subset_1 @ G @ C )
                              & ? [H: $i] :
                                  ( ( m1_subset_1 @ H @ D )
                                  & ? [I: $i] :
                                      ( ( m1_subset_1 @ I @ E )
                                      & ( A
                                        = ( k4_mcart_1 @ F @ G @ H @ I ) ) ) ) ) ) )
                    & ( ? [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                          & ? [G: $i] :
                              ( ( m1_subset_1 @ G @ C )
                              & ? [H: $i] :
                                  ( ( m1_subset_1 @ H @ D )
                                  & ? [I: $i] :
                                      ( ( m1_subset_1 @ I @ E )
                                      & ( A
                                        = ( k4_mcart_1 @ F @ G @ H @ I ) ) ) ) ) )
                     => ( r2_hidden @ A @ ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2074]) ).

thf(258,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( r3_binop_1 @ A @ C @ B )
          <=> ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ( ( k1_binop_1 @ B @ C @ D )
                    = D )
                  & ( ( k1_binop_1 @ B @ D @ C )
                    = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_binop_1) ).

thf(3998,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( ( r3_binop_1 @ A @ C @ B )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( ( k1_binop_1 @ B @ C @ D )
                      = D )
                    & ( ( k1_binop_1 @ B @ D @ C )
                      = D ) ) ) )
            & ( ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( ( k1_binop_1 @ B @ C @ D )
                      = D )
                    & ( ( k1_binop_1 @ B @ D @ C )
                      = D ) ) )
             => ( r3_binop_1 @ A @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(546,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
                         => ( ( ( ( k8_mcart_1 @ A @ B @ C @ D @ E )
                                = ( k8_mcart_1 @ A @ B @ C @ D @ F ) )
                              & ( ( k9_mcart_1 @ A @ B @ C @ D @ E )
                                = ( k9_mcart_1 @ A @ B @ C @ D @ F ) )
                              & ( ( k10_mcart_1 @ A @ B @ C @ D @ E )
                                = ( k10_mcart_1 @ A @ B @ C @ D @ F ) )
                              & ( ( k11_mcart_1 @ A @ B @ C @ D @ E )
                                = ( k11_mcart_1 @ A @ B @ C @ D @ F ) ) )
                           => ( E = F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_domain_1) ).

thf(5355,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
                         => ( ( ( ( k8_mcart_1 @ A @ B @ C @ D @ E )
                                = ( k8_mcart_1 @ A @ B @ C @ D @ F ) )
                              & ( ( k9_mcart_1 @ A @ B @ C @ D @ E )
                                = ( k9_mcart_1 @ A @ B @ C @ D @ F ) )
                              & ( ( k10_mcart_1 @ A @ B @ C @ D @ E )
                                = ( k10_mcart_1 @ A @ B @ C @ D @ F ) )
                              & ( ( k11_mcart_1 @ A @ B @ C @ D @ E )
                                = ( k11_mcart_1 @ A @ B @ C @ D @ F ) ) )
                           => ( E = F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(2369,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) ) )
     => ( m1_subset_1 @ ( k13_mcart_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_mcart_1) ).

thf(13961,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) ) )
     => ( m1_subset_1 @ ( k13_mcart_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2369]) ).

thf(143,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_pboole @ C @ A ) )
     => ? [D: $i] : ( m3_pboole @ D @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_pboole) ).

thf(3374,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_pboole @ C @ A ) )
     => ? [D: $i] : ( m3_pboole @ D @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(1951,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( k2_zfmisc_1 @ A @ B ) )
    <=> ! [D: $i] :
          ( ( r2_hidden @ D @ C )
        <=> ? [E: $i,F: $i] :
              ( ( r2_hidden @ E @ A )
              & ( r2_hidden @ F @ B )
              & ( D
                = ( k4_tarski @ E @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).

thf(11981,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C
          = ( k2_zfmisc_1 @ A @ B ) )
       => ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ? [E: $i,F: $i] :
                  ( ( r2_hidden @ E @ A )
                  & ( r2_hidden @ F @ B )
                  & ( D
                    = ( k4_tarski @ E @ F ) ) ) )
            & ( ? [E: $i,F: $i] :
                  ( ( r2_hidden @ E @ A )
                  & ( r2_hidden @ F @ B )
                  & ( D
                    = ( k4_tarski @ E @ F ) ) )
             => ( r2_hidden @ D @ C ) ) ) )
      & ( ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ? [E: $i,F: $i] :
                  ( ( r2_hidden @ E @ A )
                  & ( r2_hidden @ F @ B )
                  & ( D
                    = ( k4_tarski @ E @ F ) ) ) )
            & ( ? [E: $i,F: $i] :
                  ( ( r2_hidden @ E @ A )
                  & ( r2_hidden @ F @ B )
                  & ( D
                    = ( k4_tarski @ E @ F ) ) )
             => ( r2_hidden @ D @ C ) ) )
       => ( C
          = ( k2_zfmisc_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1951]) ).

thf(332,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ( m1_subset_1 @ ( k4_finseq_1 @ A ) @ ( k1_zfmisc_1 @ k5_numbers ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_finseq_1) ).

thf(4353,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ( m1_subset_1 @ ( k4_finseq_1 @ A ) @ ( k1_zfmisc_1 @ k5_numbers ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(1853,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D ) )
     => ~ ( v1_xboole_0 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_subset_1) ).

thf(11463,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D ) )
     => ~ ( v1_xboole_0 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1853]) ).

thf(892,axiom,
    ! [A: $i] :
      ( ( k1_setfam_1 @ ( k1_tarski @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_setfam_1) ).

thf(6905,plain,
    ! [A: $i] :
      ( ( k1_setfam_1 @ ( k1_tarski @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(1821,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k6_enumset1 @ A @ A @ A @ A @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_enumset1) ).

thf(11285,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k6_enumset1 @ A @ A @ A @ A @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1821]) ).

thf(2488,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( m1_subset_1 @ ( k9_domain_1 @ A @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_domain_1) ).

thf(14455,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( m1_subset_1 @ ( k9_domain_1 @ A @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2488]) ).

thf(942,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( r2_hidden @ ( k1_relat_1 @ B ) @ A )
              & ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) )
           => ( r2_hidden @ ( k4_card_3 @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_yellow_6) ).

thf(7124,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( r2_hidden @ ( k1_relat_1 @ B ) @ A )
              & ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) )
           => ( r2_hidden @ ( k4_card_3 @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).

thf(1207,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( r2_hidden @ C @ A )
        | ( r1_tarski @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_zfmisc_1) ).

thf(8310,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( r2_hidden @ C @ A )
        | ( r1_tarski @ A @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).

thf(1313,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ( E != k1_xboole_0 )
        & ( F != k1_xboole_0 )
        & ? [G: $i] :
            ( ( m1_subset_1 @ G @ ( k3_zfmisc_1 @ A @ B @ C ) )
            & ? [H: $i] :
                ( ( m1_subset_1 @ H @ ( k3_zfmisc_1 @ D @ E @ F ) )
                & ( G = H )
                & ~ ( ( ( k5_mcart_1 @ A @ B @ C @ G )
                      = ( k5_mcart_1 @ D @ E @ F @ H ) )
                    & ( ( k6_mcart_1 @ A @ B @ C @ G )
                      = ( k6_mcart_1 @ D @ E @ F @ H ) )
                    & ( ( k7_mcart_1 @ A @ B @ C @ G )
                      = ( k7_mcart_1 @ D @ E @ F @ H ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_mcart_1) ).

thf(8819,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ( E != k1_xboole_0 )
        & ( F != k1_xboole_0 )
        & ? [G: $i] :
            ( ( m1_subset_1 @ G @ ( k3_zfmisc_1 @ A @ B @ C ) )
            & ? [H: $i] :
                ( ( m1_subset_1 @ H @ ( k3_zfmisc_1 @ D @ E @ F ) )
                & ( G = H )
                & ~ ( ( ( k5_mcart_1 @ A @ B @ C @ G )
                      = ( k5_mcart_1 @ D @ E @ F @ H ) )
                    & ( ( k6_mcart_1 @ A @ B @ C @ G )
                      = ( k6_mcart_1 @ D @ E @ F @ H ) )
                    & ( ( k7_mcart_1 @ A @ B @ C @ G )
                      = ( k7_mcart_1 @ D @ E @ F @ H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).

thf(730,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( r1_partfun1 @ A @ ( k1_funct_4 @ B @ C ) )
               => ( r1_partfun1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_funct_4) ).

thf(6149,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( r1_partfun1 @ A @ ( k1_funct_4 @ B @ C ) )
               => ( r1_partfun1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(836,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) )
     => ( r1_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_xboole_1) ).

thf(6626,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) )
     => ( r1_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(614,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_mcart_1 @ A @ B @ C @ D )
      = ( k3_mcart_1 @ ( k4_tarski @ A @ B ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_mcart_1) ).

thf(5604,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_mcart_1 @ A @ B @ C @ D )
      = ( k3_mcart_1 @ ( k4_tarski @ A @ B ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(385,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( C
                  = ( k15_funct_3 @ A @ B ) )
              <=> ( ( ( k1_relat_1 @ C )
                    = ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                  & ! [D: $i,E: $i] :
                      ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                        & ( r2_hidden @ E @ ( k1_relat_1 @ B ) ) )
                     => ( ( k1_funct_1 @ C @ ( k4_tarski @ D @ E ) )
                        = ( k4_tarski @ ( k1_funct_1 @ A @ D ) @ ( k1_funct_1 @ B @ E ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_3) ).

thf(4664,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( C
                    = ( k15_funct_3 @ A @ B ) )
                 => ( ( ( k1_relat_1 @ C )
                      = ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                    & ! [D: $i,E: $i] :
                        ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                          & ( r2_hidden @ E @ ( k1_relat_1 @ B ) ) )
                       => ( ( k1_funct_1 @ C @ ( k4_tarski @ D @ E ) )
                          = ( k4_tarski @ ( k1_funct_1 @ A @ D ) @ ( k1_funct_1 @ B @ E ) ) ) ) ) )
                & ( ( ( ( k1_relat_1 @ C )
                      = ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                    & ! [D: $i,E: $i] :
                        ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                          & ( r2_hidden @ E @ ( k1_relat_1 @ B ) ) )
                       => ( ( k1_funct_1 @ C @ ( k4_tarski @ D @ E ) )
                          = ( k4_tarski @ ( k1_funct_1 @ A @ D ) @ ( k1_funct_1 @ B @ E ) ) ) ) )
                 => ( C
                    = ( k15_funct_3 @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(1261,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( ! [G: $i] :
            ( ( m1_subset_1 @ G @ A )
           => ! [H: $i] :
                ( ( m1_subset_1 @ H @ B )
               => ! [I: $i] :
                    ( ( m1_subset_1 @ I @ C )
                   => ! [J: $i] :
                        ( ( m1_subset_1 @ J @ D )
                       => ( ( F
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( E = H ) ) ) ) ) )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 )
          | ( C = k1_xboole_0 )
          | ( D = k1_xboole_0 )
          | ( E
            = ( k9_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_mcart_1) ).

thf(8571,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( ! [G: $i] :
            ( ( m1_subset_1 @ G @ A )
           => ! [H: $i] :
                ( ( m1_subset_1 @ H @ B )
               => ! [I: $i] :
                    ( ( m1_subset_1 @ I @ C )
                   => ! [J: $i] :
                        ( ( m1_subset_1 @ J @ D )
                       => ( ( F
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( E = H ) ) ) ) ) )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 )
          | ( C = k1_xboole_0 )
          | ( D = k1_xboole_0 )
          | ( E
            = ( k9_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).

thf(763,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_relat_1) ).

thf(6310,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(1555,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B )
        & ( v1_finset_1 @ C ) )
     => ( v1_finset_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc15_finset_1) ).

thf(9941,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B )
        & ( v1_finset_1 @ C ) )
     => ( v1_finset_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1555]) ).

thf(2461,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ~ ( v1_xboole_0 @ ( k7_setfam_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_card_fil) ).

thf(14334,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ~ ( v1_xboole_0 @ ( k7_setfam_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2461]) ).

thf(2270,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( ( v1_funct_1 @ ( k5_funct_4 @ A @ B @ C @ D @ E ) )
        & ( v1_funct_2 @ ( k5_funct_4 @ A @ B @ C @ D @ E ) @ ( k2_tarski @ B @ C ) @ A )
        & ( m2_relset_1 @ ( k5_funct_4 @ A @ B @ C @ D @ E ) @ ( k2_tarski @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_funct_4) ).

thf(13580,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( ( v1_funct_1 @ ( k5_funct_4 @ A @ B @ C @ D @ E ) )
        & ( v1_funct_2 @ ( k5_funct_4 @ A @ B @ C @ D @ E ) @ ( k2_tarski @ B @ C ) @ A )
        & ( m2_relset_1 @ ( k5_funct_4 @ A @ B @ C @ D @ E ) @ ( k2_tarski @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2270]) ).

thf(419,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( B
              = ( k1_funct_3 @ A ) )
          <=> ( ( ( k1_relat_1 @ B )
                = ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) )
              & ! [C: $i] :
                  ( ( r1_tarski @ C @ ( k1_relat_1 @ A ) )
                 => ( ( k1_funct_1 @ B @ C )
                    = ( k9_relat_1 @ A @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_3) ).

thf(4830,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( B
                = ( k1_funct_3 @ A ) )
             => ( ( ( k1_relat_1 @ B )
                  = ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) )
                & ! [C: $i] :
                    ( ( r1_tarski @ C @ ( k1_relat_1 @ A ) )
                   => ( ( k1_funct_1 @ B @ C )
                      = ( k9_relat_1 @ A @ C ) ) ) ) )
            & ( ( ( ( k1_relat_1 @ B )
                  = ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) )
                & ! [C: $i] :
                    ( ( r1_tarski @ C @ ( k1_relat_1 @ A ) )
                   => ( ( k1_funct_1 @ B @ C )
                      = ( k9_relat_1 @ A @ C ) ) ) )
             => ( B
                = ( k1_funct_3 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(2065,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ! [E: $i] :
                ( ( r2_hidden @ E @ A )
               => ( ( k1_funct_1 @ C @ E )
                  = ( k1_funct_1 @ D @ E ) ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_2) ).

thf(12621,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ! [E: $i] :
                ( ( r2_hidden @ E @ A )
               => ( ( k1_funct_1 @ C @ E )
                  = ( k1_funct_1 @ D @ E ) ) )
           => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2065]) ).

thf(323,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ ( k10_finseq_1 @ A @ B ) )
      & ( v1_funct_1 @ ( k10_finseq_1 @ A @ B ) )
      & ( v1_finset_1 @ ( k10_finseq_1 @ A @ B ) )
      & ( v1_finseq_1 @ ( k10_finseq_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_finseq_1) ).

thf(4317,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ ( k10_finseq_1 @ A @ B ) )
      & ( v1_funct_1 @ ( k10_finseq_1 @ A @ B ) )
      & ( v1_finset_1 @ ( k10_finseq_1 @ A @ B ) )
      & ( v1_finseq_1 @ ( k10_finseq_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(1767,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( C
          = ( k1_tarski @ B ) )
       => ( ( ( k2_cantor_1 @ A @ C )
            = ( k2_tarski @ B @ A ) )
          & ( ( k1_cantor_1 @ A @ C )
            = ( k2_tarski @ B @ k1_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_yellow_9) ).

thf(10982,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( C
          = ( k1_tarski @ B ) )
       => ( ( ( k2_cantor_1 @ A @ C )
            = ( k2_tarski @ B @ A ) )
          & ( ( k1_cantor_1 @ A @ C )
            = ( k2_tarski @ B @ k1_xboole_0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1767]) ).

thf(1792,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ C @ B )
     => ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
        & ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
        & ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funcop_1) ).

thf(11115,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ C @ B )
     => ( ( v1_funct_1 @ ( k2_funcop_1 @ A @ C ) )
        & ( v1_funct_2 @ ( k2_funcop_1 @ A @ C ) @ A @ B )
        & ( m2_relset_1 @ ( k2_funcop_1 @ A @ C ) @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1792]) ).

thf(210,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( ( k9_relat_1 @ B @ A )
          = k1_xboole_0 )
      <=> ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_relat_1) ).

thf(3734,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( ( ( k9_relat_1 @ B @ A )
            = k1_xboole_0 )
         => ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) )
        & ( ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A )
         => ( ( k9_relat_1 @ B @ A )
            = k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(65,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i,D: $i] :
          ( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
            & ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
            & ( r2_hidden @ D @ ( k1_relat_1 @ A ) ) )
         => ( ( k5_relat_1 @ ( k11_finseq_1 @ B @ C @ D ) @ A )
            = ( k11_finseq_1 @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ A @ C ) @ ( k1_funct_1 @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_finseq_2) ).

thf(3014,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i,D: $i] :
          ( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
            & ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
            & ( r2_hidden @ D @ ( k1_relat_1 @ A ) ) )
         => ( ( k5_relat_1 @ ( k11_finseq_1 @ B @ C @ D ) @ A )
            = ( k11_finseq_1 @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ A @ C ) @ ( k1_funct_1 @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(28,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_relat_1) ).

thf(2730,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(1410,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( ( v1_relat_1 @ D )
                & ( v1_funct_1 @ D ) )
             => ! [E: $i] :
                  ( ( ( k7_relat_1 @ A @ C )
                    = ( k7_relat_1 @ B @ C ) )
                 => ( ( k7_relat_1 @ ( k5_funcop_1 @ D @ E @ A ) @ C )
                    = ( k7_relat_1 @ ( k5_funcop_1 @ D @ E @ B ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funcop_1) ).

thf(9240,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( ( v1_relat_1 @ D )
                & ( v1_funct_1 @ D ) )
             => ! [E: $i] :
                  ( ( ( k7_relat_1 @ A @ C )
                    = ( k7_relat_1 @ B @ C ) )
                 => ( ( k7_relat_1 @ ( k5_funcop_1 @ D @ E @ A ) @ C )
                    = ( k7_relat_1 @ ( k5_funcop_1 @ D @ E @ B ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410]) ).

thf(641,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
      & ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funcop_1) ).

thf(5746,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
      & ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(1282,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( r1_tarski @ ( k5_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_relset_2) ).

thf(8674,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( r1_tarski @ ( k5_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).

thf(2383,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_pboole @ ( k3_pre_circ @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_pre_circ) ).

thf(14019,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_pboole @ ( k3_pre_circ @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2383]) ).

thf(638,axiom,
    ! [A: $i,B: $i] :
      ( ( k5_xboole_0 @ A @ B )
      = ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_xboole_0) ).

thf(5727,plain,
    ! [A: $i,B: $i] :
      ( ( k5_xboole_0 @ A @ B )
      = ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(2362,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(13927,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2362]) ).

thf(1514,axiom,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s2_multop_1 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s2_multop_1 )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ f1_s2_multop_1 )
               => ? [D: $i] :
                    ( ( m1_subset_1 @ D @ f1_s2_multop_1 )
                    & ( p1_s2_multop_1 @ A @ B @ C @ D ) ) ) ) )
   => ? [A: $i] :
        ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k3_zfmisc_1 @ f1_s2_multop_1 @ f1_s2_multop_1 @ f1_s2_multop_1 ) @ f1_s2_multop_1 )
        & ( m2_relset_1 @ A @ ( k3_zfmisc_1 @ f1_s2_multop_1 @ f1_s2_multop_1 @ f1_s2_multop_1 ) @ f1_s2_multop_1 )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s2_multop_1 )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ f1_s2_multop_1 )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ f1_s2_multop_1 )
                   => ( p1_s2_multop_1 @ B @ C @ D @ ( k2_multop_1 @ f1_s2_multop_1 @ f1_s2_multop_1 @ f1_s2_multop_1 @ f1_s2_multop_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_multop_1) ).

thf(9725,plain,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s2_multop_1 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s2_multop_1 )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ f1_s2_multop_1 )
               => ? [D: $i] :
                    ( ( m1_subset_1 @ D @ f1_s2_multop_1 )
                    & ( p1_s2_multop_1 @ A @ B @ C @ D ) ) ) ) )
   => ? [A: $i] :
        ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k3_zfmisc_1 @ f1_s2_multop_1 @ f1_s2_multop_1 @ f1_s2_multop_1 ) @ f1_s2_multop_1 )
        & ( m2_relset_1 @ A @ ( k3_zfmisc_1 @ f1_s2_multop_1 @ f1_s2_multop_1 @ f1_s2_multop_1 ) @ f1_s2_multop_1 )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s2_multop_1 )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ f1_s2_multop_1 )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ f1_s2_multop_1 )
                   => ( p1_s2_multop_1 @ B @ C @ D @ ( k2_multop_1 @ f1_s2_multop_1 @ f1_s2_multop_1 @ f1_s2_multop_1 @ f1_s2_multop_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1514]) ).

thf(1375,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H )
      = ( k2_xboole_0 @ ( k2_enumset1 @ A @ B @ C @ D ) @ ( k2_enumset1 @ E @ F @ G @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_enumset1) ).

thf(9039,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H )
      = ( k2_xboole_0 @ ( k2_enumset1 @ A @ B @ C @ D ) @ ( k2_enumset1 @ E @ F @ G @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).

thf(1158,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ~ ( ( ( B = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ( r1_partfun1 @ C @ D )
              & ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t186_partfun1) ).

thf(8126,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ~ ( ( ( B = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ( r1_partfun1 @ C @ D )
              & ( r1_xboole_0 @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).

thf(2184,axiom,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k2_qc_lang1 )
     => ( ( k23_qc_lang1 @ A )
        = ( k1_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k23_qc_lang1) ).

thf(13263,plain,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k2_qc_lang1 )
     => ( ( k23_qc_lang1 @ A )
        = ( k1_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2184]) ).

thf(1594,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( r2_hidden @ B @ C )
       => ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_mssubfam) ).

thf(10117,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( r2_hidden @ B @ C )
       => ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1594]) ).

thf(2139,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( ( k2_cat_5 @ A @ B @ C @ D )
        = ( k18_mcart_1 @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_cat_5) ).

thf(13044,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( ( k2_cat_5 @ A @ B @ C @ D )
        = ( k18_mcart_1 @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2139]) ).

thf(347,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                 => ( ( ( v1_binop_1 @ C @ A )
                      & ( v1_binop_1 @ D @ B ) )
                  <=> ( v1_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_filter_1) ).

thf(4471,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                 => ( ( ( ( v1_binop_1 @ C @ A )
                        & ( v1_binop_1 @ D @ B ) )
                     => ( v1_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) )
                    & ( ( v1_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
                     => ( ( v1_binop_1 @ C @ A )
                        & ( v1_binop_1 @ D @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(2071,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( k1_zfmisc_1 @ A ) )
    <=> ! [C: $i] :
          ( ( r2_hidden @ C @ B )
        <=> ( r1_tarski @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).

thf(12657,plain,
    ! [A: $i,B: $i] :
      ( ( ( B
          = ( k1_zfmisc_1 @ A ) )
       => ! [C: $i] :
            ( ( ( r2_hidden @ C @ B )
             => ( r1_tarski @ C @ A ) )
            & ( ( r1_tarski @ C @ A )
             => ( r2_hidden @ C @ B ) ) ) )
      & ( ! [C: $i] :
            ( ( ( r2_hidden @ C @ B )
             => ( r1_tarski @ C @ A ) )
            & ( ( r1_tarski @ C @ A )
             => ( r2_hidden @ C @ B ) ) )
       => ( B
          = ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2071]) ).

thf(1135,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k3_enumset1 @ A @ B @ C @ D @ E )
      = ( k2_xboole_0 @ ( k1_enumset1 @ A @ B @ C ) @ ( k2_tarski @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_enumset1) ).

thf(8037,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k3_enumset1 @ A @ B @ C @ D @ E )
      = ( k2_xboole_0 @ ( k1_enumset1 @ A @ B @ C ) @ ( k2_tarski @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).

thf(405,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i,D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ( ( ( v1_binop_1 @ D @ B )
                  & ( v2_binop_1 @ D @ B )
                  & ( v3_binop_1 @ D @ B )
                  & ( v1_setwiseo @ D @ B ) )
               => ! [E: $i] :
                    ( ( ( v1_funct_1 @ E )
                      & ( v1_funct_2 @ E @ A @ ( k5_finsub_1 @ C ) )
                      & ( m2_relset_1 @ E @ A @ ( k5_finsub_1 @ C ) ) )
                   => ! [F: $i] :
                        ( ( ( v1_funct_1 @ F )
                          & ( v1_funct_2 @ F @ ( k5_finsub_1 @ C ) @ B )
                          & ( m2_relset_1 @ F @ ( k5_finsub_1 @ C ) @ B ) )
                       => ( ( ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ ( k1_setwiseo @ C ) )
                              = ( k3_binop_1 @ B @ D ) )
                            & ! [G: $i] :
                                ( ( m1_subset_1 @ G @ ( k5_finsub_1 @ C ) )
                               => ! [H: $i] :
                                    ( ( m1_subset_1 @ H @ ( k5_finsub_1 @ C ) )
                                   => ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ ( k5_setwiseo @ C @ G @ H ) )
                                      = ( k2_binop_1 @ B @ B @ B @ D @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ G ) @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ H ) ) ) ) ) )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ ( k5_finsub_1 @ A ) )
                             => ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ ( k10_setwiseo @ A @ C @ G @ E ) )
                                = ( k7_setwiseo @ A @ B @ D @ G @ ( k7_funct_2 @ A @ ( k5_finsub_1 @ C ) @ B @ E @ F ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_setwiseo) ).

thf(4771,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i,D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ( ( ( v1_binop_1 @ D @ B )
                  & ( v2_binop_1 @ D @ B )
                  & ( v3_binop_1 @ D @ B )
                  & ( v1_setwiseo @ D @ B ) )
               => ! [E: $i] :
                    ( ( ( v1_funct_1 @ E )
                      & ( v1_funct_2 @ E @ A @ ( k5_finsub_1 @ C ) )
                      & ( m2_relset_1 @ E @ A @ ( k5_finsub_1 @ C ) ) )
                   => ! [F: $i] :
                        ( ( ( v1_funct_1 @ F )
                          & ( v1_funct_2 @ F @ ( k5_finsub_1 @ C ) @ B )
                          & ( m2_relset_1 @ F @ ( k5_finsub_1 @ C ) @ B ) )
                       => ( ( ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ ( k1_setwiseo @ C ) )
                              = ( k3_binop_1 @ B @ D ) )
                            & ! [G: $i] :
                                ( ( m1_subset_1 @ G @ ( k5_finsub_1 @ C ) )
                               => ! [H: $i] :
                                    ( ( m1_subset_1 @ H @ ( k5_finsub_1 @ C ) )
                                   => ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ ( k5_setwiseo @ C @ G @ H ) )
                                      = ( k2_binop_1 @ B @ B @ B @ D @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ G ) @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ H ) ) ) ) ) )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ ( k5_finsub_1 @ A ) )
                             => ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ B @ F @ ( k10_setwiseo @ A @ C @ G @ E ) )
                                = ( k7_setwiseo @ A @ B @ D @ G @ ( k7_funct_2 @ A @ ( k5_finsub_1 @ C ) @ B @ E @ F ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(1638,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ A @ B @ C ) )
          & ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ B @ C @ A ) )
          & ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ C @ A @ B ) ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_mcart_1) ).

thf(10292,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ A @ B @ C ) )
          & ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ B @ C @ A ) )
          & ~ ( r1_tarski @ A @ ( k3_zfmisc_1 @ C @ A @ B ) ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1638]) ).

thf(1723,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_pboole @ D @ A )
        & ( m1_pboole @ E @ B ) )
     => ? [F: $i] : ( m1_functor0 @ F @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_functor0) ).

thf(10682,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_pboole @ D @ A )
        & ( m1_pboole @ E @ B ) )
     => ? [F: $i] : ( m1_functor0 @ F @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1723]) ).

thf(319,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( r1_tarski @ A @ B )
           => ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
              & ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).

thf(4302,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( r1_tarski @ A @ B )
           => ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
              & ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(805,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) ) )
     => ( m1_subset_1 @ ( k3_ens_1 @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_ens_1) ).

thf(6487,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) ) )
     => ( m1_subset_1 @ ( k3_ens_1 @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(1016,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( k2_funct_4 @ ( k5_relat_1 @ ( k15_funct_3 @ B @ C ) @ A ) )
                = ( k5_relat_1 @ ( k15_funct_3 @ C @ B ) @ ( k2_funct_4 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_altcat_2) ).

thf(7509,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( k2_funct_4 @ ( k5_relat_1 @ ( k15_funct_3 @ B @ C ) @ A ) )
                = ( k5_relat_1 @ ( k15_funct_3 @ C @ B ) @ ( k2_funct_4 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(938,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ B @ A )
        & ( m1_relset_1 @ D @ B @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( ( k7_funcop_1 @ A @ B @ C @ D @ E )
        = ( k4_funcop_1 @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_funcop_1) ).

thf(7112,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ B @ A )
        & ( m1_relset_1 @ D @ B @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( ( k7_funcop_1 @ A @ B @ C @ D @ E )
        = ( k4_funcop_1 @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).

thf(114,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( r1_partfun1 @ A @ ( k1_funct_4 @ B @ C ) )
               => ( r1_partfun1 @ ( k7_relat_1 @ A @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ C ) ) ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_4) ).

thf(3258,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( r1_partfun1 @ A @ ( k1_funct_4 @ B @ C ) )
               => ( r1_partfun1 @ ( k7_relat_1 @ A @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ C ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(2558,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D ) )
     => ( ( r2_hidden @ A @ ( a_3_8_domain_1 @ B @ C @ D ) )
      <=> ? [E: $i,F: $i,G: $i] :
            ( ( m1_subset_1 @ E @ B )
            & ( m1_subset_1 @ F @ C )
            & ( m1_subset_1 @ G @ D )
            & ( A
              = ( k4_domain_1 @ B @ C @ D @ E @ F @ G ) )
            & ( p1_s3_domain_1 @ E @ F @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_8_domain_1) ).

thf(14751,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D ) )
     => ( ( ( r2_hidden @ A @ ( a_3_8_domain_1 @ B @ C @ D ) )
         => ? [E: $i,F: $i,G: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( m1_subset_1 @ F @ C )
              & ( m1_subset_1 @ G @ D )
              & ( A
                = ( k4_domain_1 @ B @ C @ D @ E @ F @ G ) )
              & ( p1_s3_domain_1 @ E @ F @ G ) ) )
        & ( ? [E: $i,F: $i,G: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( m1_subset_1 @ F @ C )
              & ( m1_subset_1 @ G @ D )
              & ( A
                = ( k4_domain_1 @ B @ C @ D @ E @ F @ G ) )
              & ( p1_s3_domain_1 @ E @ F @ G ) )
         => ( r2_hidden @ A @ ( a_3_8_domain_1 @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2558]) ).

thf(2093,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
     => ( ( v1_funct_1 @ ( k10_cat_2 @ A @ B @ C @ D ) )
        & ( m2_relset_1 @ ( k10_cat_2 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_cat_2) ).

thf(12782,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
     => ( ( v1_funct_1 @ ( k10_cat_2 @ A @ B @ C @ D ) )
        & ( m2_relset_1 @ ( k10_cat_2 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2093]) ).

thf(2395,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k1_classes2 @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_classes2) ).

thf(14051,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k1_classes2 @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2395]) ).

thf(2324,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
     => ! [D: $i] :
          ( ( m1_nat_lat @ D @ A @ B @ C )
         => ( m2_subset_1 @ D @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_nat_lat) ).

thf(13788,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
     => ! [D: $i] :
          ( ( m1_nat_lat @ D @ A @ B @ C )
         => ( m2_subset_1 @ D @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2324]) ).

thf(1326,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_card_fil @ B @ A ) )
     => ( ( k2_card_fil @ A @ ( k2_card_fil @ A @ B ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k2_card_fil) ).

thf(8870,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_card_fil @ B @ A ) )
     => ( ( k2_card_fil @ A @ ( k2_card_fil @ A @ B ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).

thf(1913,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).

thf(11740,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1913]) ).

thf(2323,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ( r1_tarski @ ( k1_ens_1 @ B ) @ ( k1_ens_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ens_1) ).

thf(13786,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ( r1_tarski @ ( k1_ens_1 @ B ) @ ( k1_ens_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2323]) ).

thf(2236,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( v1_funct_1 @ ( k8_ens_1 @ A ) )
        & ( v1_funct_2 @ ( k8_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ A )
        & ( m2_relset_1 @ ( k8_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_ens_1) ).

thf(13474,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( v1_funct_1 @ ( k8_ens_1 @ A ) )
        & ( v1_funct_2 @ ( k8_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ A )
        & ( m2_relset_1 @ ( k8_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2236]) ).

thf(1575,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r1_tarski @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).

thf(10025,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r1_tarski @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1575]) ).

thf(690,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( ! [G: $i] :
            ( ( m1_subset_1 @ G @ A )
           => ! [H: $i] :
                ( ( m1_subset_1 @ H @ B )
               => ! [I: $i] :
                    ( ( m1_subset_1 @ I @ C )
                   => ! [J: $i] :
                        ( ( m1_subset_1 @ J @ D )
                       => ( ( F
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( E = I ) ) ) ) ) )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 )
          | ( C = k1_xboole_0 )
          | ( D = k1_xboole_0 )
          | ( E
            = ( k10_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_mcart_1) ).

thf(5974,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( ! [G: $i] :
            ( ( m1_subset_1 @ G @ A )
           => ! [H: $i] :
                ( ( m1_subset_1 @ H @ B )
               => ! [I: $i] :
                    ( ( m1_subset_1 @ I @ C )
                   => ! [J: $i] :
                        ( ( m1_subset_1 @ J @ D )
                       => ( ( F
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( E = I ) ) ) ) ) )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 )
          | ( C = k1_xboole_0 )
          | ( D = k1_xboole_0 )
          | ( E
            = ( k10_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(1203,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( r1_binop_1 @ A @ B @ C )
              <=> ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ( ( k2_binop_1 @ A @ A @ A @ C @ B @ D )
                      = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_binop_1) ).

thf(8293,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( ( r1_binop_1 @ A @ B @ C )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ( ( k2_binop_1 @ A @ A @ A @ C @ B @ D )
                        = D ) ) )
                & ( ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ( ( k2_binop_1 @ A @ A @ A @ C @ B @ D )
                        = D ) )
                 => ( r1_binop_1 @ A @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).

thf(2268,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k6_enumset1 @ A @ A @ A @ B @ C @ D @ E @ F )
      = ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_enumset1) ).

thf(13575,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k6_enumset1 @ A @ A @ A @ B @ C @ D @ E @ F )
      = ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2268]) ).

thf(2399,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ A ) )
     => ( m1_subset_1 @ ( k2_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relset_2) ).

thf(14061,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ A ) )
     => ( m1_subset_1 @ ( k2_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2399]) ).

thf(2085,axiom,
    ! [A: $i,B: $i] :
      ~ ( v1_xboole_0 @ ( k4_partfun1 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_partfun1) ).

thf(12750,plain,
    ! [A: $i,B: $i] :
      ~ ( v1_xboole_0 @ ( k4_partfun1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2085]) ).

thf(1924,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( ( k1_cat_5 @ A @ B @ C @ D )
        = ( k17_mcart_1 @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_cat_5) ).

thf(11838,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( ( k1_cat_5 @ A @ B @ C @ D )
        = ( k17_mcart_1 @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1924]) ).

thf(1572,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ? [C: $i] :
          ( ( v1_finset_1 @ C )
          & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
          & ( r1_tarski @ C @ B )
          & ( ( k5_setfam_1 @ A @ C )
            = ( k5_setfam_1 @ A @ B ) )
          & ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
             => ~ ( ( r2_hidden @ D @ C )
                  & ( r1_tarski @ D @ ( k5_setfam_1 @ A @ ( k6_subset_1 @ ( k1_zfmisc_1 @ A ) @ C @ ( k6_domain_1 @ ( k1_zfmisc_1 @ A ) @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_waybel14) ).

thf(10014,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ? [C: $i] :
          ( ( v1_finset_1 @ C )
          & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
          & ( r1_tarski @ C @ B )
          & ( ( k5_setfam_1 @ A @ C )
            = ( k5_setfam_1 @ A @ B ) )
          & ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
             => ~ ( ( r2_hidden @ D @ C )
                  & ( r1_tarski @ D @ ( k5_setfam_1 @ A @ ( k6_subset_1 @ ( k1_zfmisc_1 @ A ) @ C @ ( k6_domain_1 @ ( k1_zfmisc_1 @ A ) @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1572]) ).

thf(2128,axiom,
    r1_tarski @ a_0_18_fraenkel @ f1_s10_fraenkel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s10_fraenkel) ).

thf(12981,plain,
    r1_tarski @ a_0_18_fraenkel @ f1_s10_fraenkel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2128]) ).

thf(968,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v7_monoid_0 @ B @ A )
          <=> ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ( ( ( k2_binop_1 @ A @ A @ A @ B @ D @ C )
                            = ( k2_binop_1 @ A @ A @ A @ B @ E @ C ) )
                         => ( D = E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_monoid_0) ).

thf(7258,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( v7_monoid_0 @ B @ A )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( ( k2_binop_1 @ A @ A @ A @ B @ D @ C )
                              = ( k2_binop_1 @ A @ A @ A @ B @ E @ C ) )
                           => ( D = E ) ) ) ) ) )
            & ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( ( k2_binop_1 @ A @ A @ A @ B @ D @ C )
                              = ( k2_binop_1 @ A @ A @ A @ B @ E @ C ) )
                           => ( D = E ) ) ) ) )
             => ( v7_monoid_0 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).

thf(1640,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finsub_1) ).

thf(10309,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1640]) ).

thf(652,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( v1_partfun1 @ C @ A @ B )
       => ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ A @ B )
          & ( m2_relset_1 @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_funct_2) ).

thf(5787,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( v1_partfun1 @ C @ A @ B )
       => ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ A @ B )
          & ( m2_relset_1 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(342,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
          & ! [C: $i] :
              ~ ( r2_hidden @ C @ ( k2_relat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_relat_1) ).

thf(4411,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
          & ! [C: $i] :
              ~ ( r2_hidden @ C @ ( k2_relat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(1581,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C ) )
     => ( ( r2_hidden @ A @ ( a_2_3_domain_1 @ B @ C ) )
      <=> ? [D: $i,E: $i] :
            ( ( m1_subset_1 @ D @ B )
            & ( m1_subset_1 @ E @ C )
            & ( A
              = ( k1_domain_1 @ B @ C @ D @ E ) )
            & ( p1_s2_domain_1 @ D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_3_domain_1) ).

thf(10046,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C ) )
     => ( ( ( r2_hidden @ A @ ( a_2_3_domain_1 @ B @ C ) )
         => ? [D: $i,E: $i] :
              ( ( m1_subset_1 @ D @ B )
              & ( m1_subset_1 @ E @ C )
              & ( A
                = ( k1_domain_1 @ B @ C @ D @ E ) )
              & ( p1_s2_domain_1 @ D @ E ) ) )
        & ( ? [D: $i,E: $i] :
              ( ( m1_subset_1 @ D @ B )
              & ( m1_subset_1 @ E @ C )
              & ( A
                = ( k1_domain_1 @ B @ C @ D @ E ) )
              & ( p1_s2_domain_1 @ D @ E ) )
         => ( r2_hidden @ A @ ( a_2_3_domain_1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1581]) ).

thf(2389,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( B
            = ( a_2_1_domain_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_domain_1) ).

thf(14034,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( B
            = ( a_2_1_domain_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2389]) ).

thf(2538,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( r1_filter_2 @ A @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_filter_2) ).

thf(14686,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( r1_filter_2 @ A @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2538]) ).

thf(298,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( r1_tarski @ A @ B )
                  & ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ C ) ) )
               => ( r1_tarski @ A @ ( k1_funct_4 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_pre_circ) ).

thf(4205,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( r1_tarski @ A @ B )
                  & ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ C ) ) )
               => ( r1_tarski @ A @ ( k1_funct_4 @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(1225,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( ( r1_tarski @ A @ B )
               => ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_relat_1) ).

thf(8394,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( ( r1_tarski @ A @ B )
               => ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).

thf(969,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_realset1 @ C @ A @ B ) )
     => ( ( v1_funct_1 @ ( k2_realset1 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k2_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C )
        & ( m2_relset_1 @ ( k2_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_realset1) ).

thf(7268,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_realset1 @ C @ A @ B ) )
     => ( ( v1_funct_1 @ ( k2_realset1 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k2_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C )
        & ( m2_relset_1 @ ( k2_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(2172,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_realset1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tex_2) ).

thf(13195,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_realset1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2172]) ).

thf(1176,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k2_xboole_0 @ A @ B )
        = k1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_xboole_1) ).

thf(8190,plain,
    ! [A: $i,B: $i] :
      ( ( ( k2_xboole_0 @ A @ B )
        = k1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).

thf(157,axiom,
    ! [A: $i] :
      ( ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( ( k1_relat_1 @ B )
                    = A )
                  & ( ( k1_relat_1 @ C )
                    = A ) )
               => ( B = C ) ) ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_1) ).

thf(3431,plain,
    ! [A: $i] :
      ( ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( ( k1_relat_1 @ B )
                    = A )
                  & ( ( k1_relat_1 @ C )
                    = A ) )
               => ( B = C ) ) ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(1086,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( ( v1_funct_1 @ H )
                                    & ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ A @ B ) @ C )
                                    & ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                                 => ! [I: $i] :
                                      ( ( m2_finseq_1 @ I @ A )
                                     => ! [J: $i] :
                                          ( ( m2_finseq_1 @ J @ B )
                                         => ( ( ( I
                                                = ( k10_finseq_1 @ D @ E ) )
                                              & ( J
                                                = ( k10_finseq_1 @ F @ G ) ) )
                                           => ( ( k3_funcop_1 @ H @ I @ J )
                                              = ( k10_finseq_1 @ ( k2_binop_1 @ A @ B @ C @ H @ D @ F ) @ ( k2_binop_1 @ A @ B @ C @ H @ E @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_finseq_2) ).

thf(7786,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( ( v1_funct_1 @ H )
                                    & ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ A @ B ) @ C )
                                    & ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                                 => ! [I: $i] :
                                      ( ( m2_finseq_1 @ I @ A )
                                     => ! [J: $i] :
                                          ( ( m2_finseq_1 @ J @ B )
                                         => ( ( ( I
                                                = ( k10_finseq_1 @ D @ E ) )
                                              & ( J
                                                = ( k10_finseq_1 @ F @ G ) ) )
                                           => ( ( k3_funcop_1 @ H @ I @ J )
                                              = ( k10_finseq_1 @ ( k2_binop_1 @ A @ B @ C @ H @ D @ F ) @ ( k2_binop_1 @ A @ B @ C @ H @ E @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).

thf(1010,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k3_enumset1 @ A @ B @ C @ D @ E )
      = ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k1_enumset1 @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_enumset1) ).

thf(7492,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k3_enumset1 @ A @ B @ C @ D @ E )
      = ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k1_enumset1 @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).

thf(949,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_finset_1 @ A )
       => ( v1_finset_1 @ ( k9_relat_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finset_1) ).

thf(7144,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_finset_1 @ A )
       => ( v1_finset_1 @ ( k9_relat_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).

thf(366,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
            = ( k2_relat_1 @ A ) )
          & ( ( k2_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
            = ( k2_relat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_1) ).

thf(4583,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
            = ( k2_relat_1 @ A ) )
          & ( ( k2_relat_1 @ ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A ) )
            = ( k2_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(1780,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( r2_hidden @ C @ ( k4_partfun1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_partfun1) ).

thf(11064,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( r2_hidden @ C @ ( k4_partfun1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1780]) ).

thf(1891,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
     => ( B = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_partfun1) ).

thf(11656,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
     => ( B = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1891]) ).

thf(101,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_relat_1 @ ( k10_finseq_1 @ A @ B ) )
      = ( k2_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_finseq_2) ).

thf(3199,plain,
    ! [A: $i,B: $i] :
      ( ( k2_relat_1 @ ( k10_finseq_1 @ A @ B ) )
      = ( k2_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(1439,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ( ( v2_binop_1 @ C @ B )
                           => ( ( k8_funcop_1 @ B @ A @ C @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) @ D )
                              = ( k8_funcop_1 @ B @ A @ C @ E @ ( k8_funcop_1 @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_funcop_1) ).

thf(9336,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ( ( v2_binop_1 @ C @ B )
                           => ( ( k8_funcop_1 @ B @ A @ C @ ( k2_binop_1 @ B @ B @ B @ C @ E @ F ) @ D )
                              = ( k8_funcop_1 @ B @ A @ C @ E @ ( k8_funcop_1 @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1439]) ).

thf(674,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ A @ B )
       => ( v1_relat_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_relat_1) ).

thf(5888,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ A @ B )
       => ( v1_relat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(2017,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_eqrel_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ( ( C
                  = ( k2_borsuk_1 @ A @ B ) )
              <=> ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ( r2_hidden @ D @ ( k8_funct_2 @ A @ B @ C @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_borsuk_1) ).

thf(12362,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_eqrel_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ( ( ( C
                    = ( k2_borsuk_1 @ A @ B ) )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ( r2_hidden @ D @ ( k8_funct_2 @ A @ B @ C @ D ) ) ) )
                & ( ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ( r2_hidden @ D @ ( k8_funct_2 @ A @ B @ C @ D ) ) )
                 => ( C
                    = ( k2_borsuk_1 @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2017]) ).

thf(297,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( C
            = ( k9_relat_1 @ A @ B ) )
        <=> ! [D: $i] :
              ( ( r2_hidden @ D @ C )
            <=> ? [E: $i] :
                  ( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
                  & ( r2_hidden @ E @ B )
                  & ( D
                    = ( k1_funct_1 @ A @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).

thf(4173,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( ( C
              = ( k9_relat_1 @ A @ B ) )
           => ! [D: $i] :
                ( ( ( r2_hidden @ D @ C )
                 => ? [E: $i] :
                      ( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
                      & ( r2_hidden @ E @ B )
                      & ( D
                        = ( k1_funct_1 @ A @ E ) ) ) )
                & ( ? [E: $i] :
                      ( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
                      & ( r2_hidden @ E @ B )
                      & ( D
                        = ( k1_funct_1 @ A @ E ) ) )
                 => ( r2_hidden @ D @ C ) ) ) )
          & ( ! [D: $i] :
                ( ( ( r2_hidden @ D @ C )
                 => ? [E: $i] :
                      ( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
                      & ( r2_hidden @ E @ B )
                      & ( D
                        = ( k1_funct_1 @ A @ E ) ) ) )
                & ( ? [E: $i] :
                      ( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
                      & ( r2_hidden @ E @ B )
                      & ( D
                        = ( k1_funct_1 @ A @ E ) ) )
                 => ( r2_hidden @ D @ C ) ) )
           => ( C
              = ( k9_relat_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(479,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ( ( k2_funct_2 @ A @ A @ B @ A )
        = ( k2_relat_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funct_2) ).

thf(5084,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ( ( k2_funct_2 @ A @ A @ B @ A )
        = ( k2_relat_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(1029,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ ( k4_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_1) ).

thf(7564,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ ( k4_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).

thf(2541,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
        & ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) ) )
     => ( m1_subset_1 @ ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_mcart_1) ).

thf(14697,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
        & ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) ) )
     => ( m1_subset_1 @ ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2541]) ).

thf(1472,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( r1_xboole_0 @ A @ B )
        & ( r1_tarski @ A @ C )
        & ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_xboole_1) ).

thf(9490,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( r1_xboole_0 @ A @ B )
        & ( r1_tarski @ A @ C )
        & ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472]) ).

thf(276,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v8_monoid_0 @ B @ A )
          <=> ( ( v6_monoid_0 @ B @ A )
              & ( v7_monoid_0 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_monoid_0) ).

thf(4072,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( v8_monoid_0 @ B @ A )
             => ( ( v6_monoid_0 @ B @ A )
                & ( v7_monoid_0 @ B @ A ) ) )
            & ( ( ( v6_monoid_0 @ B @ A )
                & ( v7_monoid_0 @ B @ A ) )
             => ( v8_monoid_0 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(2397,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k5_classes2 @ A @ B @ C )
        = ( k5_classes2 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_classes2) ).

thf(14056,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k5_classes2 @ A @ B @ C )
        = ( k5_classes2 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2397]) ).

thf(262,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ B ) )
     => ! [C: $i] :
          ( ( m2_filter_1 @ C @ A @ B )
         => ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_filter_1) ).

thf(4018,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ B ) )
     => ! [C: $i] :
          ( ( m2_filter_1 @ C @ A @ B )
         => ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(1437,axiom,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k1_numbers )
     => ( m1_subset_1 @ ( k7_binop_2 @ A ) @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_binop_2) ).

thf(9330,plain,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k1_numbers )
     => ( m1_subset_1 @ ( k7_binop_2 @ A ) @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1437]) ).

thf(1706,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m2_realset1 @ C @ A @ B )
         => ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_realset1) ).

thf(10591,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m2_realset1 @ C @ A @ B )
         => ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1706]) ).

thf(2039,axiom,
    ! [A: $i,B: $i] :
      ( ( v4_finsub_1 @ B )
     => ( ( B
          = ( k5_finsub_1 @ A ) )
      <=> ! [C: $i] :
            ( ( r2_hidden @ C @ B )
          <=> ( ( r1_tarski @ C @ A )
              & ( v1_finset_1 @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_finsub_1) ).

thf(12453,plain,
    ! [A: $i,B: $i] :
      ( ( v4_finsub_1 @ B )
     => ( ( ( B
            = ( k5_finsub_1 @ A ) )
         => ! [C: $i] :
              ( ( ( r2_hidden @ C @ B )
               => ( ( r1_tarski @ C @ A )
                  & ( v1_finset_1 @ C ) ) )
              & ( ( ( r1_tarski @ C @ A )
                  & ( v1_finset_1 @ C ) )
               => ( r2_hidden @ C @ B ) ) ) )
        & ( ! [C: $i] :
              ( ( ( r2_hidden @ C @ B )
               => ( ( r1_tarski @ C @ A )
                  & ( v1_finset_1 @ C ) ) )
              & ( ( ( r1_tarski @ C @ A )
                  & ( v1_finset_1 @ C ) )
               => ( r2_hidden @ C @ B ) ) )
         => ( B
            = ( k5_finsub_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2039]) ).

thf(1824,axiom,
    r1_tarski @ a_0_32_fraenkel @ f2_s17_fraenkel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s17_fraenkel) ).

thf(11293,plain,
    r1_tarski @ a_0_32_fraenkel @ f2_s17_fraenkel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1824]) ).

thf(123,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) )
     => ! [D: $i] :
          ( ( m1_pboole @ D @ ( k2_zfmisc_1 @ A @ B ) )
         => ( ! [E: $i,F: $i] :
                ( ( ( r2_hidden @ E @ A )
                  & ( r2_hidden @ F @ B ) )
               => ( ( k1_binop_1 @ C @ E @ F )
                  = ( k1_binop_1 @ D @ E @ F ) ) )
           => ( r6_pboole @ ( k2_zfmisc_1 @ A @ B ) @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_altcat_1) ).

thf(3295,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) )
     => ! [D: $i] :
          ( ( m1_pboole @ D @ ( k2_zfmisc_1 @ A @ B ) )
         => ( ! [E: $i,F: $i] :
                ( ( ( r2_hidden @ E @ A )
                  & ( r2_hidden @ F @ B ) )
               => ( ( k1_binop_1 @ C @ E @ F )
                  = ( k1_binop_1 @ D @ E @ F ) ) )
           => ( r6_pboole @ ( k2_zfmisc_1 @ A @ B ) @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(1383,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( k1_funct_4 @ ( k1_funct_4 @ A @ B ) @ C )
                = ( k1_funct_4 @ A @ ( k1_funct_4 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_4) ).

thf(9071,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( k1_funct_4 @ ( k1_funct_4 @ A @ B ) @ C )
                = ( k1_funct_4 @ A @ ( k1_funct_4 @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383]) ).

thf(1273,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_xboole_0 @ A @ B )
     => ( r1_xboole_0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).

thf(8627,plain,
    ! [A: $i,B: $i] :
      ( ( r1_xboole_0 @ A @ B )
     => ( r1_xboole_0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).

thf(788,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
        = ( k1_tarski @ A ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_zfmisc_1) ).

thf(6419,plain,
    ! [A: $i,B: $i] :
      ( ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
        = ( k1_tarski @ A ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(1343,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_xboole_0 @ B )
     => ( ( v1_xboole_0 @ ( k2_funcop_1 @ B @ A ) )
        & ( v1_relat_1 @ ( k2_funcop_1 @ B @ A ) )
        & ( v1_funct_1 @ ( k2_funcop_1 @ B @ A ) )
        & ( v2_funct_1 @ ( k2_funcop_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funcop_1) ).

thf(8934,plain,
    ! [A: $i,B: $i] :
      ( ( v1_xboole_0 @ B )
     => ( ( v1_xboole_0 @ ( k2_funcop_1 @ B @ A ) )
        & ( v1_relat_1 @ ( k2_funcop_1 @ B @ A ) )
        & ( v1_funct_1 @ ( k2_funcop_1 @ B @ A ) )
        & ( v2_funct_1 @ ( k2_funcop_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).

thf(2064,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r1_tarski @ D @ ( k1_enumset1 @ A @ B @ C ) )
    <=> ~ ( ( D != k1_xboole_0 )
          & ( D
           != ( k1_tarski @ A ) )
          & ( D
           != ( k1_tarski @ B ) )
          & ( D
           != ( k1_tarski @ C ) )
          & ( D
           != ( k2_tarski @ A @ B ) )
          & ( D
           != ( k2_tarski @ B @ C ) )
          & ( D
           != ( k2_tarski @ A @ C ) )
          & ( D
           != ( k1_enumset1 @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_waybel18) ).

thf(12593,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ D @ ( k1_enumset1 @ A @ B @ C ) )
       => ~ ( ( D != k1_xboole_0 )
            & ( D
             != ( k1_tarski @ A ) )
            & ( D
             != ( k1_tarski @ B ) )
            & ( D
             != ( k1_tarski @ C ) )
            & ( D
             != ( k2_tarski @ A @ B ) )
            & ( D
             != ( k2_tarski @ B @ C ) )
            & ( D
             != ( k2_tarski @ A @ C ) )
            & ( D
             != ( k1_enumset1 @ A @ B @ C ) ) ) )
      & ( ~ ( ( D != k1_xboole_0 )
            & ( D
             != ( k1_tarski @ A ) )
            & ( D
             != ( k1_tarski @ B ) )
            & ( D
             != ( k1_tarski @ C ) )
            & ( D
             != ( k2_tarski @ A @ B ) )
            & ( D
             != ( k2_tarski @ B @ C ) )
            & ( D
             != ( k2_tarski @ A @ C ) )
            & ( D
             != ( k1_enumset1 @ A @ B @ C ) ) )
       => ( r1_tarski @ D @ ( k1_enumset1 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2064]) ).

thf(1935,axiom,
    ! [A: $i] :
      ( ! [B: $i,C: $i] :
          ~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
     => ( ( ( k1_funct_5 @ A )
          = k1_xboole_0 )
        & ( ( k2_funct_5 @ A )
          = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_5) ).

thf(11891,plain,
    ! [A: $i] :
      ( ! [B: $i,C: $i] :
          ~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
     => ( ( ( k1_funct_5 @ A )
          = k1_xboole_0 )
        & ( ( k2_funct_5 @ A )
          = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1935]) ).

thf(682,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ( ( v2_funct_1 @ C )
           => ! [D: $i] :
                ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
               => ! [E: $i] :
                    ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
                   => ( ( r1_tarski @ E @ ( k2_funct_2 @ A @ B @ C @ D ) )
                     => ( r1_tarski @ ( k3_funct_2 @ A @ B @ C @ E ) @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funct_7) ).

thf(5946,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ( ( v2_funct_1 @ C )
           => ! [D: $i] :
                ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
               => ! [E: $i] :
                    ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
                   => ( ( r1_tarski @ E @ ( k2_funct_2 @ A @ B @ C @ D ) )
                     => ( r1_tarski @ ( k3_funct_2 @ A @ B @ C @ E ) @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(1897,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( B != k1_xboole_0 )
       => ( r1_tarski @ ( k8_setfam_1 @ A @ B ) @ ( k5_setfam_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_mssubfam) ).

thf(11676,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( B != k1_xboole_0 )
       => ( r1_tarski @ ( k8_setfam_1 @ A @ B ) @ ( k5_setfam_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1897]) ).

thf(269,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_relat_1 @ C @ ( k6_relat_1 @ A ) ) ) )
      <=> ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
          & ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_1) ).

thf(4050,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_relat_1 @ C @ ( k6_relat_1 @ A ) ) ) )
         => ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
            & ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) )
        & ( ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
            & ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) )
         => ( r2_hidden @ B @ ( k1_relat_1 @ ( k5_relat_1 @ C @ ( k6_relat_1 @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(1812,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ! [D: $i,E: $i,F: $i] :
          ( ( ( g1_vectsp_1 @ A @ B @ C )
            = ( g1_vectsp_1 @ D @ E @ F ) )
         => ( ( A = D )
            & ( B = E )
            & ( C = F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_vectsp_1) ).

thf(11215,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ! [D: $i,E: $i,F: $i] :
          ( ( ( g1_vectsp_1 @ A @ B @ C )
            = ( g1_vectsp_1 @ D @ E @ F ) )
         => ( ( A = D )
            & ( B = E )
            & ( C = F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1812]) ).

thf(1544,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ~ ( r2_hidden @ D @ B )
                <=> ( r2_hidden @ D @ C ) ) )
           => ( B
              = ( k3_subset_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_subset_1) ).

thf(9860,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ( ~ ( r2_hidden @ D @ B )
                   => ( r2_hidden @ D @ C ) )
                  & ( ( r2_hidden @ D @ C )
                   => ~ ( r2_hidden @ D @ B ) ) ) )
           => ( B
              = ( k3_subset_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1544]) ).

thf(1841,axiom,
    ! [A: $i] :
      ( ( k1_pcomps_1 @ A )
      = ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).

thf(11389,plain,
    ! [A: $i] :
      ( ( k1_pcomps_1 @ A )
      = ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1841]) ).

thf(1587,axiom,
    ! [A: $i] :
      ( ( m1_pboole @ A @ k1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_pboole) ).

thf(10085,plain,
    ! [A: $i] :
      ( ( m1_pboole @ A @ k1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1587]) ).

thf(397,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
       => ( ( k2_funct_4 @ ( k2_funct_4 @ C ) )
          = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funct_4) ).

thf(4724,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
       => ( ( k2_funct_4 @ ( k2_funct_4 @ C ) )
          = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(1059,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( ( k2_partfun1 @ A @ B @ C @ D )
        = ( k7_relat_1 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_partfun1) ).

thf(7677,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( ( k2_partfun1 @ A @ B @ C @ D )
        = ( k7_relat_1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(2218,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_fraenkel @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_fraenkel) ).

thf(13414,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_fraenkel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2218]) ).

thf(1917,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( A = B )
       => ( ( k1_cqc_lang @ A @ B @ C @ D )
          = C ) )
      & ( ( A != B )
       => ( ( k1_cqc_lang @ A @ B @ C @ D )
          = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_cqc_lang) ).

thf(11748,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( A = B )
       => ( ( k1_cqc_lang @ A @ B @ C @ D )
          = C ) )
      & ( ( A != B )
       => ( ( k1_cqc_lang @ A @ B @ C @ D )
          = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1917]) ).

thf(704,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( k5_relat_1 @ ( k5_funcop_1 @ C @ D @ B ) @ A )
                  = ( k5_funcop_1 @ ( k5_relat_1 @ C @ A ) @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_funcop_1) ).

thf(6054,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( k5_relat_1 @ ( k5_funcop_1 @ C @ D @ B ) @ A )
                  = ( k5_funcop_1 @ ( k5_relat_1 @ C @ A ) @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(1250,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) )
        = ( k9_relat_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_relat_1) ).

thf(8526,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) )
        = ( k9_relat_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).

thf(978,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ B @ A )
            & ( m2_relset_1 @ D @ B @ A ) )
         => ( ( ( k1_partfun1 @ B @ A @ A @ B @ D @ C )
              = ( k6_partfun1 @ B ) )
           => ( ( k2_relat_1 @ C )
              = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_funct_2) ).

thf(7317,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ B @ A )
            & ( m2_relset_1 @ D @ B @ A ) )
         => ( ( ( k1_partfun1 @ B @ A @ A @ B @ D @ C )
              = ( k6_partfun1 @ B ) )
           => ( ( k2_relat_1 @ C )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(138,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_pboole @ C @ A ) )
     => ! [D: $i] :
          ( ( m3_pboole @ D @ A @ B @ C )
         => ( m1_pboole @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_pboole) ).

thf(3357,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_pboole @ C @ A ) )
     => ! [D: $i] :
          ( ( m3_pboole @ D @ A @ B @ C )
         => ( m1_pboole @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(1131,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( m1_relset_1 @ E @ A @ B )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( m2_relset_1 @ ( k7_relset_1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relset_1) ).

thf(8018,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( m1_relset_1 @ E @ A @ B )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( m2_relset_1 @ ( k7_relset_1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).

thf(657,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ( ( m1_subset_1 @ ( k3_mcart_1 @ B @ C @ D ) @ A )
                        & ( m1_subset_1 @ ( k4_mcart_1 @ B @ C @ D @ E ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_grcat_1) ).

thf(5805,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ( ( m1_subset_1 @ ( k3_mcart_1 @ B @ C @ D ) @ A )
                        & ( m1_subset_1 @ ( k4_mcart_1 @ B @ C @ D @ E ) @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(535,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_tarski @ A @ B )
      = ( k2_tarski @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

thf(5311,plain,
    ! [A: $i,B: $i] :
      ( ( k2_tarski @ A @ B )
      = ( k2_tarski @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(821,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( r2_hidden @ A @ ( k3_zfmisc_1 @ B @ C @ D ) )
        & ! [E: $i,F: $i,G: $i] :
            ~ ( ( r2_hidden @ E @ B )
              & ( r2_hidden @ F @ C )
              & ( r2_hidden @ G @ D )
              & ( A
                = ( k3_mcart_1 @ E @ F @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_mcart_1) ).

thf(6559,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( r2_hidden @ A @ ( k3_zfmisc_1 @ B @ C @ D ) )
        & ! [E: $i,F: $i,G: $i] :
            ~ ( ( r2_hidden @ E @ B )
              & ( r2_hidden @ F @ C )
              & ( r2_hidden @ G @ D )
              & ( A
                = ( k3_mcart_1 @ E @ F @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(1850,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( r2_hidden @ A @ ( a_2_0_borsuk_1 @ B @ C ) )
      <=> ? [D: $i] :
            ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
            & ( A
              = ( k3_tarski @ D ) )
            & ( r2_hidden @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_borsuk_1) ).

thf(11446,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( ( r2_hidden @ A @ ( a_2_0_borsuk_1 @ B @ C ) )
         => ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
              & ( A
                = ( k3_tarski @ D ) )
              & ( r2_hidden @ D @ C ) ) )
        & ( ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
              & ( A
                = ( k3_tarski @ D ) )
              & ( r2_hidden @ D @ C ) )
         => ( r2_hidden @ A @ ( a_2_0_borsuk_1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1850]) ).

thf(124,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_xboole_0 @ B @ C ) )
         => ( ( k1_funct_4 @ ( k7_relat_1 @ A @ B ) @ ( k7_relat_1 @ A @ C ) )
            = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_funct_4) ).

thf(3300,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_xboole_0 @ B @ C ) )
         => ( ( k1_funct_4 @ ( k7_relat_1 @ A @ B ) @ ( k7_relat_1 @ A @ C ) )
            = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(2444,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
        & ( m2_relset_1 @ E @ B @ C ) )
     => ( ( r2_hidden @ A @ ( a_4_0_relset_2 @ B @ C @ D @ E ) )
      <=> ? [F: $i] :
            ( ( m1_subset_1 @ F @ B )
            & ( A
              = ( k2_relset_2 @ B @ C @ E @ F ) )
            & ( r2_hidden @ F @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_0_relset_2) ).

thf(14238,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
        & ( m2_relset_1 @ E @ B @ C ) )
     => ( ( ( r2_hidden @ A @ ( a_4_0_relset_2 @ B @ C @ D @ E ) )
         => ? [F: $i] :
              ( ( m1_subset_1 @ F @ B )
              & ( A
                = ( k2_relset_2 @ B @ C @ E @ F ) )
              & ( r2_hidden @ F @ D ) ) )
        & ( ? [F: $i] :
              ( ( m1_subset_1 @ F @ B )
              & ( A
                = ( k2_relset_2 @ B @ C @ E @ F ) )
              & ( r2_hidden @ F @ D ) )
         => ( r2_hidden @ A @ ( a_4_0_relset_2 @ B @ C @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2444]) ).

thf(1948,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( B != k1_xboole_0 )
       => ( ( k5_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
          = ( k6_subset_1 @ A @ ( k2_subset_1 @ A ) @ ( k6_setfam_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).

thf(11971,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( B != k1_xboole_0 )
       => ( ( k5_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
          = ( k6_subset_1 @ A @ ( k2_subset_1 @ A ) @ ( k6_setfam_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1948]) ).

thf(1302,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).

thf(8759,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).

thf(733,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
     => ( ( k5_setwiseo @ A @ B @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k5_setwiseo) ).

thf(6157,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
     => ( ( k5_setwiseo @ A @ B @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(1241,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( ( ( v1_funct_1 @ C )
          & ( v1_partfun1 @ C @ A @ B ) )
       => ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_2) ).

thf(8479,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( ( ( v1_funct_1 @ C )
          & ( v1_partfun1 @ C @ A @ B ) )
       => ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).

thf(1523,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_enumset1 @ A @ A @ A @ B @ C )
      = ( k1_enumset1 @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_enumset1) ).

thf(9781,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_enumset1 @ A @ A @ A @ B @ C )
      = ( k1_enumset1 @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1523]) ).

thf(1960,axiom,
    ! [A: $i] :
      ( ( r1_tarski @ A @ k1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).

thf(12041,plain,
    ! [A: $i] :
      ( ( r1_tarski @ A @ k1_xboole_0 )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1960]) ).

thf(1709,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( B
          = ( k1_tarski @ A ) )
       => ( ( k7_setfam_1 @ A @ B )
          = ( k1_tarski @ k1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_setfam_1) ).

thf(10602,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( B
          = ( k1_tarski @ A ) )
       => ( ( k7_setfam_1 @ A @ B )
          = ( k1_tarski @ k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1709]) ).

thf(223,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( k1_relat_1 @ C )
          = ( k2_zfmisc_1 @ A @ B ) )
       => ( ( k1_relat_1 @ ( k2_funct_4 @ C ) )
          = ( k2_zfmisc_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_funct_4) ).

thf(3851,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( k1_relat_1 @ C )
          = ( k2_zfmisc_1 @ A @ B ) )
       => ( ( k1_relat_1 @ ( k2_funct_4 @ C ) )
          = ( k2_zfmisc_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(395,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k4_relat_1 @ ( k3_xboole_0 @ A @ B ) )
            = ( k3_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_relat_1) ).

thf(4718,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k4_relat_1 @ ( k3_xboole_0 @ A @ B ) )
            = ( k3_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(2068,axiom,
    ! [A: $i] :
      ( ( k1_enumset1 @ A @ A @ A )
      = ( k1_tarski @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_enumset1) ).

thf(12638,plain,
    ! [A: $i] :
      ( ( k1_enumset1 @ A @ A @ A )
      = ( k1_tarski @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2068]) ).

thf(797,axiom,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ( r2_realset1 @ A @ B @ C )
              <=> ( ( m1_realset1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ A @ B )
                  & ( v1_funct_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) )
                  & ( v1_funct_2 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) )
                  & ( m2_relset_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_realset1) ).

thf(6451,plain,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ( ( r2_realset1 @ A @ B @ C )
                 => ( ( m1_realset1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ A @ B )
                    & ( v1_funct_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) )
                    & ( v1_funct_2 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) )
                    & ( m2_relset_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) ) )
                & ( ( ( m1_realset1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ A @ B )
                    & ( v1_funct_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) )
                    & ( v1_funct_2 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) )
                    & ( m2_relset_1 @ ( k4_xboole_0 @ ( k1_realset1 @ B @ A ) @ ( k1_tarski @ C ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) ) )
                 => ( r2_realset1 @ A @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(1398,axiom,
    ( ( k1_funct_2 @ k1_xboole_0 @ k1_xboole_0 )
    = ( k1_tarski @ ( k6_relat_1 @ k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_altcat_1) ).

thf(9167,plain,
    ( ( k1_funct_2 @ k1_xboole_0 @ k1_xboole_0 )
    = ( k1_tarski @ ( k6_relat_1 @ k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398]) ).

thf(1692,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
        = ( k4_zfmisc_1 @ E @ F @ G @ H ) )
     => ( ( A = k1_xboole_0 )
        | ( B = k1_xboole_0 )
        | ( C = k1_xboole_0 )
        | ( D = k1_xboole_0 )
        | ( ( A = E )
          & ( B = F )
          & ( C = G )
          & ( D = H ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_mcart_1) ).

thf(10538,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
        = ( k4_zfmisc_1 @ E @ F @ G @ H ) )
     => ( ( A = k1_xboole_0 )
        | ( B = k1_xboole_0 )
        | ( C = k1_xboole_0 )
        | ( D = k1_xboole_0 )
        | ( ( A = E )
          & ( B = F )
          & ( C = G )
          & ( D = H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1692]) ).

thf(2056,axiom,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m3_realset1 @ C @ A @ B )
             => ( ( v1_funct_1 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
                & ( v1_funct_2 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
                & ( m2_relset_1 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_realset1) ).

thf(12554,plain,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m3_realset1 @ C @ A @ B )
             => ( ( v1_funct_1 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
                & ( v1_funct_2 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
                & ( m2_relset_1 @ ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2056]) ).

thf(2274,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
     => ( v1_finset_1 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finsub_1) ).

thf(13600,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
     => ( v1_finset_1 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2274]) ).

thf(52,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ ( k10_finseq_1 @ A @ B ) )
      & ( v1_funct_1 @ ( k10_finseq_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_finseq_1) ).

thf(2965,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ ( k10_finseq_1 @ A @ B ) )
      & ( v1_funct_1 @ ( k10_finseq_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(2446,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
     => ( m1_subset_1 @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).

thf(14253,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
     => ( m1_subset_1 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2446]) ).

thf(999,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v5_monoid_0 @ B @ A )
          <=> ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ? [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                        & ? [F: $i] :
                            ( ( m1_subset_1 @ F @ A )
                            & ( ( k2_binop_1 @ A @ A @ A @ B @ C @ E )
                              = D )
                            & ( ( k2_binop_1 @ A @ A @ A @ B @ F @ C )
                              = D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_monoid_0) ).

thf(7408,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( v5_monoid_0 @ B @ A )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ? [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                          & ? [F: $i] :
                              ( ( m1_subset_1 @ F @ A )
                              & ( ( k2_binop_1 @ A @ A @ A @ B @ C @ E )
                                = D )
                              & ( ( k2_binop_1 @ A @ A @ A @ B @ F @ C )
                                = D ) ) ) ) ) )
            & ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ? [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                          & ? [F: $i] :
                              ( ( m1_subset_1 @ F @ A )
                              & ( ( k2_binop_1 @ A @ A @ A @ B @ C @ E )
                                = D )
                              & ( ( k2_binop_1 @ A @ A @ A @ B @ F @ C )
                                = D ) ) ) ) )
             => ( v5_monoid_0 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

thf(1138,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( ( k2_xboole_0 @ ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_zfmisc_1) ).

thf(8050,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( ( k2_xboole_0 @ ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).

thf(474,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
            & ! [F: $i] :
                ( ( m1_subset_1 @ F @ A )
               => ~ ( ( r2_hidden @ F @ C )
                    & ( E
                      = ( k1_funct_1 @ D @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_funct_2) ).

thf(5059,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ~ ( ( r2_hidden @ E @ ( k2_funct_2 @ A @ B @ D @ C ) )
            & ! [F: $i] :
                ( ( m1_subset_1 @ F @ A )
               => ~ ( ( r2_hidden @ F @ C )
                    & ( E
                      = ( k1_funct_1 @ D @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(2134,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ A @ ( k5_finsub_1 @ A ) )
            & ( m2_relset_1 @ B @ A @ ( k5_finsub_1 @ A ) ) )
         => ( ( B
              = ( k11_setwiseo @ A ) )
          <=> ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ( ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ B @ C )
                  = ( k2_setwiseo @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_setwiseo) ).

thf(12998,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ A @ ( k5_finsub_1 @ A ) )
            & ( m2_relset_1 @ B @ A @ ( k5_finsub_1 @ A ) ) )
         => ( ( ( B
                = ( k11_setwiseo @ A ) )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ( ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ B @ C )
                    = ( k2_setwiseo @ A @ C ) ) ) )
            & ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ( ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ B @ C )
                    = ( k2_setwiseo @ A @ C ) ) )
             => ( B
                = ( k11_setwiseo @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2134]) ).

thf(2042,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( r2_hidden @ A @ ( a_1_0_pua2mss1 @ B ) )
      <=> ? [C: $i] :
            ( ( m1_subset_1 @ C @ B )
            & ( A
              = ( k1_tarski @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_pua2mss1) ).

thf(12485,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( ( r2_hidden @ A @ ( a_1_0_pua2mss1 @ B ) )
         => ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A
                = ( k1_tarski @ C ) ) ) )
        & ( ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A
                = ( k1_tarski @ C ) ) )
         => ( r2_hidden @ A @ ( a_1_0_pua2mss1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2042]) ).

thf(1505,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( k3_zfmisc_1 @ A @ B @ C )
        = ( k3_zfmisc_1 @ D @ E @ F ) )
     => ( ( A = k1_xboole_0 )
        | ( B = k1_xboole_0 )
        | ( C = k1_xboole_0 )
        | ( ( A = D )
          & ( B = E )
          & ( C = F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_mcart_1) ).

thf(9616,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( k3_zfmisc_1 @ A @ B @ C )
        = ( k3_zfmisc_1 @ D @ E @ F ) )
     => ( ( A = k1_xboole_0 )
        | ( B = k1_xboole_0 )
        | ( C = k1_xboole_0 )
        | ( ( A = D )
          & ( B = E )
          & ( C = F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505]) ).

thf(441,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ( ( k9_relat_1 @ ( k15_funct_3 @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
            = ( k2_zfmisc_1 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_funct_3) ).

thf(4935,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ( ( k9_relat_1 @ ( k15_funct_3 @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
            = ( k2_zfmisc_1 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(264,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ( ( k4_finseq_1 @ A )
        = ( k1_relat_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_finseq_1) ).

thf(4033,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ( ( k4_finseq_1 @ A )
        = ( k1_relat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ! [D: $i] :
              ( ( ( v1_relat_1 @ D )
                & ( v1_funct_1 @ D ) )
             => ( ( ( A
                    = ( k2_relat_1 @ B ) )
                  & ( ( k1_relat_1 @ C )
                    = A )
                  & ( ( k1_relat_1 @ D )
                    = A )
                  & ( ( k5_relat_1 @ B @ C )
                    = ( k5_relat_1 @ B @ D ) ) )
               => ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_funct_1) ).

thf(2618,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ! [D: $i] :
              ( ( ( v1_relat_1 @ D )
                & ( v1_funct_1 @ D ) )
             => ( ( ( A
                    = ( k2_relat_1 @ B ) )
                  & ( ( k1_relat_1 @ C )
                    = A )
                  & ( ( k1_relat_1 @ D )
                    = A )
                  & ( ( k5_relat_1 @ B @ C )
                    = ( k5_relat_1 @ B @ D ) ) )
               => ( C = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(211,axiom,
    ! [A: $i] :
      ( ? [B: $i,C: $i] :
          ( A
          = ( k4_tarski @ B @ C ) )
     => ( ( A
         != ( k1_mcart_1 @ A ) )
        & ( A
         != ( k2_mcart_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_mcart_1) ).

thf(3739,plain,
    ! [A: $i] :
      ( ? [B: $i,C: $i] :
          ( A
          = ( k4_tarski @ B @ C ) )
     => ( ( A
         != ( k1_mcart_1 @ A ) )
        & ( A
         != ( k2_mcart_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(2198,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k6_enumset1 @ A @ A @ A @ A @ B @ C @ D @ E )
      = ( k3_enumset1 @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_enumset1) ).

thf(13305,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k6_enumset1 @ A @ A @ A @ A @ B @ C @ D @ E )
      = ( k3_enumset1 @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2198]) ).

thf(1356,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ A @ C )
        & ( r1_xboole_0 @ B @ C ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_xboole_1) ).

thf(8977,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ A @ C )
        & ( r1_xboole_0 @ B @ C ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).

thf(483,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_xboole_1) ).

thf(5096,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(1793,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k3_setwiseo @ A @ B @ C ) @ ( k5_finsub_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_setwiseo) ).

thf(11119,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k3_setwiseo @ A @ B @ C ) @ ( k5_finsub_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1793]) ).

thf(2478,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ( k7_ens_1 @ A @ B @ C )
                = ( a_3_0_ens_1 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_ens_1) ).

thf(14410,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ( k7_ens_1 @ A @ B @ C )
                = ( a_3_0_ens_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2478]) ).

thf(2145,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ C )
        & ( v1_fraenkel @ C ) )
     => ( ( m1_fraenkel @ C @ A @ B )
      <=> ! [D: $i] :
            ( ( m1_subset_1 @ D @ C )
           => ( ( v1_funct_1 @ D )
              & ( v1_funct_2 @ D @ A @ B )
              & ( m2_relset_1 @ D @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_fraenkel) ).

thf(13077,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ C )
        & ( v1_fraenkel @ C ) )
     => ( ( ( m1_fraenkel @ C @ A @ B )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ C )
             => ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) ) ) )
        & ( ! [D: $i] :
              ( ( m1_subset_1 @ D @ C )
             => ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) ) )
         => ( m1_fraenkel @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2145]) ).

thf(1518,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( v1_funct_1 @ ( k1_oppcat_1 @ A @ B @ C @ D ) )
        & ( m2_relset_1 @ ( k1_oppcat_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_oppcat_1) ).

thf(9743,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( v1_funct_1 @ ( k1_oppcat_1 @ A @ B @ C @ D ) )
        & ( m2_relset_1 @ ( k1_oppcat_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1518]) ).

thf(2581,axiom,
    ? [A: $i] :
      ( ( m1_subset_1 @ A @ ( k5_finsub_1 @ f1_s24_fraenkel ) )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s24_fraenkel )
         => ( ( r2_hidden @ B @ A )
          <=> ? [C: $i] :
                ( ( m1_subset_1 @ C @ f2_s24_fraenkel )
                & ( r2_hidden @ C @ f3_s24_fraenkel )
                & ( B
                  = ( f4_s24_fraenkel @ C ) )
                & ( p1_s24_fraenkel @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s24_fraenkel) ).

thf(14874,plain,
    ? [A: $i] :
      ( ( m1_subset_1 @ A @ ( k5_finsub_1 @ f1_s24_fraenkel ) )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s24_fraenkel )
         => ( ( ( r2_hidden @ B @ A )
             => ? [C: $i] :
                  ( ( m1_subset_1 @ C @ f2_s24_fraenkel )
                  & ( r2_hidden @ C @ f3_s24_fraenkel )
                  & ( B
                    = ( f4_s24_fraenkel @ C ) )
                  & ( p1_s24_fraenkel @ B @ C ) ) )
            & ( ? [C: $i] :
                  ( ( m1_subset_1 @ C @ f2_s24_fraenkel )
                  & ( r2_hidden @ C @ f3_s24_fraenkel )
                  & ( B
                    = ( f4_s24_fraenkel @ C ) )
                  & ( p1_s24_fraenkel @ B @ C ) )
             => ( r2_hidden @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2581]) ).

thf(1839,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( r2_hidden @ C @ A )
         => ( r1_tarski @ C @ B ) )
     => ( r1_tarski @ ( k3_tarski @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_zfmisc_1) ).

thf(11384,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( r2_hidden @ C @ A )
         => ( r1_tarski @ C @ B ) )
     => ( r1_tarski @ ( k3_tarski @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1839]) ).

thf(281,axiom,
    ? [A: $i] :
      ( ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A )
      & ( v1_finset_1 @ A )
      & ( v1_finseq_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finseq_1) ).

thf(4087,plain,
    ? [A: $i] :
      ( ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A )
      & ( v1_finset_1 @ A )
      & ( v1_finseq_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(2009,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k4_partfun1 @ C @ A ) @ ( k4_partfun1 @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_partfun1) ).

thf(12315,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k4_partfun1 @ C @ A ) @ ( k4_partfun1 @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2009]) ).

thf(1111,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( r1_tarski @ ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) @ ( k9_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_3) ).

thf(7909,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( r1_tarski @ ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) @ ( k9_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).

thf(1657,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ( ! [E: $i] :
                        ( ( r2_hidden @ E @ A )
                      <=> ? [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                            & ? [G: $i] :
                                ( ( m1_subset_1 @ G @ C )
                                & ? [H: $i] :
                                    ( ( m1_subset_1 @ H @ D )
                                    & ( E
                                      = ( k3_mcart_1 @ F @ G @ H ) ) ) ) ) )
                   => ( A
                      = ( k3_zfmisc_1 @ B @ C @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_domain_1) ).

thf(10405,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ( ! [E: $i] :
                        ( ( ( r2_hidden @ E @ A )
                         => ? [F: $i] :
                              ( ( m1_subset_1 @ F @ B )
                              & ? [G: $i] :
                                  ( ( m1_subset_1 @ G @ C )
                                  & ? [H: $i] :
                                      ( ( m1_subset_1 @ H @ D )
                                      & ( E
                                        = ( k3_mcart_1 @ F @ G @ H ) ) ) ) ) )
                        & ( ? [F: $i] :
                              ( ( m1_subset_1 @ F @ B )
                              & ? [G: $i] :
                                  ( ( m1_subset_1 @ G @ C )
                                  & ? [H: $i] :
                                      ( ( m1_subset_1 @ H @ D )
                                      & ( E
                                        = ( k3_mcart_1 @ F @ G @ H ) ) ) ) )
                         => ( r2_hidden @ E @ A ) ) )
                   => ( A
                      = ( k3_zfmisc_1 @ B @ C @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1657]) ).

thf(807,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
     => ( v2_funct_1 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_partfun1) ).

thf(6498,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
     => ( v2_funct_1 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(515,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_xboole_1) ).

thf(5246,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k4_xboole_0 @ C @ B ) @ ( k4_xboole_0 @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(1633,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( k2_zfmisc_1 @ A @ B )
        = ( k2_zfmisc_1 @ C @ D ) )
     => ( ( A = k1_xboole_0 )
        | ( B = k1_xboole_0 )
        | ( ( A = C )
          & ( B = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).

thf(10273,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( k2_zfmisc_1 @ A @ B )
        = ( k2_zfmisc_1 @ C @ D ) )
     => ( ( A = k1_xboole_0 )
        | ( B = k1_xboole_0 )
        | ( ( A = C )
          & ( B = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1633]) ).

thf(1118,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k2_tarski @ C @ D ) )
      = ( k2_tarski @ ( k3_mcart_1 @ A @ B @ C ) @ ( k3_mcart_1 @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_mcart_1) ).

thf(7954,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k2_tarski @ C @ D ) )
      = ( k2_tarski @ ( k3_mcart_1 @ A @ B @ C ) @ ( k3_mcart_1 @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).

thf(1735,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
     => ( ( k4_relset_2 @ A @ B @ C @ D )
        = ( k9_relat_1 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_2) ).

thf(10784,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) )
     => ( ( k4_relset_2 @ A @ B @ C @ D )
        = ( k9_relat_1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1735]) ).

thf(1286,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ C @ A )
       => ( ( ( B = k1_xboole_0 )
            & ( A != k1_xboole_0 ) )
          | ( r1_tarski @ C @ ( k3_funct_2 @ A @ B @ D @ ( k2_funct_2 @ A @ B @ D @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_funct_2) ).

thf(8686,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ C @ A )
       => ( ( ( B = k1_xboole_0 )
            & ( A != k1_xboole_0 ) )
          | ( r1_tarski @ C @ ( k3_funct_2 @ A @ B @ D @ ( k2_funct_2 @ A @ B @ D @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).

thf(499,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k1_finsub_1 @ A @ B @ C )
        = ( k2_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_finsub_1) ).

thf(5169,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k1_finsub_1 @ A @ B @ C )
        = ( k2_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(677,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i,C: $i] :
          ( ( C
            = ( k9_relat_1 @ A @ B ) )
        <=> ! [D: $i] :
              ( ( r2_hidden @ D @ C )
            <=> ? [E: $i] :
                  ( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
                  & ( r2_hidden @ E @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).

thf(5897,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( C
              = ( k9_relat_1 @ A @ B ) )
           => ! [D: $i] :
                ( ( ( r2_hidden @ D @ C )
                 => ? [E: $i] :
                      ( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
                      & ( r2_hidden @ E @ B ) ) )
                & ( ? [E: $i] :
                      ( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
                      & ( r2_hidden @ E @ B ) )
                 => ( r2_hidden @ D @ C ) ) ) )
          & ( ! [D: $i] :
                ( ( ( r2_hidden @ D @ C )
                 => ? [E: $i] :
                      ( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
                      & ( r2_hidden @ E @ B ) ) )
                & ( ? [E: $i] :
                      ( ( r2_hidden @ ( k4_tarski @ E @ D ) @ A )
                      & ( r2_hidden @ E @ B ) )
                 => ( r2_hidden @ D @ C ) ) )
           => ( C
              = ( k9_relat_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(882,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( m2_filter_1 @ C @ A @ B )
              <=> ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ A )
                           => ! [G: $i] :
                                ( ( m1_subset_1 @ G @ A )
                               => ( ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
                                    & ( r2_hidden @ ( k1_domain_1 @ A @ A @ F @ G ) @ B ) )
                                 => ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ G ) ) @ B ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_filter_1) ).

thf(6863,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( ( m2_filter_1 @ C @ A @ B )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ! [F: $i] :
                              ( ( m1_subset_1 @ F @ A )
                             => ! [G: $i] :
                                  ( ( m1_subset_1 @ G @ A )
                                 => ( ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
                                      & ( r2_hidden @ ( k1_domain_1 @ A @ A @ F @ G ) @ B ) )
                                   => ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ G ) ) @ B ) ) ) ) ) ) )
                & ( ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ! [F: $i] :
                              ( ( m1_subset_1 @ F @ A )
                             => ! [G: $i] :
                                  ( ( m1_subset_1 @ G @ A )
                                 => ( ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
                                      & ( r2_hidden @ ( k1_domain_1 @ A @ A @ F @ G ) @ B ) )
                                   => ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ G ) ) @ B ) ) ) ) ) )
                 => ( m2_filter_1 @ C @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(1441,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( v1_funct_1 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) )
                  & ( v1_funct_2 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) @ A @ B )
                  & ( m2_relset_1 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_lattice2) ).

thf(9341,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( v1_funct_1 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) )
                  & ( v1_funct_2 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) @ A @ B )
                  & ( m2_relset_1 @ ( k1_funct_4 @ C @ ( k2_partfun1 @ A @ B @ D @ E ) ) @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441]) ).

thf(2220,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r1_tarski @ ( k2_funcop_1 @ A @ B ) @ ( k2_funcop_1 @ C @ D ) )
     => ( r1_tarski @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_4) ).

thf(13420,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r1_tarski @ ( k2_funcop_1 @ A @ B ) @ ( k2_funcop_1 @ C @ D ) )
     => ( r1_tarski @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2220]) ).

thf(215,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ? [B: $i,C: $i] : ( r1_tarski @ ( k1_relat_1 @ ( k2_funct_4 @ A ) ) @ ( k2_zfmisc_1 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_funct_4) ).

thf(3756,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ? [B: $i,C: $i] : ( r1_tarski @ ( k1_relat_1 @ ( k2_funct_4 @ A ) ) @ ( k2_zfmisc_1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(2589,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k8_classes2 @ A @ B @ C )
        = ( k8_classes2 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k8_classes2) ).

thf(14917,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k8_classes2 @ A @ B @ C )
        = ( k8_classes2 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2589]) ).

thf(1845,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ B @ C )
            & ( m2_relset_1 @ E @ B @ C ) )
         => ( ~ ( ( B = k1_xboole_0 )
                & ( C != k1_xboole_0 )
                & ( A != k1_xboole_0 ) )
           => ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
              & ( v1_funct_2 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C )
              & ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_2) ).

thf(11408,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ B @ C )
            & ( m2_relset_1 @ E @ B @ C ) )
         => ( ~ ( ( B = k1_xboole_0 )
                & ( C != k1_xboole_0 )
                & ( A != k1_xboole_0 ) )
           => ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
              & ( v1_funct_2 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C )
              & ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1845]) ).

thf(1911,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) )
        & ( r1_tarski @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).

thf(11728,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) )
        & ( r1_tarski @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1911]) ).

thf(2339,axiom,
    ( ( f3_s11_funct_2 != f4_s11_funct_2 )
   => ? [A: $i] :
        ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
        & ( m2_relset_1 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
        & ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f3_s11_funct_2 )
          = f5_s11_funct_2 )
        & ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f4_s11_funct_2 )
          = f6_s11_funct_2 )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s11_funct_2 )
           => ~ ( ( B != f3_s11_funct_2 )
                & ( B != f4_s11_funct_2 )
                & ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ B )
                 != ( f7_s11_funct_2 @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s11_funct_2) ).

thf(13833,plain,
    ( ( f3_s11_funct_2 != f4_s11_funct_2 )
   => ? [A: $i] :
        ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
        & ( m2_relset_1 @ A @ f1_s11_funct_2 @ f2_s11_funct_2 )
        & ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f3_s11_funct_2 )
          = f5_s11_funct_2 )
        & ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ f4_s11_funct_2 )
          = f6_s11_funct_2 )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s11_funct_2 )
           => ~ ( ( B != f3_s11_funct_2 )
                & ( B != f4_s11_funct_2 )
                & ( ( k8_funct_2 @ f1_s11_funct_2 @ f2_s11_funct_2 @ A @ B )
                 != ( f7_s11_funct_2 @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2339]) ).

thf(35,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ~ ( ( A != k1_xboole_0 )
          & ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
          & ( ( k9_relat_1 @ B @ A )
            = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t152_relat_1) ).

thf(2750,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ~ ( ( A != k1_xboole_0 )
          & ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
          & ( ( k9_relat_1 @ B @ A )
            = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(1624,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ( k4_classes2 @ A @ B )
        = ( k1_setfam_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_classes2) ).

thf(10233,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ( k4_classes2 @ A @ B )
        = ( k1_setfam_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1624]) ).

thf(984,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_cat_1 @ A @ B @ C )
      = ( k3_cqc_lang @ ( k4_tarski @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_cat_1) ).

thf(7337,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_cat_1 @ A @ B @ C )
      = ( k3_cqc_lang @ ( k4_tarski @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).

thf(1945,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
             => ( ( k10_setwiseo @ A @ B @ D @ C )
                = ( k3_tarski @ ( k8_setwiseo @ A @ ( k5_finsub_1 @ B ) @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_setwiseo) ).

thf(11954,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
             => ( ( k10_setwiseo @ A @ B @ D @ C )
                = ( k3_tarski @ ( k8_setwiseo @ A @ ( k5_finsub_1 @ B ) @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1945]) ).

thf(1797,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ B @ C )
       => ( ( ( B = k1_xboole_0 )
            & ( A != k1_xboole_0 ) )
          | ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ C )
            & ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_2) ).

thf(11143,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ B @ C )
       => ( ( ( B = k1_xboole_0 )
            & ( A != k1_xboole_0 ) )
          | ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ C )
            & ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1797]) ).

thf(1344,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ ( k1_funct_3 @ A ) )
        & ( v1_funct_1 @ ( k1_funct_3 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_3) ).

thf(8939,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ ( k1_funct_3 @ A ) )
        & ( v1_funct_1 @ ( k1_funct_3 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).

thf(1096,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
        = ( k1_tarski @ A ) )
    <=> ( ~ ( r2_hidden @ A @ C )
        & ( ( r2_hidden @ B @ C )
          | ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_zfmisc_1) ).

thf(7830,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
          = ( k1_tarski @ A ) )
       => ( ~ ( r2_hidden @ A @ C )
          & ( ( r2_hidden @ B @ C )
            | ( A = B ) ) ) )
      & ( ( ~ ( r2_hidden @ A @ C )
          & ( ( r2_hidden @ B @ C )
            | ( A = B ) ) )
       => ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
          = ( k1_tarski @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).

thf(493,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( ! [B: $i] :
              ~ ( ( r2_hidden @ B @ A )
                & ( B = k1_xboole_0 ) )
          & ! [B: $i,C: $i] :
              ( ( ( r2_hidden @ B @ A )
                & ( r2_hidden @ C @ A ) )
             => ( ( B = C )
                | ( r1_xboole_0 @ B @ C ) ) )
          & ! [B: $i] :
            ? [C: $i] :
              ( ( r2_hidden @ C @ A )
              & ! [D: $i] :
                  ( ( k3_xboole_0 @ B @ C )
                 != ( k1_tarski @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_wellord2) ).

thf(5137,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( ! [B: $i] :
              ~ ( ( r2_hidden @ B @ A )
                & ( B = k1_xboole_0 ) )
          & ! [B: $i,C: $i] :
              ( ( ( r2_hidden @ B @ A )
                & ( r2_hidden @ C @ A ) )
             => ( ( B = C )
                | ( r1_xboole_0 @ B @ C ) ) )
          & ! [B: $i] :
            ? [C: $i] :
              ( ( r2_hidden @ C @ A )
              & ! [D: $i] :
                  ( ( k3_xboole_0 @ B @ C )
                 != ( k1_tarski @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(1835,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
     => ( ( k10_funcop_1 @ A @ B @ C @ ( k10_funcop_1 @ A @ B @ C @ D ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k10_funcop_1) ).

thf(11367,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
     => ( ( k10_funcop_1 @ A @ B @ C @ ( k10_funcop_1 @ A @ B @ C @ D ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1835]) ).

thf(228,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_relat_1) ).

thf(3870,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(104,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ( ( ( v3_binop_1 @ C @ A )
                      & ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A )
                      & ( r6_binop_1 @ A @ D @ C ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                       => ( ( E != k1_xboole_0 )
                         => ! [F: $i] :
                              ( ( ( v1_funct_1 @ F )
                                & ( v1_funct_2 @ F @ B @ A )
                                & ( m2_relset_1 @ F @ B @ A ) )
                             => ! [G: $i] :
                                  ( ( m1_subset_1 @ G @ A )
                                 => ( ( k2_binop_1 @ A @ A @ A @ D @ ( k7_setwiseo @ B @ A @ C @ E @ F ) @ G )
                                    = ( k7_setwiseo @ B @ A @ C @ E @ ( k7_funcop_1 @ A @ B @ D @ F @ G ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_setwiseo) ).

thf(3211,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ( ( ( v3_binop_1 @ C @ A )
                      & ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A )
                      & ( r6_binop_1 @ A @ D @ C ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                       => ( ( E != k1_xboole_0 )
                         => ! [F: $i] :
                              ( ( ( v1_funct_1 @ F )
                                & ( v1_funct_2 @ F @ B @ A )
                                & ( m2_relset_1 @ F @ B @ A ) )
                             => ! [G: $i] :
                                  ( ( m1_subset_1 @ G @ A )
                                 => ( ( k2_binop_1 @ A @ A @ A @ D @ ( k7_setwiseo @ B @ A @ C @ E @ F ) @ G )
                                    = ( k7_setwiseo @ B @ A @ C @ E @ ( k7_funcop_1 @ A @ B @ D @ F @ G ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(1148,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_tarski @ A @ B )
           => ( r1_tarski @ ( k2_funct_4 @ A ) @ ( k2_funct_4 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_yellow20) ).

thf(8094,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_tarski @ A @ B )
           => ( r1_tarski @ ( k2_funct_4 @ A ) @ ( k2_funct_4 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).

thf(236,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ( ( ( v3_binop_1 @ D @ A )
                      & ( v1_binop_1 @ D @ A )
                      & ( v2_binop_1 @ D @ A )
                      & ( v1_setwiseo @ D @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                       => ! [F: $i] :
                            ( ( ( v1_funct_1 @ F )
                              & ( v1_funct_2 @ F @ B @ C )
                              & ( m2_relset_1 @ F @ B @ C ) )
                           => ! [G: $i] :
                                ( ( ( v1_funct_1 @ G )
                                  & ( v1_funct_2 @ G @ C @ A )
                                  & ( m2_relset_1 @ G @ C @ A ) )
                               => ( ( k7_setwiseo @ C @ A @ D @ ( k8_setwiseo @ B @ C @ F @ E ) @ G )
                                  = ( k7_setwiseo @ B @ A @ D @ E @ ( k7_funct_2 @ B @ C @ A @ F @ G ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_setwiseo) ).

thf(3906,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ( ( ( v3_binop_1 @ D @ A )
                      & ( v1_binop_1 @ D @ A )
                      & ( v2_binop_1 @ D @ A )
                      & ( v1_setwiseo @ D @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                       => ! [F: $i] :
                            ( ( ( v1_funct_1 @ F )
                              & ( v1_funct_2 @ F @ B @ C )
                              & ( m2_relset_1 @ F @ B @ C ) )
                           => ! [G: $i] :
                                ( ( ( v1_funct_1 @ G )
                                  & ( v1_funct_2 @ G @ C @ A )
                                  & ( m2_relset_1 @ G @ C @ A ) )
                               => ( ( k7_setwiseo @ C @ A @ D @ ( k8_setwiseo @ B @ C @ F @ E ) @ G )
                                  = ( k7_setwiseo @ B @ A @ D @ E @ ( k7_funct_2 @ B @ C @ A @ F @ G ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(1078,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_pboole @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k2_relat_1 @ B ) )
             => ? [D: $i] :
                  ( ( r2_hidden @ D @ A )
                  & ( C
                    = ( k1_funct_1 @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_pboole) ).

thf(7760,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_pboole @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k2_relat_1 @ B ) )
             => ? [D: $i] :
                  ( ( r2_hidden @ D @ A )
                  & ( C
                    = ( k1_funct_1 @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).

thf(367,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ( ( ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A )
                      & ( v3_binop_1 @ C @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
                           => ( ( r1_tarski @ E @ F )
                             => ( ( E = k1_xboole_0 )
                                | ( ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ E @ D ) @ ( k7_setwiseo @ B @ A @ C @ F @ D ) )
                                  = ( k7_setwiseo @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_setwiseo) ).

thf(4588,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ( ( ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A )
                      & ( v3_binop_1 @ C @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
                           => ( ( r1_tarski @ E @ F )
                             => ( ( E = k1_xboole_0 )
                                | ( ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ E @ D ) @ ( k7_setwiseo @ B @ A @ C @ F @ D ) )
                                  = ( k7_setwiseo @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(1421,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( k2_funct_4 @ ( k5_relat_1 @ A @ B ) )
            = ( k5_relat_1 @ ( k2_funct_4 @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_altcat_2) ).

thf(9272,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( k2_funct_4 @ ( k5_relat_1 @ A @ B ) )
            = ( k5_relat_1 @ ( k2_funct_4 @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421]) ).

thf(1077,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( r1_tarski @ ( k2_relat_1 @ ( k2_funct_4 @ A ) ) @ ( k2_relat_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_funct_4) ).

thf(7758,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( r1_tarski @ ( k2_relat_1 @ ( k2_funct_4 @ A ) ) @ ( k2_relat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).

thf(300,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
    <=> ( v2_funct_1 @ ( k10_finseq_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_finseq_3) ).

thf(4211,plain,
    ! [A: $i,B: $i] :
      ( ( ( A != B )
       => ( v2_funct_1 @ ( k10_finseq_1 @ A @ B ) ) )
      & ( ( v2_funct_1 @ ( k10_finseq_1 @ A @ B ) )
       => ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(1498,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( v1_realset1 @ A )
      <=> ? [B: $i] :
            ( ( m1_subset_1 @ B @ A )
            & ( A
              = ( k6_domain_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tex_2) ).

thf(9589,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( ( v1_realset1 @ A )
         => ? [B: $i] :
              ( ( m1_subset_1 @ B @ A )
              & ( A
                = ( k6_domain_1 @ A @ B ) ) ) )
        & ( ? [B: $i] :
              ( ( m1_subset_1 @ B @ A )
              & ( A
                = ( k6_domain_1 @ A @ B ) ) )
         => ( v1_realset1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498]) ).

thf(2005,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
           => ( r1_tarski @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_subset_1) ).

thf(12306,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
           => ( r1_tarski @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2005]) ).

thf(2586,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
         => ( ( k7_setfam_1 @ A @ B )
            = ( a_2_1_card_fil @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_card_fil) ).

thf(14900,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
         => ( ( k7_setfam_1 @ A @ B )
            = ( a_2_1_card_fil @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2586]) ).

thf(97,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( k1_relat_1 @ ( k5_relat_1 @ B @ A ) )
              = ( k1_relat_1 @ B ) )
           => ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_1) ).

thf(3184,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( k1_relat_1 @ ( k5_relat_1 @ B @ A ) )
              = ( k1_relat_1 @ B ) )
           => ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(1475,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k4_enumset1 @ A @ B @ C @ D @ E @ F )
      = ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k2_enumset1 @ C @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_enumset1) ).

thf(9501,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k4_enumset1 @ A @ B @ C @ D @ E @ F )
      = ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k2_enumset1 @ C @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1475]) ).

thf(881,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
      = ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_1) ).

thf(6860,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
      = ( k2_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(348,axiom,
    ! [A: $i] :
      ( ( v1_finset_1 @ A )
    <=> ? [B: $i] :
          ( ( v1_relat_1 @ B )
          & ( v1_funct_1 @ B )
          & ( v1_finseq_1 @ B )
          & ( A
            = ( k2_relat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_finseq_1) ).

thf(4475,plain,
    ! [A: $i] :
      ( ( ( v1_finset_1 @ A )
       => ? [B: $i] :
            ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B )
            & ( v1_finseq_1 @ B )
            & ( A
              = ( k2_relat_1 @ B ) ) ) )
      & ( ? [B: $i] :
            ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B )
            & ( v1_finseq_1 @ B )
            & ( A
              = ( k2_relat_1 @ B ) ) )
       => ( v1_finset_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(1496,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G )
      = ( k2_xboole_0 @ ( k2_enumset1 @ A @ B @ C @ D ) @ ( k1_enumset1 @ E @ F @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_enumset1) ).

thf(9584,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G )
      = ( k2_xboole_0 @ ( k2_enumset1 @ A @ B @ C @ D ) @ ( k1_enumset1 @ E @ F @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496]) ).

thf(1688,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ C @ A ) )
          | ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ C ) ) )
        & ~ ( r1_tarski @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_zfmisc_1) ).

thf(10523,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ C @ A ) )
          | ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ C ) ) )
        & ~ ( r1_tarski @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1688]) ).

thf(1516,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( k1_ens_1 @ A )
        = ( k3_tarski @ ( a_1_0_ens_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ens_1) ).

thf(9738,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( k1_ens_1 @ A )
        = ( k3_tarski @ ( a_1_0_ens_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516]) ).

thf(1296,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ? [C: $i] :
          ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
          & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
          & ! [D: $i] :
              ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
             => ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_realset1) ).

thf(8742,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ? [C: $i] :
          ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
          & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
          & ! [D: $i] :
              ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
             => ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).

thf(686,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ B ) )
     => ( ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) )
        & ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).

thf(5961,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ B ) )
     => ( ( v1_xboole_0 @ ( k5_relat_1 @ A @ B ) )
        & ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(951,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( r1_xboole_0 @ A @ B )
     => ( ( k3_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) )
        = ( k1_setfam_1 @ ( k3_setfam_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_setfam_1) ).

thf(7148,plain,
    ! [A: $i,B: $i] :
      ( ~ ( r1_xboole_0 @ A @ B )
     => ( ( k3_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) )
        = ( k1_setfam_1 @ ( k3_setfam_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(672,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( r2_hidden @ A @ ( k2_xboole_0 @ C @ D ) )
        & ( r2_hidden @ B @ ( k2_xboole_0 @ C @ D ) )
        & ~ ( ( r2_hidden @ A @ ( k4_xboole_0 @ C @ D ) )
            & ( r2_hidden @ B @ ( k4_xboole_0 @ C @ D ) ) )
        & ~ ( ( r2_hidden @ A @ D )
            & ( r2_hidden @ B @ D ) )
        & ~ ( ( r2_hidden @ A @ ( k4_xboole_0 @ C @ D ) )
            & ( r2_hidden @ B @ D ) )
        & ~ ( ( r2_hidden @ A @ D )
            & ( r2_hidden @ B @ ( k4_xboole_0 @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_latsum_1) ).

thf(5875,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( r2_hidden @ A @ ( k2_xboole_0 @ C @ D ) )
        & ( r2_hidden @ B @ ( k2_xboole_0 @ C @ D ) )
        & ~ ( ( r2_hidden @ A @ ( k4_xboole_0 @ C @ D ) )
            & ( r2_hidden @ B @ ( k4_xboole_0 @ C @ D ) ) )
        & ~ ( ( r2_hidden @ A @ D )
            & ( r2_hidden @ B @ D ) )
        & ~ ( ( r2_hidden @ A @ ( k4_xboole_0 @ C @ D ) )
            & ( r2_hidden @ B @ D ) )
        & ~ ( ( r2_hidden @ A @ D )
            & ( r2_hidden @ B @ ( k4_xboole_0 @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(642,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_realset1 @ C @ A @ B )
         => ( ( v1_funct_1 @ ( k1_realset1 @ B @ C ) )
            & ( v1_funct_2 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C )
            & ( m2_relset_1 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_realset1) ).

thf(5751,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_realset1 @ C @ A @ B )
         => ( ( v1_funct_1 @ ( k1_realset1 @ B @ C ) )
            & ( v1_funct_2 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C )
            & ( m2_relset_1 @ ( k1_realset1 @ B @ C ) @ ( k2_zfmisc_1 @ C @ C ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(708,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t154_relat_1) ).

thf(6064,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(596,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
         => ( ( ( k12_mcart_1 @ A @ B @ C @ D )
             != k1_xboole_0 )
           => ( ( ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ A @ ( k9_funct_3 @ A @ B ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
                = C )
              & ( ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ B @ ( k10_funct_3 @ A @ B ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
                = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_borsuk_1) ).

thf(5545,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
         => ( ( ( k12_mcart_1 @ A @ B @ C @ D )
             != k1_xboole_0 )
           => ( ( ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ A @ ( k9_funct_3 @ A @ B ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
                = C )
              & ( ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ B @ ( k10_funct_3 @ A @ B ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
                = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(1280,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( k7_relat_1 @ B @ A )
        = ( k3_xboole_0 @ B @ ( k2_zfmisc_1 @ A @ ( k2_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_relat_1) ).

thf(8668,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( k7_relat_1 @ B @ A )
        = ( k3_xboole_0 @ B @ ( k2_zfmisc_1 @ A @ ( k2_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).

thf(1860,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ! [D: $i,E: $i,F: $i] :
          ( ( ( g1_rlvect_1 @ A @ B @ C )
            = ( g1_rlvect_1 @ D @ E @ F ) )
         => ( ( A = D )
            & ( B = E )
            & ( C = F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_rlvect_1) ).

thf(11499,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ! [D: $i,E: $i,F: $i] :
          ( ( ( g1_rlvect_1 @ A @ B @ C )
            = ( g1_rlvect_1 @ D @ E @ F ) )
         => ( ( A = D )
            & ( B = E )
            & ( C = F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1860]) ).

thf(1325,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( k1_funct_4 @ k1_xboole_0 @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_4) ).

thf(8867,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( k1_funct_4 @ k1_xboole_0 @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).

thf(1157,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_xboole_1) ).

thf(8123,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).

thf(2224,axiom,
    ! [A: $i] : ( r1_tarski @ A @ ( k6_lattice5 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_lattice5) ).

thf(13440,plain,
    ! [A: $i] : ( r1_tarski @ A @ ( k6_lattice5 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2224]) ).

thf(1117,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
        & ( r1_tarski @ ( k4_xboole_0 @ B @ A ) @ C ) )
     => ( r1_tarski @ ( k5_xboole_0 @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_xboole_1) ).

thf(7952,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
        & ( r1_tarski @ ( k4_xboole_0 @ B @ A ) @ C ) )
     => ( r1_tarski @ ( k5_xboole_0 @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).

thf(390,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( ( ( k1_relat_1 @ A )
                        = ( k1_relat_1 @ B ) )
                      & ( ( k1_relat_1 @ D )
                        = ( k1_relat_1 @ C ) )
                      & ( ( k13_funct_3 @ A @ B )
                        = ( k13_funct_3 @ D @ C ) ) )
                   => ( ( A = D )
                      & ( B = C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_funct_3) ).

thf(4700,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( ( ( k1_relat_1 @ A )
                        = ( k1_relat_1 @ B ) )
                      & ( ( k1_relat_1 @ D )
                        = ( k1_relat_1 @ C ) )
                      & ( ( k13_funct_3 @ A @ B )
                        = ( k13_funct_3 @ D @ C ) ) )
                   => ( ( A = D )
                      & ( B = C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(1733,axiom,
    ! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_zfmisc_1) ).

thf(10779,plain,
    ! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1733]) ).

thf(1876,axiom,
    ! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).

thf(11597,plain,
    ! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1876]) ).

thf(1568,axiom,
    ! [A: $i] :
      ~ ( ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i] :
                  ( B
                 != ( k4_tarski @ C @ D ) ) )
        & ! [B: $i,C: $i] :
            ~ ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funct_4) ).

thf(9997,plain,
    ! [A: $i] :
      ~ ( ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i] :
                  ( B
                 != ( k4_tarski @ C @ D ) ) )
        & ! [B: $i,C: $i] :
            ~ ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1568]) ).

thf(1054,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( v1_relat_1 @ E )
     => ( ( ( ( r1_xboole_0 @ A @ B )
            & ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
            & ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
            & ( r2_hidden @ C @ A ) )
         => ( ~ ( r2_hidden @ C @ B )
            & ~ ( r2_hidden @ D @ A )
            & ( r2_hidden @ D @ B ) ) )
        & ( ( ( r1_xboole_0 @ A @ B )
            & ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
            & ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
            & ( r2_hidden @ D @ B ) )
         => ( ~ ( r2_hidden @ D @ A )
            & ~ ( r2_hidden @ C @ B )
            & ( r2_hidden @ C @ A ) ) )
        & ( ( ( r1_xboole_0 @ A @ B )
            & ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
            & ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
            & ( r2_hidden @ C @ B ) )
         => ( ~ ( r2_hidden @ C @ A )
            & ~ ( r2_hidden @ D @ B )
            & ( r2_hidden @ D @ A ) ) )
        & ( ( ( r1_xboole_0 @ A @ B )
            & ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
            & ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
            & ( r2_hidden @ D @ A ) )
         => ( ~ ( r2_hidden @ C @ A )
            & ~ ( r2_hidden @ D @ B )
            & ( r2_hidden @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_sysrel) ).

thf(7657,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( v1_relat_1 @ E )
     => ( ( ( ( r1_xboole_0 @ A @ B )
            & ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
            & ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
            & ( r2_hidden @ C @ A ) )
         => ( ~ ( r2_hidden @ C @ B )
            & ~ ( r2_hidden @ D @ A )
            & ( r2_hidden @ D @ B ) ) )
        & ( ( ( r1_xboole_0 @ A @ B )
            & ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
            & ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
            & ( r2_hidden @ D @ B ) )
         => ( ~ ( r2_hidden @ D @ A )
            & ~ ( r2_hidden @ C @ B )
            & ( r2_hidden @ C @ A ) ) )
        & ( ( ( r1_xboole_0 @ A @ B )
            & ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
            & ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
            & ( r2_hidden @ C @ B ) )
         => ( ~ ( r2_hidden @ C @ A )
            & ~ ( r2_hidden @ D @ B )
            & ( r2_hidden @ D @ A ) ) )
        & ( ( ( r1_xboole_0 @ A @ B )
            & ( r1_tarski @ E @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) )
            & ( r2_hidden @ ( k4_tarski @ C @ D ) @ E )
            & ( r2_hidden @ D @ A ) )
         => ( ~ ( r2_hidden @ C @ A )
            & ~ ( r2_hidden @ D @ B )
            & ( r2_hidden @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).

thf(1799,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m1_relset_1 @ E @ A @ B )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ C @ D )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( ( r4_nattra_1 @ A @ B @ C @ D @ E @ F )
      <=> ( E = F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r4_nattra_1) ).

thf(11159,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m1_relset_1 @ E @ A @ B )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ C @ D )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( ( ( r4_nattra_1 @ A @ B @ C @ D @ E @ F )
         => ( E = F ) )
        & ( ( E = F )
         => ( r4_nattra_1 @ A @ B @ C @ D @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1799]) ).

thf(2084,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( k7_relat_1 @ C @ E )
                        = ( k7_relat_1 @ D @ E ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ( ( r2_hidden @ F @ E )
                           => ( ( k8_funct_2 @ A @ B @ C @ F )
                              = ( k8_funct_2 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_fraenkel) ).

thf(12747,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( k7_relat_1 @ C @ E )
                        = ( k7_relat_1 @ D @ E ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ( ( r2_hidden @ F @ E )
                           => ( ( k8_funct_2 @ A @ B @ C @ F )
                              = ( k8_funct_2 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2084]) ).

thf(1020,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
      = ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_xboole_1) ).

thf(7533,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
      = ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(1794,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ A @ B )
            & ( m2_relset_1 @ E @ A @ B ) )
         => ! [F: $i] :
              ( ( ( v1_funct_1 @ F )
                & ( v1_funct_2 @ F @ A @ C )
                & ( m2_relset_1 @ F @ A @ C ) )
             => ! [G: $i] :
                  ( ( ( v1_funct_1 @ G )
                    & ( v1_funct_2 @ G @ A @ C )
                    & ( m2_relset_1 @ G @ A @ C ) )
                 => ( ( ( k13_funct_3 @ D @ F )
                      = ( k13_funct_3 @ E @ G ) )
                   => ( ( ( B = k1_xboole_0 )
                        & ( A != k1_xboole_0 ) )
                      | ( ( C = k1_xboole_0 )
                        & ( A != k1_xboole_0 ) )
                      | ( ( D = E )
                        & ( F = G ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_funct_3) ).

thf(11121,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ A @ B )
            & ( m2_relset_1 @ E @ A @ B ) )
         => ! [F: $i] :
              ( ( ( v1_funct_1 @ F )
                & ( v1_funct_2 @ F @ A @ C )
                & ( m2_relset_1 @ F @ A @ C ) )
             => ! [G: $i] :
                  ( ( ( v1_funct_1 @ G )
                    & ( v1_funct_2 @ G @ A @ C )
                    & ( m2_relset_1 @ G @ A @ C ) )
                 => ( ( ( k13_funct_3 @ D @ F )
                      = ( k13_funct_3 @ E @ G ) )
                   => ( ( ( B = k1_xboole_0 )
                        & ( A != k1_xboole_0 ) )
                      | ( ( C = k1_xboole_0 )
                        & ( A != k1_xboole_0 ) )
                      | ( ( D = E )
                        & ( F = G ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1794]) ).

thf(370,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( k1_relat_1 @ A )
                  = ( k1_relat_1 @ B ) )
               => ( ( k1_relat_1 @ ( k5_relat_1 @ C @ A ) )
                  = ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_funcop_1) ).

thf(4604,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( k1_relat_1 @ A )
                  = ( k1_relat_1 @ B ) )
               => ( ( k1_relat_1 @ ( k5_relat_1 @ C @ A ) )
                  = ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(1170,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( v1_relat_1 @ D )
     => ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ D @ ( k6_relat_1 @ C ) ) )
      <=> ( ( r2_hidden @ B @ C )
          & ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_relat_1) ).

thf(8170,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( v1_relat_1 @ D )
     => ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ D @ ( k6_relat_1 @ C ) ) )
         => ( ( r2_hidden @ B @ C )
            & ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) ) )
        & ( ( ( r2_hidden @ B @ C )
            & ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) )
         => ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ D @ ( k6_relat_1 @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).

thf(2424,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_realset1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( ~ ( v1_xboole_0 @ B )
              & ( v1_realset1 @ B ) )
           => ( ~ ( v1_xboole_0 @ B )
              & ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_tex_2) ).

thf(14162,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_realset1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( ~ ( v1_xboole_0 @ B )
              & ( v1_realset1 @ B ) )
           => ( ~ ( v1_xboole_0 @ B )
              & ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2424]) ).

thf(1099,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
     => ( ( k1_funct_1 @ ( k1_funct_3 @ ( k10_funct_3 @ B @ C ) ) @ A )
        = ( k2_funct_2 @ ( k2_zfmisc_1 @ B @ C ) @ C @ ( k10_funct_3 @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_borsuk_1) ).

thf(7849,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
     => ( ( k1_funct_1 @ ( k1_funct_3 @ ( k10_funct_3 @ B @ C ) ) @ A )
        = ( k2_funct_2 @ ( k2_zfmisc_1 @ B @ C ) @ C @ ( k10_funct_3 @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).

thf(554,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( k5_relat_1 @ ( k15_funct_3 @ B @ D ) @ ( k15_funct_3 @ A @ C ) )
                    = ( k15_funct_3 @ ( k5_relat_1 @ B @ A ) @ ( k5_relat_1 @ D @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_funct_3) ).

thf(5406,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( k5_relat_1 @ ( k15_funct_3 @ B @ D ) @ ( k15_funct_3 @ A @ C ) )
                    = ( k15_funct_3 @ ( k5_relat_1 @ B @ A ) @ ( k5_relat_1 @ D @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(1758,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m3_realset1 @ C @ A @ B )
         => ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_realset1) ).

thf(10943,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m3_realset1 @ C @ A @ B )
         => ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1758]) ).

thf(1936,axiom,
    ? [A: $i] :
      ( ( v1_funct_1 @ A )
      & ( v1_funct_2 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
      & ( m2_relset_1 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s4_funct_2 )
         => ( ( k8_funct_2 @ f1_s4_funct_2 @ f2_s4_funct_2 @ A @ B )
            = ( f3_s4_funct_2 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_funct_2) ).

thf(11897,plain,
    ? [A: $i] :
      ( ( v1_funct_1 @ A )
      & ( v1_funct_2 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
      & ( m2_relset_1 @ A @ f1_s4_funct_2 @ f2_s4_funct_2 )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s4_funct_2 )
         => ( ( k8_funct_2 @ f1_s4_funct_2 @ f2_s4_funct_2 @ A @ B )
            = ( f3_s4_funct_2 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1936]) ).

thf(50,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( B
            = ( k4_card_3 @ A ) )
        <=> ! [C: $i] :
              ( ( r2_hidden @ C @ B )
            <=> ? [D: $i] :
                  ( ( v1_relat_1 @ D )
                  & ( v1_funct_1 @ D )
                  & ( C = D )
                  & ( ( k1_relat_1 @ D )
                    = ( k1_relat_1 @ A ) )
                  & ! [E: $i] :
                      ( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
                     => ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_card_3) ).

thf(2910,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( B
              = ( k4_card_3 @ A ) )
           => ! [C: $i] :
                ( ( ( r2_hidden @ C @ B )
                 => ? [D: $i] :
                      ( ( v1_relat_1 @ D )
                      & ( v1_funct_1 @ D )
                      & ( C = D )
                      & ( ( k1_relat_1 @ D )
                        = ( k1_relat_1 @ A ) )
                      & ! [E: $i] :
                          ( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
                         => ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ A @ E ) ) ) ) )
                & ( ? [D: $i] :
                      ( ( v1_relat_1 @ D )
                      & ( v1_funct_1 @ D )
                      & ( C = D )
                      & ( ( k1_relat_1 @ D )
                        = ( k1_relat_1 @ A ) )
                      & ! [E: $i] :
                          ( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
                         => ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ A @ E ) ) ) )
                 => ( r2_hidden @ C @ B ) ) ) )
          & ( ! [C: $i] :
                ( ( ( r2_hidden @ C @ B )
                 => ? [D: $i] :
                      ( ( v1_relat_1 @ D )
                      & ( v1_funct_1 @ D )
                      & ( C = D )
                      & ( ( k1_relat_1 @ D )
                        = ( k1_relat_1 @ A ) )
                      & ! [E: $i] :
                          ( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
                         => ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ A @ E ) ) ) ) )
                & ( ? [D: $i] :
                      ( ( v1_relat_1 @ D )
                      & ( v1_funct_1 @ D )
                      & ( C = D )
                      & ( ( k1_relat_1 @ D )
                        = ( k1_relat_1 @ A ) )
                      & ! [E: $i] :
                          ( ( r2_hidden @ E @ ( k1_relat_1 @ A ) )
                         => ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ A @ E ) ) ) )
                 => ( r2_hidden @ C @ B ) ) )
           => ( B
              = ( k4_card_3 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(1084,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
           => ( r1_partfun1 @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t171_partfun1) ).

thf(7782,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
           => ( r1_partfun1 @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).

thf(1491,axiom,
    ( ( r2_hidden @ f2_s1_card_fil @ a_0_0_card_fil )
   => ( p1_s1_card_fil @ f2_s1_card_fil ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_card_fil) ).

thf(9571,plain,
    ( ( r2_hidden @ f2_s1_card_fil @ a_0_0_card_fil )
   => ( p1_s1_card_fil @ f2_s1_card_fil ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1491]) ).

thf(1279,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ~ ( ( A != k1_xboole_0 )
          & ( B != k1_xboole_0 )
          & ( C != k1_xboole_0 )
          & ( D != k1_xboole_0 )
          & ? [F: $i,G: $i,H: $i,I: $i] :
              ( ( E
                = ( k4_mcart_1 @ F @ G @ H @ I ) )
              & ~ ( ( ( k8_mcart_1 @ A @ B @ C @ D @ E )
                    = F )
                  & ( ( k9_mcart_1 @ A @ B @ C @ D @ E )
                    = G )
                  & ( ( k10_mcart_1 @ A @ B @ C @ D @ E )
                    = H )
                  & ( ( k11_mcart_1 @ A @ B @ C @ D @ E )
                    = I ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_mcart_1) ).

thf(8655,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ~ ( ( A != k1_xboole_0 )
          & ( B != k1_xboole_0 )
          & ( C != k1_xboole_0 )
          & ( D != k1_xboole_0 )
          & ? [F: $i,G: $i,H: $i,I: $i] :
              ( ( E
                = ( k4_mcart_1 @ F @ G @ H @ I ) )
              & ~ ( ( ( k8_mcart_1 @ A @ B @ C @ D @ E )
                    = F )
                  & ( ( k9_mcart_1 @ A @ B @ C @ D @ E )
                    = G )
                  & ( ( k10_mcart_1 @ A @ B @ C @ D @ E )
                    = H )
                  & ( ( k11_mcart_1 @ A @ B @ C @ D @ E )
                    = I ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).

thf(1004,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( k1_funct_4 @ A @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k1_funct_4) ).

thf(7471,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( k1_funct_4 @ A @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).

thf(125,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v2_binop_1 @ B @ A )
          <=> ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) )
                          = ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ B @ C @ D ) @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_binop_1) ).

thf(3303,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( v2_binop_1 @ B @ A )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) )
                            = ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ B @ C @ D ) @ E ) ) ) ) ) )
            & ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) )
                            = ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ B @ C @ D ) @ E ) ) ) ) )
             => ( v2_binop_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(2216,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_funcop_1 @ ( k1_tarski @ A ) @ B )
      = ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_4) ).

thf(13408,plain,
    ! [A: $i,B: $i] :
      ( ( k2_funcop_1 @ ( k1_tarski @ A ) @ B )
      = ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2216]) ).

thf(919,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k6_setfam_1 @ A @ B )
        = ( k1_setfam_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).

thf(7022,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k6_setfam_1 @ A @ B )
        = ( k1_setfam_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).

thf(1341,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                         => ! [G: $i] :
                              ( ( m2_finseq_1 @ G @ A )
                             => ( ( G
                                  = ( k12_finseq_1 @ A @ D ) )
                               => ( ( k4_funcop_1 @ F @ G @ E )
                                  = ( k12_finseq_1 @ C @ ( k2_binop_1 @ A @ B @ C @ F @ D @ E ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_finseq_2) ).

thf(8927,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                         => ! [G: $i] :
                              ( ( m2_finseq_1 @ G @ A )
                             => ( ( G
                                  = ( k12_finseq_1 @ A @ D ) )
                               => ( ( k4_funcop_1 @ F @ G @ E )
                                  = ( k12_finseq_1 @ C @ ( k2_binop_1 @ A @ B @ C @ F @ D @ E ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341]) ).

thf(1205,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_tarski @ B @ A )
           => ( ( k1_funct_4 @ A @ B )
              = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_lattice2) ).

thf(8302,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_tarski @ B @ A )
           => ( ( k1_funct_4 @ A @ B )
              = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).

thf(429,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_relat_1 @ B ) )
     => ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).

thf(4888,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_relat_1 @ B ) )
     => ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(1720,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( B != k1_xboole_0 )
       => ( ( k5_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
          = ( k3_subset_1 @ A @ ( k6_setfam_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_tops_2) ).

thf(10652,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( B != k1_xboole_0 )
       => ( ( k5_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
          = ( k3_subset_1 @ A @ ( k6_setfam_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1720]) ).

thf(1460,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_relat_1 @ B ) )
     => ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).

thf(9440,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_relat_1 @ B ) )
     => ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460]) ).

thf(760,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ! [D: $i] :
            ~ ( ( r2_hidden @ D @ B )
              & ( ( k3_funct_2 @ A @ B @ C @ ( k1_tarski @ D ) )
                = k1_xboole_0 ) )
      <=> ( ( k2_relat_1 @ C )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funct_2) ).

thf(6296,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ! [D: $i] :
              ~ ( ( r2_hidden @ D @ B )
                & ( ( k3_funct_2 @ A @ B @ C @ ( k1_tarski @ D ) )
                  = k1_xboole_0 ) )
         => ( ( k2_relat_1 @ C )
            = B ) )
        & ( ( ( k2_relat_1 @ C )
            = B )
         => ! [D: $i] :
              ~ ( ( r2_hidden @ D @ B )
                & ( ( k3_funct_2 @ A @ B @ C @ ( k1_tarski @ D ) )
                  = k1_xboole_0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(1026,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_pboole @ D @ ( k2_zfmisc_1 @ A @ A ) )
        & ( m1_pboole @ E @ ( k2_zfmisc_1 @ B @ B ) )
        & ( m1_functor0 @ F @ ( k2_zfmisc_1 @ A @ A ) @ ( k2_zfmisc_1 @ B @ B ) @ ( k16_funct_3 @ A @ A @ B @ B @ C @ C ) @ D @ E ) )
     => ( ( k2_functor0 @ A @ B @ C @ D @ E @ F )
        = ( k2_funct_4 @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_functor0) ).

thf(7550,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_pboole @ D @ ( k2_zfmisc_1 @ A @ A ) )
        & ( m1_pboole @ E @ ( k2_zfmisc_1 @ B @ B ) )
        & ( m1_functor0 @ F @ ( k2_zfmisc_1 @ A @ A ) @ ( k2_zfmisc_1 @ B @ B ) @ ( k16_funct_3 @ A @ A @ B @ B @ C @ C ) @ D @ E ) )
     => ( ( k2_functor0 @ A @ B @ C @ D @ E @ F )
        = ( k2_funct_4 @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(1682,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
        & ( v1_setfam_1 @ ( k1_tarski @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_setfam_1) ).

thf(10506,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
        & ( v1_setfam_1 @ ( k1_tarski @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1682]) ).

thf(1868,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ B @ C @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_enumset1) ).

thf(11550,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ B @ C @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1868]) ).

thf(1603,axiom,
    ~ ( v1_xboole_0 @ k1_qc_lang1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_qc_lang1) ).

thf(10139,plain,
    ~ ( v1_xboole_0 @ k1_qc_lang1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1603]) ).

thf(461,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_partfun1 @ A @ B )
          <=> ? [C: $i] :
                ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C )
                & ( r1_tarski @ A @ C )
                & ( r1_tarski @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_partfun1) ).

thf(5017,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( r1_partfun1 @ A @ B )
             => ? [C: $i] :
                  ( ( v1_relat_1 @ C )
                  & ( v1_funct_1 @ C )
                  & ( r1_tarski @ A @ C )
                  & ( r1_tarski @ B @ C ) ) )
            & ( ? [C: $i] :
                  ( ( v1_relat_1 @ C )
                  & ( v1_funct_1 @ C )
                  & ( r1_tarski @ A @ C )
                  & ( r1_tarski @ B @ C ) )
             => ( r1_partfun1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(1223,axiom,
    ! [A: $i] :
      ( ( v4_finsub_1 @ A )
    <=> ! [B: $i,C: $i] :
          ( ( ( r2_hidden @ B @ A )
            & ( r2_hidden @ C @ A ) )
         => ( ( r2_hidden @ ( k2_xboole_0 @ B @ C ) @ A )
            & ( r2_hidden @ ( k4_xboole_0 @ B @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_finsub_1) ).

thf(8382,plain,
    ! [A: $i] :
      ( ( ( v4_finsub_1 @ A )
       => ! [B: $i,C: $i] :
            ( ( ( r2_hidden @ B @ A )
              & ( r2_hidden @ C @ A ) )
           => ( ( r2_hidden @ ( k2_xboole_0 @ B @ C ) @ A )
              & ( r2_hidden @ ( k4_xboole_0 @ B @ C ) @ A ) ) ) )
      & ( ! [B: $i,C: $i] :
            ( ( ( r2_hidden @ B @ A )
              & ( r2_hidden @ C @ A ) )
           => ( ( r2_hidden @ ( k2_xboole_0 @ B @ C ) @ A )
              & ( r2_hidden @ ( k4_xboole_0 @ B @ C ) @ A ) ) )
       => ( v4_finsub_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).

thf(1802,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ A )
                & ( m2_relset_1 @ C @ A @ A ) )
             => ( ( m1_filter_1 @ C @ A @ B )
              <=> ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
                         => ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k8_funct_2 @ A @ A @ C @ D ) @ ( k8_funct_2 @ A @ A @ C @ E ) ) @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_filter_1) ).

thf(11170,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ A )
                & ( m2_relset_1 @ C @ A @ A ) )
             => ( ( ( m1_filter_1 @ C @ A @ B )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
                           => ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k8_funct_2 @ A @ A @ C @ D ) @ ( k8_funct_2 @ A @ A @ C @ E ) ) @ B ) ) ) ) )
                & ( ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( r2_hidden @ ( k1_domain_1 @ A @ A @ D @ E ) @ B )
                           => ( r2_hidden @ ( k1_domain_1 @ A @ A @ ( k8_funct_2 @ A @ A @ C @ D ) @ ( k8_funct_2 @ A @ A @ C @ E ) ) @ B ) ) ) )
                 => ( m1_filter_1 @ C @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1802]) ).

thf(851,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( k2_zfmisc_1 @ A @ B )
            = ( a_2_0_domain_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_domain_1) ).

thf(6684,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( k2_zfmisc_1 @ A @ B )
            = ( a_2_0_domain_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(727,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_relat_1) ).

thf(6139,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(1957,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(12029,plain,
    ! [A: $i] : ( r1_tarski @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1957]) ).

thf(628,axiom,
    ! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_xboole_1) ).

thf(5697,plain,
    ! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(2157,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ( ( ( E
                                = ( k1_realset1 @ C @ B ) )
                              & ( F
                                = ( k1_realset1 @ D @ B ) )
                              & ( r6_binop_1 @ A @ C @ D ) )
                           => ( r6_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_filter_2) ).

thf(13141,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ( ( ( E
                                = ( k1_realset1 @ C @ B ) )
                              & ( F
                                = ( k1_realset1 @ D @ B ) )
                              & ( r6_binop_1 @ A @ C @ D ) )
                           => ( r6_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2157]) ).

thf(2036,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ C @ A )
     => ( ( r1_tarski @ A @ B )
       => ( m2_relset_1 @ D @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_relset_1) ).

thf(12446,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ C @ A )
     => ( ( r1_tarski @ A @ B )
       => ( m2_relset_1 @ D @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2036]) ).

thf(2029,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_relset_1 @ C @ B @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
                  <=> ? [E: $i] :
                        ( ( m1_subset_1 @ E @ B )
                        & ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_relset_1) ).

thf(12425,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_relset_1 @ C @ B @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
                     => ? [E: $i] :
                          ( ( m1_subset_1 @ E @ B )
                          & ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) )
                    & ( ? [E: $i] :
                          ( ( m1_subset_1 @ E @ B )
                          & ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) )
                     => ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2029]) ).

thf(1896,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( v1_funct_1 @ ( k4_funcop_1 @ C @ D @ E ) )
                        & ( v1_funct_2 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B )
                        & ( m2_relset_1 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funcop_1) ).

thf(11672,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( v1_funct_1 @ ( k4_funcop_1 @ C @ D @ E ) )
                        & ( v1_funct_2 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B )
                        & ( m2_relset_1 @ ( k4_funcop_1 @ C @ D @ E ) @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1896]) ).

thf(1405,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( r1_tarski @ ( k5_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_relat_1) ).

thf(9209,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( r1_tarski @ ( k5_relat_1 @ A @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405]) ).

thf(2040,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).

thf(12474,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2040]) ).

thf(2464,axiom,
    ! [A: $i] :
      ( ( r2_hidden @ A @ a_0_2_domain_1 )
    <=> ? [B: $i,C: $i] :
          ( ( m1_subset_1 @ B @ f1_s9_domain_1 )
          & ( m1_subset_1 @ C @ f2_s9_domain_1 )
          & ( A
            = ( f4_s9_domain_1 @ B @ C ) )
          & ( p1_s9_domain_1 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_2_domain_1) ).

thf(14342,plain,
    ! [A: $i] :
      ( ( ( r2_hidden @ A @ a_0_2_domain_1 )
       => ? [B: $i,C: $i] :
            ( ( m1_subset_1 @ B @ f1_s9_domain_1 )
            & ( m1_subset_1 @ C @ f2_s9_domain_1 )
            & ( A
              = ( f4_s9_domain_1 @ B @ C ) )
            & ( p1_s9_domain_1 @ B @ C ) ) )
      & ( ? [B: $i,C: $i] :
            ( ( m1_subset_1 @ B @ f1_s9_domain_1 )
            & ( m1_subset_1 @ C @ f2_s9_domain_1 )
            & ( A
              = ( f4_s9_domain_1 @ B @ C ) )
            & ( p1_s9_domain_1 @ B @ C ) )
       => ( r2_hidden @ A @ a_0_2_domain_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2464]) ).

thf(1270,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).

thf(8613,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).

thf(257,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ( ( ( v1_binop_1 @ C @ B )
                  & ( v2_binop_1 @ C @ B )
                  & ( v3_binop_1 @ C @ B ) )
               => ! [D: $i] :
                    ( ( ( v1_funct_1 @ D )
                      & ( v1_funct_2 @ D @ A @ B )
                      & ( m2_relset_1 @ D @ A @ B ) )
                   => ! [E: $i] :
                        ( ( ( v1_funct_1 @ E )
                          & ( v1_funct_2 @ E @ A @ B )
                          & ( m2_relset_1 @ E @ A @ B ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k5_finsub_1 @ A ) )
                           => ! [G: $i] :
                                ( ( m1_subset_1 @ G @ ( k5_finsub_1 @ A ) )
                               => ( ( ( k2_funct_2 @ A @ B @ D @ F )
                                    = ( k2_funct_2 @ A @ B @ E @ G ) )
                                 => ( ( F = k1_xboole_0 )
                                    | ( ( k7_setwiseo @ A @ B @ C @ F @ D )
                                      = ( k7_setwiseo @ A @ B @ C @ G @ E ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_setwiseo) ).

thf(3995,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ( ( ( v1_binop_1 @ C @ B )
                  & ( v2_binop_1 @ C @ B )
                  & ( v3_binop_1 @ C @ B ) )
               => ! [D: $i] :
                    ( ( ( v1_funct_1 @ D )
                      & ( v1_funct_2 @ D @ A @ B )
                      & ( m2_relset_1 @ D @ A @ B ) )
                   => ! [E: $i] :
                        ( ( ( v1_funct_1 @ E )
                          & ( v1_funct_2 @ E @ A @ B )
                          & ( m2_relset_1 @ E @ A @ B ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k5_finsub_1 @ A ) )
                           => ! [G: $i] :
                                ( ( m1_subset_1 @ G @ ( k5_finsub_1 @ A ) )
                               => ( ( ( k2_funct_2 @ A @ B @ D @ F )
                                    = ( k2_funct_2 @ A @ B @ E @ G ) )
                                 => ( ( F = k1_xboole_0 )
                                    | ( ( k7_setwiseo @ A @ B @ C @ F @ D )
                                      = ( k7_setwiseo @ A @ B @ C @ G @ E ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(1830,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ C @ A )
                        & ( m2_relset_1 @ E @ C @ A ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ D @ B )
                            & ( m2_relset_1 @ F @ D @ B ) )
                         => ! [G: $i] :
                              ( ( ~ ( v1_xboole_0 @ G )
                                & ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) ) )
                             => ! [H: $i] :
                                  ( ( ~ ( v1_xboole_0 @ H )
                                    & ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) ) )
                                 => ( ( k1_nattra_1 @ ( k2_zfmisc_1 @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k9_cat_2 @ C @ D @ A @ B @ E @ F ) @ ( k12_mcart_1 @ C @ D @ G @ H ) )
                                    = ( k9_cat_2 @ G @ H @ A @ B @ ( k1_nattra_1 @ C @ A @ E @ G ) @ ( k1_nattra_1 @ D @ B @ F @ H ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_nattra_1) ).

thf(11324,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ C @ A )
                        & ( m2_relset_1 @ E @ C @ A ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ D @ B )
                            & ( m2_relset_1 @ F @ D @ B ) )
                         => ! [G: $i] :
                              ( ( ~ ( v1_xboole_0 @ G )
                                & ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) ) )
                             => ! [H: $i] :
                                  ( ( ~ ( v1_xboole_0 @ H )
                                    & ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) ) )
                                 => ( ( k1_nattra_1 @ ( k2_zfmisc_1 @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k9_cat_2 @ C @ D @ A @ B @ E @ F ) @ ( k12_mcart_1 @ C @ D @ G @ H ) )
                                    = ( k9_cat_2 @ G @ H @ A @ B @ ( k1_nattra_1 @ C @ A @ E @ G ) @ ( k1_nattra_1 @ D @ B @ F @ H ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1830]) ).

thf(824,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i,D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ D @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [E: $i] :
              ( ( ( v1_funct_1 @ E )
                & ( v1_funct_2 @ E @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) )
                & ( m2_relset_1 @ E @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) ) )
             => ( ( ( ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ ( k1_setwiseo @ B ) )
                    = ( k1_setwiseo @ C ) )
                  & ! [F: $i] :
                      ( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
                     => ! [G: $i] :
                          ( ( m1_subset_1 @ G @ ( k5_finsub_1 @ B ) )
                         => ( ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ ( k5_setwiseo @ B @ F @ G ) )
                            = ( k5_setwiseo @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ F ) @ ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ G ) ) ) ) ) )
               => ! [F: $i] :
                    ( ( m1_subset_1 @ F @ ( k5_finsub_1 @ A ) )
                   => ( ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ ( k10_setwiseo @ A @ B @ F @ D ) )
                      = ( k10_setwiseo @ A @ C @ F @ ( k7_funct_2 @ A @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ D @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_setwiseo) ).

thf(6571,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i,D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ D @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [E: $i] :
              ( ( ( v1_funct_1 @ E )
                & ( v1_funct_2 @ E @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) )
                & ( m2_relset_1 @ E @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) ) )
             => ( ( ( ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ ( k1_setwiseo @ B ) )
                    = ( k1_setwiseo @ C ) )
                  & ! [F: $i] :
                      ( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
                     => ! [G: $i] :
                          ( ( m1_subset_1 @ G @ ( k5_finsub_1 @ B ) )
                         => ( ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ ( k5_setwiseo @ B @ F @ G ) )
                            = ( k5_setwiseo @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ F ) @ ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ G ) ) ) ) ) )
               => ! [F: $i] :
                    ( ( m1_subset_1 @ F @ ( k5_finsub_1 @ A ) )
                   => ( ( k8_funct_2 @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ E @ ( k10_setwiseo @ A @ B @ F @ D ) )
                      = ( k10_setwiseo @ A @ C @ F @ ( k7_funct_2 @ A @ ( k5_finsub_1 @ B ) @ ( k5_finsub_1 @ C ) @ D @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(1782,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_finset_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).

thf(11069,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_finset_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1782]) ).

thf(557,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D )
        & ( r1_xboole_0 @ B @ D ) )
     => ( r1_xboole_0 @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_xboole_1) ).

thf(5416,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D )
        & ( r1_xboole_0 @ B @ D ) )
     => ( r1_xboole_0 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(1608,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k3_setwiseo @ A @ B @ C )
        = ( k2_tarski @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_setwiseo) ).

thf(10165,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k3_setwiseo @ A @ B @ C )
        = ( k2_tarski @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1608]) ).

thf(277,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( ( v2_funct_1 @ B )
          & ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) )
       => ( ( A
            = ( k1_funct_1 @ B @ ( k1_funct_1 @ ( k2_funct_1 @ B ) @ A ) ) )
          & ( A
            = ( k1_funct_1 @ ( k5_relat_1 @ ( k2_funct_1 @ B ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).

thf(4076,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( ( v2_funct_1 @ B )
          & ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) )
       => ( ( A
            = ( k1_funct_1 @ B @ ( k1_funct_1 @ ( k2_funct_1 @ B ) @ A ) ) )
          & ( A
            = ( k1_funct_1 @ ( k5_relat_1 @ ( k2_funct_1 @ B ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(337,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r2_hidden @ A @ ( k4_card_3 @ B ) )
          <=> ( ( ( k1_relat_1 @ A )
                = ( k1_relat_1 @ B ) )
              & ! [C: $i] :
                  ( ( r2_hidden @ C @ ( k1_relat_1 @ B ) )
                 => ( r2_hidden @ ( k1_funct_1 @ A @ C ) @ ( k1_funct_1 @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_card_3) ).

thf(4370,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( r2_hidden @ A @ ( k4_card_3 @ B ) )
             => ( ( ( k1_relat_1 @ A )
                  = ( k1_relat_1 @ B ) )
                & ! [C: $i] :
                    ( ( r2_hidden @ C @ ( k1_relat_1 @ B ) )
                   => ( r2_hidden @ ( k1_funct_1 @ A @ C ) @ ( k1_funct_1 @ B @ C ) ) ) ) )
            & ( ( ( ( k1_relat_1 @ A )
                  = ( k1_relat_1 @ B ) )
                & ! [C: $i] :
                    ( ( r2_hidden @ C @ ( k1_relat_1 @ B ) )
                   => ( r2_hidden @ ( k1_funct_1 @ A @ C ) @ ( k1_funct_1 @ B @ C ) ) ) )
             => ( r2_hidden @ A @ ( k4_card_3 @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(31,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
       => ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_relset_1) ).

thf(2737,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
       => ( m2_relset_1 @ B @ A @ ( k2_relat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(1759,axiom,
    ( ~ ( v1_xboole_0 @ k4_urysohn1 )
    & ( v1_membered @ k4_urysohn1 )
    & ( v2_membered @ k4_urysohn1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_urysohn1) ).

thf(10947,plain,
    ( ~ ( v1_xboole_0 @ k4_urysohn1 )
    & ( v1_membered @ k4_urysohn1 )
    & ( v2_membered @ k4_urysohn1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1759]) ).

thf(762,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( k15_funct_3 @ A @ B )
            = ( k13_funct_3 @ ( k5_relat_1 @ ( k9_funct_3 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ A ) @ ( k5_relat_1 @ ( k10_funct_3 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_funct_3) ).

thf(6307,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( k15_funct_3 @ A @ B )
            = ( k13_funct_3 @ ( k5_relat_1 @ ( k9_funct_3 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ A ) @ ( k5_relat_1 @ ( k10_funct_3 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(887,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ C @ A ) )
      = ( k3_xboole_0 @ ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ C ) ) @ ( k2_xboole_0 @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_xboole_1) ).

thf(6884,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ C @ A ) )
      = ( k3_xboole_0 @ ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ C ) ) @ ( k2_xboole_0 @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).

thf(1317,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ ( k15_funct_3 @ A @ A ) )
       => ( v2_funct_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_functor0) ).

thf(8842,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ ( k15_funct_3 @ A @ A ) )
       => ( v2_funct_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).

thf(862,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i,D: $i,E: $i] :
          ( ( k3_multop_1 @ A @ B @ C @ D @ E )
          = ( k1_funct_1 @ A @ ( k4_mcart_1 @ B @ C @ D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_multop_1) ).

thf(6741,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i,D: $i,E: $i] :
          ( ( k3_multop_1 @ A @ B @ C @ D @ E )
          = ( k1_funct_1 @ A @ ( k4_mcart_1 @ B @ C @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(1976,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v4_orders_3 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_orders_3) ).

thf(12127,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v4_orders_3 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1976]) ).

thf(152,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v1_relat_1 @ ( k1_relat_1 @ A ) )
              & ( r1_tarski @ ( k2_funct_4 @ A ) @ ( k2_funct_4 @ B ) ) )
           => ( r1_tarski @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_yellow20) ).

thf(3418,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v1_relat_1 @ ( k1_relat_1 @ A ) )
              & ( r1_tarski @ ( k2_funct_4 @ A ) @ ( k2_funct_4 @ B ) ) )
           => ( r1_tarski @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(1447,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k4_xboole_0 @ ( k1_funct_5 @ A ) @ ( k1_funct_5 @ B ) ) @ ( k1_funct_5 @ ( k4_xboole_0 @ A @ B ) ) )
      & ( r1_tarski @ ( k4_xboole_0 @ ( k2_funct_5 @ A ) @ ( k2_funct_5 @ B ) ) @ ( k2_funct_5 @ ( k4_xboole_0 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_5) ).

thf(9384,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k4_xboole_0 @ ( k1_funct_5 @ A ) @ ( k1_funct_5 @ B ) ) @ ( k1_funct_5 @ ( k4_xboole_0 @ A @ B ) ) )
      & ( r1_tarski @ ( k4_xboole_0 @ ( k2_funct_5 @ A ) @ ( k2_funct_5 @ B ) ) @ ( k2_funct_5 @ ( k4_xboole_0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447]) ).

thf(439,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( r1_tarski @ ( k1_funct_5 @ ( k9_relat_1 @ ( k15_funct_3 @ A @ B ) @ C ) ) @ ( k9_relat_1 @ A @ ( k1_funct_5 @ C ) ) )
              & ( r1_tarski @ ( k2_funct_5 @ ( k9_relat_1 @ ( k15_funct_3 @ A @ B ) @ C ) ) @ ( k9_relat_1 @ B @ ( k2_funct_5 @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_waybel20) ).

thf(4925,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( r1_tarski @ ( k1_funct_5 @ ( k9_relat_1 @ ( k15_funct_3 @ A @ B ) @ C ) ) @ ( k9_relat_1 @ A @ ( k1_funct_5 @ C ) ) )
              & ( r1_tarski @ ( k2_funct_5 @ ( k9_relat_1 @ ( k15_funct_3 @ A @ B ) @ C ) ) @ ( k9_relat_1 @ B @ ( k2_funct_5 @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(2142,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) )
            = ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_subset_1) ).

thf(13059,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) )
            = ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2142]) ).

thf(714,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] : ( m1_fraenkel @ ( k1_funct_2 @ B @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_fraenkel) ).

thf(6092,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] : ( m1_fraenkel @ ( k1_funct_2 @ B @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(198,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( ( k1_relat_1 @ A )
          = k1_xboole_0 )
      <=> ( ( k2_relat_1 @ A )
          = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).

thf(3679,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( ( ( k1_relat_1 @ A )
            = k1_xboole_0 )
         => ( ( k2_relat_1 @ A )
            = k1_xboole_0 ) )
        & ( ( ( k2_relat_1 @ A )
            = k1_xboole_0 )
         => ( ( k1_relat_1 @ A )
            = k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(1866,axiom,
    ! [A: $i] :
    ? [B: $i] : ( m1_finseq_2 @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_finseq_2) ).

thf(11545,plain,
    ! [A: $i] :
    ? [B: $i] : ( m1_finseq_2 @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1866]) ).

thf(1471,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
           => ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_funct_1) ).

thf(9488,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
           => ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471]) ).

thf(1984,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( k5_ens_1 @ A @ B )
            = ( k1_domain_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ B ) ) @ ( k1_domain_1 @ A @ A @ B @ B ) @ ( k6_partfun1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_ens_1) ).

thf(12159,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( k5_ens_1 @ A @ B )
            = ( k1_domain_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ B ) ) @ ( k1_domain_1 @ A @ A @ B @ B ) @ ( k6_partfun1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1984]) ).

thf(2314,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
        & ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ D ) ) )
     => ( ( r2_hidden @ A @ ( a_6_0_domain_1 @ B @ C @ D @ E @ F @ G ) )
      <=> ? [H: $i,I: $i,J: $i] :
            ( ( m1_subset_1 @ H @ B )
            & ( m1_subset_1 @ I @ C )
            & ( m1_subset_1 @ J @ D )
            & ( A
              = ( k4_domain_1 @ B @ C @ D @ H @ I @ J ) )
            & ( r2_hidden @ H @ E )
            & ( r2_hidden @ I @ F )
            & ( r2_hidden @ J @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_6_0_domain_1) ).

thf(13746,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
        & ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ D ) ) )
     => ( ( ( r2_hidden @ A @ ( a_6_0_domain_1 @ B @ C @ D @ E @ F @ G ) )
         => ? [H: $i,I: $i,J: $i] :
              ( ( m1_subset_1 @ H @ B )
              & ( m1_subset_1 @ I @ C )
              & ( m1_subset_1 @ J @ D )
              & ( A
                = ( k4_domain_1 @ B @ C @ D @ H @ I @ J ) )
              & ( r2_hidden @ H @ E )
              & ( r2_hidden @ I @ F )
              & ( r2_hidden @ J @ G ) ) )
        & ( ? [H: $i,I: $i,J: $i] :
              ( ( m1_subset_1 @ H @ B )
              & ( m1_subset_1 @ I @ C )
              & ( m1_subset_1 @ J @ D )
              & ( A
                = ( k4_domain_1 @ B @ C @ D @ H @ I @ J ) )
              & ( r2_hidden @ H @ E )
              & ( r2_hidden @ I @ F )
              & ( r2_hidden @ J @ G ) )
         => ( r2_hidden @ A @ ( a_6_0_domain_1 @ B @ C @ D @ E @ F @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2314]) ).

thf(876,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( A = B )
          <=> ! [C: $i,D: $i] :
                ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
              <=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).

thf(6820,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( ( A = B )
             => ! [C: $i,D: $i] :
                  ( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
                   => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
                  & ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
                   => ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) )
            & ( ! [C: $i,D: $i] :
                  ( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
                   => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
                  & ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
                   => ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) )
             => ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(2352,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ A ) )
     => ( m1_subset_1 @ ( k3_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relset_2) ).

thf(13892,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ A ) )
     => ( m1_subset_1 @ ( k3_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2352]) ).

thf(2287,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( v1_finset_1 @ ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_finset_1) ).

thf(13649,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( v1_finset_1 @ ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2287]) ).

thf(186,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ( ( ( ( k1_relat_1 @ C )
                = B )
              & ( ( k1_relat_1 @ D )
                = B )
              & ( r2_hidden @ A @ B ) )
           => ( ( k1_funct_1 @ ( k13_funct_3 @ C @ D ) @ A )
              = ( k4_tarski @ ( k1_funct_1 @ C @ A ) @ ( k1_funct_1 @ D @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_funct_3) ).

thf(3610,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ( ( ( ( k1_relat_1 @ C )
                = B )
              & ( ( k1_relat_1 @ D )
                = B )
              & ( r2_hidden @ A @ B ) )
           => ( ( k1_funct_1 @ ( k13_funct_3 @ C @ D ) @ A )
              = ( k4_tarski @ ( k1_funct_1 @ C @ A ) @ ( k1_funct_1 @ D @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(1049,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ! [B: $i] :
            ( ( m1_subset_1 @ B @ A )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ( ( r2_hidden @ ( k5_xboole_0 @ B @ C ) @ A )
                  & ( r2_hidden @ ( k2_xboole_0 @ B @ C ) @ A ) ) ) )
       => ( v4_finsub_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finsub_1) ).

thf(7640,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ! [B: $i] :
            ( ( m1_subset_1 @ B @ A )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ( ( r2_hidden @ ( k5_xboole_0 @ B @ C ) @ A )
                  & ( r2_hidden @ ( k2_xboole_0 @ B @ C ) @ A ) ) ) )
       => ( v4_finsub_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).

thf(384,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( v2_funct_1 @ B ) )
           => ( ( k2_funct_1 @ ( k15_funct_3 @ A @ B ) )
              = ( k15_funct_3 @ ( k2_funct_1 @ A ) @ ( k2_funct_1 @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_functor0) ).

thf(4661,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( v2_funct_1 @ B ) )
           => ( ( k2_funct_1 @ ( k15_funct_3 @ A @ B ) )
              = ( k15_funct_3 @ ( k2_funct_1 @ A ) @ ( k2_funct_1 @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(1634,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(10278,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1634]) ).

thf(1600,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( r1_tarski @ ( k7_setfam_1 @ A @ B ) @ ( k7_setfam_1 @ A @ C ) )
           => ( r1_tarski @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_setfam_1) ).

thf(10133,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( r1_tarski @ ( k7_setfam_1 @ A @ B ) @ ( k7_setfam_1 @ A @ C ) )
           => ( r1_tarski @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1600]) ).

thf(1374,axiom,
    ! [A: $i,B: $i] :
      ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
      = ( k1_tarski @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_zfmisc_1) ).

thf(9036,plain,
    ! [A: $i,B: $i] :
      ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
      = ( k1_tarski @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).

thf(2260,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) )
     => ( ( A = k1_xboole_0 )
        | ( v1_finset_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finset_1) ).

thf(13547,plain,
    ! [A: $i,B: $i] :
      ( ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) )
     => ( ( A = k1_xboole_0 )
        | ( v1_finset_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2260]) ).

thf(2183,axiom,
    ! [A: $i] :
      ( ( k2_subset_1 @ A )
      = ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_subset_1) ).

thf(13260,plain,
    ! [A: $i] :
      ( ( k2_subset_1 @ A )
      = ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2183]) ).

thf(435,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_partfun1 @ A @ B )
          <=> ( r1_tarski @ A @ ( k1_funct_4 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_funct_4) ).

thf(4915,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( r1_partfun1 @ A @ B )
             => ( r1_tarski @ A @ ( k1_funct_4 @ A @ B ) ) )
            & ( ( r1_tarski @ A @ ( k1_funct_4 @ A @ B ) )
             => ( r1_partfun1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(2052,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i,D: $i] :
          ( ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
            | ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) )
         => ( r1_tarski @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_zfmisc_1) ).

thf(12542,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i,D: $i] :
          ( ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
            | ( r1_tarski @ ( k2_zfmisc_1 @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) )
         => ( r1_tarski @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2052]) ).

thf(1212,axiom,
    ! [A: $i] :
      ( ( k9_relat_1 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_relat_1) ).

thf(8343,plain,
    ! [A: $i] :
      ( ( k9_relat_1 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).

thf(2033,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ( ( ( r3_binop_1 @ A @ C @ E )
                              & ( r3_binop_1 @ B @ D @ F ) )
                          <=> ( r3_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_filter_1) ).

thf(12437,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ( ( ( ( r3_binop_1 @ A @ C @ E )
                                & ( r3_binop_1 @ B @ D @ F ) )
                             => ( r3_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) )
                            & ( ( r3_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) )
                             => ( ( r3_binop_1 @ A @ C @ E )
                                & ( r3_binop_1 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2033]) ).

thf(2221,axiom,
    ( ( v1_funct_1 @ k33_binop_2 )
    & ( v1_funct_2 @ k33_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( m2_relset_1 @ k33_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k33_binop_2) ).

thf(13423,plain,
    ( ( v1_funct_1 @ k33_binop_2 )
    & ( v1_funct_2 @ k33_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( m2_relset_1 @ k33_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2221]) ).

thf(2154,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
       => ( ( ( B = k1_xboole_0 )
            & ( A != k1_xboole_0 ) )
          | ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ C )
            & ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_2) ).

thf(13126,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
       => ( ( ( B = k1_xboole_0 )
            & ( A != k1_xboole_0 ) )
          | ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ C )
            & ( m2_relset_1 @ D @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2154]) ).

thf(2058,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ( r2_hidden @ k1_xboole_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_classes2) ).

thf(12561,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ( r2_hidden @ k1_xboole_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2058]) ).

thf(710,axiom,
    ( ~ ( v1_xboole_0 @ k1_numbers )
    & ( v1_membered @ k1_numbers )
    & ( v2_membered @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_membered) ).

thf(6079,plain,
    ( ~ ( v1_xboole_0 @ k1_numbers )
    & ( v1_membered @ k1_numbers )
    & ( v2_membered @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(1199,axiom,
    k5_numbers != k1_numbers,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_numbers) ).

thf(8265,plain,
    k5_numbers != k1_numbers,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).

thf(1065,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( k3_funcop_1 @ A @ B @ C )
                = ( k5_relat_1 @ ( k13_funct_3 @ B @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_funcop_1) ).

thf(7703,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( k3_funcop_1 @ A @ B @ C )
                = ( k5_relat_1 @ ( k13_funct_3 @ B @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).

thf(250,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( k1_xboole_0
     != ( k11_finseq_1 @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_finseq_3) ).

thf(3972,plain,
    ! [A: $i,B: $i,C: $i] :
      ( k1_xboole_0
     != ( k11_finseq_1 @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(2467,axiom,
    ! [A: $i] :
      ( ( v1_fraenkel @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( v1_fraenkel @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_altcat_1) ).

thf(14357,plain,
    ! [A: $i] :
      ( ( v1_fraenkel @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( v1_fraenkel @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2467]) ).

thf(2388,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k7_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).

thf(14032,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k7_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2388]) ).

thf(2197,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m2_finseq_1 @ B @ A )
         => ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k4_finseq_1 @ B ) @ A )
            & ( m2_relset_1 @ B @ ( k4_finseq_1 @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finseq_2) ).

thf(13301,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m2_finseq_1 @ B @ A )
         => ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k4_finseq_1 @ B ) @ A )
            & ( m2_relset_1 @ B @ ( k4_finseq_1 @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2197]) ).

thf(1361,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k4_enumset1 @ A @ B @ C @ D @ E @ F )
      = ( k2_xboole_0 @ ( k2_enumset1 @ A @ B @ C @ D ) @ ( k2_tarski @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_enumset1) ).

thf(8994,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k4_enumset1 @ A @ B @ C @ D @ E @ F )
      = ( k2_xboole_0 @ ( k2_enumset1 @ A @ B @ C @ D ) @ ( k2_tarski @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).

thf(2561,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_realset1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( ~ ( v1_xboole_0 @ B )
              & ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) )
           => ( ~ ( v1_xboole_0 @ B )
              & ( v1_realset1 @ B )
              & ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_tex_2) ).

thf(14766,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_realset1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( ~ ( v1_xboole_0 @ B )
              & ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) )
           => ( ~ ( v1_xboole_0 @ B )
              & ( v1_realset1 @ B )
              & ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2561]) ).

thf(1765,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k1_finsub_1 @ A @ B @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k1_finsub_1) ).

thf(10975,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k1_finsub_1 @ A @ B @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1765]) ).

thf(1919,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
        <=> ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
            & ~ ( r2_hidden @ k1_xboole_0 @ B )
            & ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                   => ( ( ( ( r2_hidden @ C @ B )
                          & ( r2_hidden @ D @ B ) )
                       => ( r2_hidden @ ( k5_subset_1 @ A @ C @ D ) @ B ) )
                      & ( ( ( r2_hidden @ C @ B )
                          & ( r1_tarski @ C @ D ) )
                       => ( r2_hidden @ D @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_card_fil) ).

thf(11766,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( m1_card_fil @ B @ A )
           => ( ~ ( v1_xboole_0 @ B )
              & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
              & ~ ( r2_hidden @ k1_xboole_0 @ B )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                     => ( ( ( ( r2_hidden @ C @ B )
                            & ( r2_hidden @ D @ B ) )
                         => ( r2_hidden @ ( k5_subset_1 @ A @ C @ D ) @ B ) )
                        & ( ( ( r2_hidden @ C @ B )
                            & ( r1_tarski @ C @ D ) )
                         => ( r2_hidden @ D @ B ) ) ) ) ) ) )
          & ( ( ~ ( v1_xboole_0 @ B )
              & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
              & ~ ( r2_hidden @ k1_xboole_0 @ B )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                     => ( ( ( ( r2_hidden @ C @ B )
                            & ( r2_hidden @ D @ B ) )
                         => ( r2_hidden @ ( k5_subset_1 @ A @ C @ D ) @ B ) )
                        & ( ( ( r2_hidden @ C @ B )
                            & ( r1_tarski @ C @ D ) )
                         => ( r2_hidden @ D @ B ) ) ) ) ) )
           => ( m1_card_fil @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1919]) ).

thf(1453,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( k2_relat_1 @ C )
          = k1_xboole_0 )
       => ( ( v1_funct_1 @ C )
          & ( m2_relset_1 @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_partfun1) ).

thf(9412,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( k2_relat_1 @ C )
          = k1_xboole_0 )
       => ( ( v1_funct_1 @ C )
          & ( m2_relset_1 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453]) ).

thf(1240,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( k5_relat_1 @ ( k3_funcop_1 @ D @ B @ C ) @ A )
                    = ( k3_funcop_1 @ ( k5_relat_1 @ D @ A ) @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_funcop_1) ).

thf(8476,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( k5_relat_1 @ ( k3_funcop_1 @ D @ B @ C ) @ A )
                    = ( k3_funcop_1 @ ( k5_relat_1 @ D @ A ) @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).

thf(1095,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_finset_1 @ A )
     => ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_finset_1) ).

thf(7827,plain,
    ! [A: $i,B: $i] :
      ( ( v1_finset_1 @ A )
     => ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).

thf(2047,axiom,
    ! [A: $i] :
      ~ ( ( v1_finset_1 @ A )
        & ( A != k1_xboole_0 )
        & ( v6_ordinal1 @ A )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ( ( r2_hidden @ C @ A )
                 => ( r1_tarski @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_finset_1) ).

thf(12510,plain,
    ! [A: $i] :
      ~ ( ( v1_finset_1 @ A )
        & ( A != k1_xboole_0 )
        & ( v6_ordinal1 @ A )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ( ( r2_hidden @ C @ A )
                 => ( r1_tarski @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2047]) ).

thf(755,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( ~ ( r1_xboole_0 @ A @ B )
          & ! [C: $i] :
              ~ ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) ) )
      & ~ ( ? [C: $i] : ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) )
          & ( r1_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).

thf(6264,plain,
    ! [A: $i,B: $i] :
      ( ~ ( ~ ( r1_xboole_0 @ A @ B )
          & ! [C: $i] :
              ~ ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) ) )
      & ~ ( ? [C: $i] : ( r2_hidden @ C @ ( k3_xboole_0 @ A @ B ) )
          & ( r1_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(1774,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_funct_1 @ ( k10_funct_3 @ A @ B ) )
      & ( v1_funct_2 @ ( k10_funct_3 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ B )
      & ( m2_relset_1 @ ( k10_funct_3 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_funct_3) ).

thf(11037,plain,
    ! [A: $i,B: $i] :
      ( ( v1_funct_1 @ ( k10_funct_3 @ A @ B ) )
      & ( v1_funct_2 @ ( k10_funct_3 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ B )
      & ( m2_relset_1 @ ( k10_funct_3 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1774]) ).

thf(1332,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k1_funct_2 @ C @ A ) @ ( k1_funct_2 @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funct_5) ).

thf(8888,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k1_funct_2 @ C @ A ) @ ( k1_funct_2 @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).

thf(1558,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
    <=> ( m1_relset_1 @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

thf(9949,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m2_relset_1 @ C @ A @ B )
       => ( m1_relset_1 @ C @ A @ B ) )
      & ( ( m1_relset_1 @ C @ A @ B )
       => ( m2_relset_1 @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1558]) ).

thf(453,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ ( k5_xboole_0 @ B @ C ) )
    <=> ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
        & ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_xboole_1) ).

thf(4989,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ ( k5_xboole_0 @ B @ C ) )
       => ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
          & ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) ) )
      & ( ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
          & ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) ) )
       => ( r1_tarski @ A @ ( k5_xboole_0 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(2267,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
     => ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
        = ( k1_tarski @ k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t176_partfun1) ).

thf(13572,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
     => ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
        = ( k1_tarski @ k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2267]) ).

thf(468,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( ( r1_xboole_0 @ A @ B )
          & ( r1_tarski @ C @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) ) )
       => ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_sysrel) ).

thf(5044,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( ( r1_xboole_0 @ A @ B )
          & ( r1_tarski @ C @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) ) )
       => ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(544,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) )
      = ( k1_tarski @ ( k3_mcart_1 @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_mcart_1) ).

thf(5349,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) )
      = ( k1_tarski @ ( k3_mcart_1 @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(1125,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( k5_relat_1 @ ( k13_funct_3 @ B @ D ) @ ( k15_funct_3 @ A @ C ) )
                    = ( k13_funct_3 @ ( k5_relat_1 @ B @ A ) @ ( k5_relat_1 @ D @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_funct_3) ).

thf(7994,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( k5_relat_1 @ ( k13_funct_3 @ B @ D ) @ ( k15_funct_3 @ A @ C ) )
                    = ( k13_funct_3 @ ( k5_relat_1 @ B @ A ) @ ( k5_relat_1 @ D @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).

thf(521,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
       => ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_relat_1) ).

thf(5266,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
       => ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(1874,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( k6_enumset1 @ A @ A @ B @ C @ D @ E @ F @ G )
      = ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_enumset1) ).

thf(11587,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( k6_enumset1 @ A @ A @ B @ C @ D @ E @ F @ G )
      = ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1874]) ).

thf(1372,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
             => ( ( ( k4_ens_1 @ A @ B )
                  = ( k3_ens_1 @ A @ C ) )
               => ( ( k6_ens_1 @ A @ B @ C )
                  = ( k4_tarski @ ( k1_domain_1 @ A @ A @ ( k3_ens_1 @ A @ B ) @ ( k4_ens_1 @ A @ C ) ) @ ( k5_relat_1 @ ( k2_mcart_1 @ B ) @ ( k2_mcart_1 @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_ens_1) ).

thf(9031,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
             => ( ( ( k4_ens_1 @ A @ B )
                  = ( k3_ens_1 @ A @ C ) )
               => ( ( k6_ens_1 @ A @ B @ C )
                  = ( k4_tarski @ ( k1_domain_1 @ A @ A @ ( k3_ens_1 @ A @ B ) @ ( k4_ens_1 @ A @ C ) ) @ ( k5_relat_1 @ ( k2_mcart_1 @ B ) @ ( k2_mcart_1 @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).

thf(2367,axiom,
    ! [A: $i] :
      ( ( r2_hidden @ A @ a_0_32_fraenkel )
    <=> ? [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s17_fraenkel )
          & ( A
            = ( f3_s17_fraenkel @ B ) )
          & ( r2_hidden @ ( f3_s17_fraenkel @ B ) @ f2_s17_fraenkel )
          & ( p1_s17_fraenkel @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_32_fraenkel) ).

thf(13949,plain,
    ! [A: $i] :
      ( ( ( r2_hidden @ A @ a_0_32_fraenkel )
       => ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s17_fraenkel )
            & ( A
              = ( f3_s17_fraenkel @ B ) )
            & ( r2_hidden @ ( f3_s17_fraenkel @ B ) @ f2_s17_fraenkel )
            & ( p1_s17_fraenkel @ B ) ) )
      & ( ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s17_fraenkel )
            & ( A
              = ( f3_s17_fraenkel @ B ) )
            & ( r2_hidden @ ( f3_s17_fraenkel @ B ) @ f2_s17_fraenkel )
            & ( p1_s17_fraenkel @ B ) )
       => ( r2_hidden @ A @ a_0_32_fraenkel ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2367]) ).

thf(685,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
     => ( ( ( k4_relset_1 @ k1_xboole_0 @ A @ B )
          = k1_xboole_0 )
        & ( ( k2_relat_1 @ B )
          = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_partfun1) ).

thf(5956,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
     => ( ( ( k4_relset_1 @ k1_xboole_0 @ A @ B )
          = k1_xboole_0 )
        & ( ( k2_relat_1 @ B )
          = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(955,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ B @ A )
     => ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).

thf(7161,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ B @ A )
     => ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).

thf(1321,axiom,
    ( ( k1_setfam_1 @ k1_xboole_0 )
    = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_setfam_1) ).

thf(8856,plain,
    ( ( k1_setfam_1 @ k1_xboole_0 )
    = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321]) ).

thf(912,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k3_tarski @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_zfmisc_1) ).

thf(6990,plain,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k3_tarski @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).

thf(2404,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( r2_hidden @ A @ ( a_1_5_domain_1 @ B ) )
      <=> ? [C: $i] :
            ( ( m1_subset_1 @ C @ B )
            & ( A = C )
            & ( p1_s6_domain_1 @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_5_domain_1) ).

thf(14075,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( ( r2_hidden @ A @ ( a_1_5_domain_1 @ B ) )
         => ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A = C )
              & ( p1_s6_domain_1 @ C ) ) )
        & ( ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A = C )
              & ( p1_s6_domain_1 @ C ) )
         => ( r2_hidden @ A @ ( a_1_5_domain_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2404]) ).

thf(1856,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ A @ C )
       => ( ( k2_partfun1 @ A @ B @ D @ C )
          = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_2) ).

thf(11471,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ A @ C )
       => ( ( k2_partfun1 @ A @ B @ D @ C )
          = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1856]) ).

thf(2101,axiom,
    ! [A: $i] :
      ( ( v2_setfam_1 @ A )
    <=> ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ~ ( r2_hidden @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_setfam_1) ).

thf(12809,plain,
    ! [A: $i] :
      ( ( ( v2_setfam_1 @ A )
       => ! [B: $i] :
            ( ~ ( v1_xboole_0 @ B )
           => ~ ( r2_hidden @ B @ A ) ) )
      & ( ! [B: $i] :
            ( ~ ( v1_xboole_0 @ B )
           => ~ ( r2_hidden @ B @ A ) )
       => ( v2_setfam_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2101]) ).

thf(2513,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ~ ( v1_xboole_0 @ ( k2_classes2 @ A @ B ) )
        & ( m1_subset_1 @ ( k2_classes2 @ A @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_classes2) ).

thf(14605,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ~ ( v1_xboole_0 @ ( k2_classes2 @ A @ B ) )
        & ( m1_subset_1 @ ( k2_classes2 @ A @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2513]) ).

thf(1292,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k5_xboole_0 @ B @ C ) )
    <=> ~ ( ( r2_hidden @ A @ B )
        <=> ( r2_hidden @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_0) ).

thf(8724,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ ( k5_xboole_0 @ B @ C ) )
       => ~ ( ( ( r2_hidden @ A @ B )
             => ( r2_hidden @ A @ C ) )
            & ( ( r2_hidden @ A @ C )
             => ( r2_hidden @ A @ B ) ) ) )
      & ( ~ ( ( ( r2_hidden @ A @ B )
             => ( r2_hidden @ A @ C ) )
            & ( ( r2_hidden @ A @ C )
             => ( r2_hidden @ A @ B ) ) )
       => ( r2_hidden @ A @ ( k5_xboole_0 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).

thf(548,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ( ( r1_partfun1 @ B @ C )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_funct_2) ).

thf(5366,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ( ( r1_partfun1 @ B @ C )
           => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(108,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( ( k2_relat_1 @ B )
                = ( k1_relat_1 @ A ) )
              & ( ( k5_relat_1 @ B @ A )
                = ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
           => ( B
              = ( k2_funct_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_1) ).

thf(3233,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( ( k2_relat_1 @ B )
                = ( k1_relat_1 @ A ) )
              & ( ( k5_relat_1 @ B @ A )
                = ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
           => ( B
              = ( k2_funct_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(930,axiom,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m2_finseq_2 @ D @ B @ ( k4_finseq_2 @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ C )
                        & ( m2_relset_1 @ E @ B @ C ) )
                     => ( m2_finseq_2 @ ( k1_partfun1 @ k5_numbers @ B @ B @ C @ D @ E ) @ C @ ( k4_finseq_2 @ A @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t133_finseq_2) ).

thf(7084,plain,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m2_finseq_2 @ D @ B @ ( k4_finseq_2 @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ C )
                        & ( m2_relset_1 @ E @ B @ C ) )
                     => ( m2_finseq_2 @ ( k1_partfun1 @ k5_numbers @ B @ B @ C @ D @ E ) @ C @ ( k4_finseq_2 @ A @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

thf(142,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_relat_1 @ E )
        & ( v1_funct_1 @ E ) )
     => ! [F: $i] :
          ( ( ( v1_relat_1 @ F )
            & ( v1_funct_1 @ F ) )
         => ( ( r2_hidden @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) @ ( k1_relat_1 @ ( k3_funct_4 @ E @ F ) ) )
           => ( ( k1_funct_1 @ ( k3_funct_4 @ E @ F ) @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
              = ( k4_tarski @ ( k1_funct_1 @ E @ ( k4_tarski @ A @ C ) ) @ ( k1_funct_1 @ F @ ( k4_tarski @ B @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_funct_4) ).

thf(3371,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_relat_1 @ E )
        & ( v1_funct_1 @ E ) )
     => ! [F: $i] :
          ( ( ( v1_relat_1 @ F )
            & ( v1_funct_1 @ F ) )
         => ( ( r2_hidden @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) @ ( k1_relat_1 @ ( k3_funct_4 @ E @ F ) ) )
           => ( ( k1_funct_1 @ ( k3_funct_4 @ E @ F ) @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
              = ( k4_tarski @ ( k1_funct_1 @ E @ ( k4_tarski @ A @ C ) ) @ ( k1_funct_1 @ F @ ( k4_tarski @ B @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(572,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_eqrel_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ A ) @ B )
             => ( C
                = ( k3_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ ( k6_domain_1 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_borsuk_1) ).

thf(5470,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_eqrel_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ A ) @ B )
             => ( C
                = ( k3_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ ( k6_domain_1 @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(895,axiom,
    ! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_sysrel) ).

thf(6915,plain,
    ! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(1771,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
             => ( ! [E: $i] :
                    ( ( m1_subset_1 @ E @ A )
                   => ( ( r2_hidden @ E @ B )
                    <=> ( ( r2_hidden @ E @ C )
                        | ( r2_hidden @ E @ D ) ) ) )
               => ( B
                  = ( k4_subset_1 @ A @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_subset_1) ).

thf(11003,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
             => ( ! [E: $i] :
                    ( ( m1_subset_1 @ E @ A )
                   => ( ( ( r2_hidden @ E @ B )
                       => ( ( r2_hidden @ E @ C )
                          | ( r2_hidden @ E @ D ) ) )
                      & ( ( ( r2_hidden @ E @ C )
                          | ( r2_hidden @ E @ D ) )
                       => ( r2_hidden @ E @ B ) ) ) )
               => ( B
                  = ( k4_subset_1 @ A @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1771]) ).

thf(485,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ! [D: $i] :
          ( ( v1_relat_1 @ D )
         => ( ( ( r1_tarski @ C @ D )
              & ( r1_tarski @ A @ B ) )
           => ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_relat_1) ).

thf(5102,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ! [D: $i] :
          ( ( v1_relat_1 @ D )
         => ( ( ( r1_tarski @ C @ D )
              & ( r1_tarski @ A @ B ) )
           => ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(416,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
       => ( ( k9_relat_1 @ B @ ( k1_tarski @ A ) )
          = ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).

thf(4821,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
       => ( ( k9_relat_1 @ B @ ( k1_tarski @ A ) )
          = ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(1939,axiom,
    ( k5_urysohn1
    = ( k4_subset_1 @ k1_numbers @ ( k4_subset_1 @ k1_numbers @ k1_urysohn1 @ k4_urysohn1 ) @ k2_urysohn1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_urysohn1) ).

thf(11908,plain,
    ( k5_urysohn1
    = ( k4_subset_1 @ k1_numbers @ ( k4_subset_1 @ k1_numbers @ k1_urysohn1 @ k4_urysohn1 ) @ k2_urysohn1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1939]) ).

thf(2345,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

thf(13860,plain,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2345]) ).

thf(1965,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ D )
        & ( r2_hidden @ D @ E )
        & ( r2_hidden @ E @ F )
        & ( r2_hidden @ F @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_ordinal1) ).

thf(12058,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ D )
        & ( r2_hidden @ D @ E )
        & ( r2_hidden @ E @ F )
        & ( r2_hidden @ F @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1965]) ).

thf(834,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
      = ( k2_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_zfmisc_1) ).

thf(6620,plain,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
      = ( k2_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(826,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_zfmisc_1) ).

thf(6582,plain,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).

thf(1119,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( k9_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
        = ( k2_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t153_relat_1) ).

thf(7957,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( k9_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
        = ( k2_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).

thf(1285,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ( ( v2_binop_1 @ C @ B )
                           => ( ( k6_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) @ E )
                              = ( k6_funcop_1 @ B @ A @ C @ D @ ( k8_funcop_1 @ B @ A @ C @ F @ E ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_funcop_1) ).

thf(8683,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ( ( v2_binop_1 @ C @ B )
                           => ( ( k6_funcop_1 @ B @ A @ C @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) @ E )
                              = ( k6_funcop_1 @ B @ A @ C @ D @ ( k8_funcop_1 @ B @ A @ C @ F @ E ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).

thf(2181,axiom,
    ! [A: $i] :
      ( ( k2_enumset1 @ A @ A @ A @ A )
      = ( k1_tarski @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_enumset1) ).

thf(13254,plain,
    ! [A: $i] :
      ( ( k2_enumset1 @ A @ A @ A @ A )
      = ( k1_tarski @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2181]) ).

thf(837,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i,D: $i] :
              ( ( ( r1_tarski @ C @ D )
                & ( ( k7_relat_1 @ A @ D )
                  = ( k7_relat_1 @ B @ D ) ) )
             => ( ( k7_relat_1 @ A @ C )
                = ( k7_relat_1 @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t188_relat_1) ).

thf(6629,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i,D: $i] :
              ( ( ( r1_tarski @ C @ D )
                & ( ( k7_relat_1 @ A @ D )
                  = ( k7_relat_1 @ B @ D ) ) )
             => ( ( k7_relat_1 @ A @ C )
                = ( k7_relat_1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(990,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ! [F: $i] :
          ( ( r2_hidden @ F @ A )
        <=> ? [G: $i,H: $i,I: $i,J: $i] :
              ( ( r2_hidden @ G @ B )
              & ( r2_hidden @ H @ C )
              & ( r2_hidden @ I @ D )
              & ( r2_hidden @ J @ E )
              & ( F
                = ( k4_mcart_1 @ G @ H @ I @ J ) ) ) )
     => ( A
        = ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_mcart_1) ).

thf(7361,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ! [F: $i] :
          ( ( ( r2_hidden @ F @ A )
           => ? [G: $i,H: $i,I: $i,J: $i] :
                ( ( r2_hidden @ G @ B )
                & ( r2_hidden @ H @ C )
                & ( r2_hidden @ I @ D )
                & ( r2_hidden @ J @ E )
                & ( F
                  = ( k4_mcart_1 @ G @ H @ I @ J ) ) ) )
          & ( ? [G: $i,H: $i,I: $i,J: $i] :
                ( ( r2_hidden @ G @ B )
                & ( r2_hidden @ H @ C )
                & ( r2_hidden @ I @ D )
                & ( r2_hidden @ J @ E )
                & ( F
                  = ( k4_mcart_1 @ G @ H @ I @ J ) ) )
           => ( r2_hidden @ F @ A ) ) )
     => ( A
        = ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(233,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
     => ( ( A
         != ( k1_mcart_1 @ A ) )
        & ( A
         != ( k2_mcart_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_mcart_1) ).

thf(3894,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
     => ( ( A
         != ( k1_mcart_1 @ A ) )
        & ( A
         != ( k2_mcart_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(2463,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( ~ ( v1_xboole_0 @ C )
                & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
             => ! [D: $i] :
                  ( ( ~ ( v1_xboole_0 @ D )
                    & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
                 => ( ( C = D )
                   => ( ( k6_funct_3 @ A @ C )
                      = ( k7_funct_2 @ D @ B @ A @ ( k6_funct_3 @ B @ D ) @ ( k6_funct_3 @ A @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_functor1) ).

thf(14338,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( ~ ( v1_xboole_0 @ C )
                & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
             => ! [D: $i] :
                  ( ( ~ ( v1_xboole_0 @ D )
                    & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
                 => ( ( C = D )
                   => ( ( k6_funct_3 @ A @ C )
                      = ( k7_funct_2 @ D @ B @ A @ ( k6_funct_3 @ B @ D ) @ ( k6_funct_3 @ A @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2463]) ).

thf(401,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( C
          = ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
       => ( ( ( k1_relat_1 @ C )
            = ( k1_tarski @ A ) )
          & ( ( k2_relat_1 @ C )
            = ( k1_tarski @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relat_1) ).

thf(4740,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( C
          = ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
       => ( ( ( k1_relat_1 @ C )
            = ( k1_tarski @ A ) )
          & ( ( k2_relat_1 @ C )
            = ( k1_tarski @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(782,axiom,
    ! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_xboole_1) ).

thf(6402,plain,
    ! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(1846,axiom,
    ! [A: $i] :
      ( ( v1_finset_1 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ~ ( ( B != k1_xboole_0 )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ B )
                    & ! [D: $i] :
                        ( ( ( r2_hidden @ D @ B )
                          & ( r1_tarski @ C @ D ) )
                       => ( D = C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finset_1) ).

thf(11420,plain,
    ! [A: $i] :
      ( ( v1_finset_1 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ~ ( ( B != k1_xboole_0 )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ B )
                    & ! [D: $i] :
                        ( ( ( r2_hidden @ D @ B )
                          & ( r1_tarski @ C @ D ) )
                       => ( D = C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1846]) ).

thf(273,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
     => ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
        & ( r2_hidden @ ( k2_mcart_1 @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_mcart_1) ).

thf(4063,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
     => ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
        & ( r2_hidden @ ( k2_mcart_1 @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(2568,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( r1_filter_2 @ A @ B @ C )
              <=> ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ( ( r2_hidden @ D @ B )
                    <=> ( r2_hidden @ D @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_filter_2) ).

thf(14789,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( ( r1_filter_2 @ A @ B @ C )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ( ( ( r2_hidden @ D @ B )
                         => ( r2_hidden @ D @ C ) )
                        & ( ( r2_hidden @ D @ C )
                         => ( r2_hidden @ D @ B ) ) ) ) )
                & ( ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ( ( ( r2_hidden @ D @ B )
                         => ( r2_hidden @ D @ C ) )
                        & ( ( r2_hidden @ D @ C )
                         => ( r2_hidden @ D @ B ) ) ) )
                 => ( r1_filter_2 @ A @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2568]) ).

thf(630,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i,D: $i] :
              ( ( ( ( k7_relat_1 @ A @ C )
                  = ( k7_relat_1 @ B @ C ) )
                & ( ( k7_relat_1 @ A @ D )
                  = ( k7_relat_1 @ B @ D ) ) )
             => ( ( k7_relat_1 @ A @ ( k2_xboole_0 @ C @ D ) )
                = ( k7_relat_1 @ B @ ( k2_xboole_0 @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t185_relat_1) ).

thf(5702,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i,D: $i] :
              ( ( ( ( k7_relat_1 @ A @ C )
                  = ( k7_relat_1 @ B @ C ) )
                & ( ( k7_relat_1 @ A @ D )
                  = ( k7_relat_1 @ B @ D ) ) )
             => ( ( k7_relat_1 @ A @ ( k2_xboole_0 @ C @ D ) )
                = ( k7_relat_1 @ B @ ( k2_xboole_0 @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(252,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ ( k1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_relat_1) ).

thf(3980,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( r1_tarski @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) @ ( k1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(532,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k3_xboole_0 @ A @ ( k1_tarski @ B ) )
        = ( k1_tarski @ B ) )
     => ( r2_hidden @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_zfmisc_1) ).

thf(5302,plain,
    ! [A: $i,B: $i] :
      ( ( ( k3_xboole_0 @ A @ ( k1_tarski @ B ) )
        = ( k1_tarski @ B ) )
     => ( r2_hidden @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(1872,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_enumset1 @ A @ B @ C )
      = ( k1_enumset1 @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_enumset1) ).

thf(11570,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_enumset1 @ A @ B @ C )
      = ( k1_enumset1 @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1872]) ).

thf(2572,axiom,
    ! [A: $i] :
      ( ( m2_relset_1 @ A @ f1_s2_pua2mss1 @ f2_s2_pua2mss1 )
     => ! [B: $i] :
          ( ( m2_relset_1 @ B @ f1_s2_pua2mss1 @ f2_s2_pua2mss1 )
         => ( ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ f1_s2_pua2mss1 )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ f2_s2_pua2mss1 )
                     => ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
                      <=> ( p1_s2_pua2mss1 @ C @ D ) ) ) )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ f1_s2_pua2mss1 )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ f2_s2_pua2mss1 )
                     => ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
                      <=> ( p1_s2_pua2mss1 @ C @ D ) ) ) ) )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_pua2mss1) ).

thf(14804,plain,
    ! [A: $i] :
      ( ( m2_relset_1 @ A @ f1_s2_pua2mss1 @ f2_s2_pua2mss1 )
     => ! [B: $i] :
          ( ( m2_relset_1 @ B @ f1_s2_pua2mss1 @ f2_s2_pua2mss1 )
         => ( ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ f1_s2_pua2mss1 )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ f2_s2_pua2mss1 )
                     => ( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
                         => ( p1_s2_pua2mss1 @ C @ D ) )
                        & ( ( p1_s2_pua2mss1 @ C @ D )
                         => ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) ) )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ f1_s2_pua2mss1 )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ f2_s2_pua2mss1 )
                     => ( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
                         => ( p1_s2_pua2mss1 @ C @ D ) )
                        & ( ( p1_s2_pua2mss1 @ C @ D )
                         => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) ) ) )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2572]) ).

thf(1643,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( v1_finset_1 @ ( k2_enumset1 @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_finset_1) ).

thf(10330,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( v1_finset_1 @ ( k2_enumset1 @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1643]) ).

thf(579,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ B @ A )
            & ( m2_relset_1 @ D @ B @ A ) )
         => ( ( ( ( k2_relat_1 @ C )
                = B )
              & ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
                = ( k6_partfun1 @ A ) )
              & ( v2_funct_1 @ C ) )
           => ( ( A = k1_xboole_0 )
              | ( B = k1_xboole_0 )
              | ( D
                = ( k2_funct_1 @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_funct_2) ).

thf(5492,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ B @ A )
            & ( m2_relset_1 @ D @ B @ A ) )
         => ( ( ( ( k2_relat_1 @ C )
                = B )
              & ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
                = ( k6_partfun1 @ A ) )
              & ( v2_funct_1 @ C ) )
           => ( ( A = k1_xboole_0 )
              | ( B = k1_xboole_0 )
              | ( D
                = ( k2_funct_1 @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(1097,axiom,
    ! [A: $i,B: $i] :
      ( ( v2_membered @ A )
     => ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
        & ( v2_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc30_membered) ).

thf(7842,plain,
    ! [A: $i,B: $i] :
      ( ( v2_membered @ A )
     => ( ( v1_membered @ ( k3_xboole_0 @ B @ A ) )
        & ( v2_membered @ ( k3_xboole_0 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).

thf(2191,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).

thf(13282,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2191]) ).

thf(570,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ B @ A ) ) ) @ ( k1_zfmisc_1 @ ( k5_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_zfmisc_1) ).

thf(5465,plain,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ B @ A ) ) ) @ ( k1_zfmisc_1 @ ( k5_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(1676,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k5_setfam_1 @ A @ B )
        = ( k3_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).

thf(10490,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k5_setfam_1 @ A @ B )
        = ( k3_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1676]) ).

thf(2013,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ D ) )
    <=> ( ( A = C )
        & ( r2_hidden @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).

thf(12340,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ D ) )
       => ( ( A = C )
          & ( r2_hidden @ B @ D ) ) )
      & ( ( ( A = C )
          & ( r2_hidden @ B @ D ) )
       => ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2013]) ).

thf(1742,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
             => ( ! [E: $i] :
                    ( ( m1_subset_1 @ E @ A )
                   => ( ( r2_hidden @ E @ B )
                    <=> ~ ( ( r2_hidden @ E @ C )
                        <=> ( r2_hidden @ E @ D ) ) ) )
               => ( B
                  = ( k7_subset_1 @ A @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_subset_1) ).

thf(10826,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
             => ( ! [E: $i] :
                    ( ( m1_subset_1 @ E @ A )
                   => ( ( ( r2_hidden @ E @ B )
                       => ~ ( ( ( r2_hidden @ E @ C )
                             => ( r2_hidden @ E @ D ) )
                            & ( ( r2_hidden @ E @ D )
                             => ( r2_hidden @ E @ C ) ) ) )
                      & ( ~ ( ( ( r2_hidden @ E @ C )
                             => ( r2_hidden @ E @ D ) )
                            & ( ( r2_hidden @ E @ D )
                             => ( r2_hidden @ E @ C ) ) )
                       => ( r2_hidden @ E @ B ) ) ) )
               => ( B
                  = ( k7_subset_1 @ A @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1742]) ).

thf(1278,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ! [B: $i] :
            ( ( m1_subset_1 @ B @ A )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ( ( r2_hidden @ ( k5_xboole_0 @ B @ C ) @ A )
                  & ( r2_hidden @ ( k4_xboole_0 @ B @ C ) @ A ) ) ) )
       => ( v4_finsub_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finsub_1) ).

thf(8651,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ! [B: $i] :
            ( ( m1_subset_1 @ B @ A )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ( ( r2_hidden @ ( k5_xboole_0 @ B @ C ) @ A )
                  & ( r2_hidden @ ( k4_xboole_0 @ B @ C ) @ A ) ) ) )
       => ( v4_finsub_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).

thf(879,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v4_monoid_0 @ B @ A )
          <=> ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ? [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                        & ( ( k2_binop_1 @ A @ A @ A @ B @ C @ E )
                          = D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_monoid_0) ).

thf(6848,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( v4_monoid_0 @ B @ A )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ? [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                          & ( ( k2_binop_1 @ A @ A @ A @ B @ C @ E )
                            = D ) ) ) ) )
            & ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ? [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                          & ( ( k2_binop_1 @ A @ A @ A @ B @ C @ E )
                            = D ) ) ) )
             => ( v4_monoid_0 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).

thf(2592,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( m1_subset_1 @ ( k1_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relset_2) ).

thf(14926,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( m1_subset_1 @ ( k1_relset_2 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2592]) ).

thf(2457,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k5_subset_1 @ A @ B @ C )
                = ( a_3_1_domain_1 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_domain_1) ).

thf(14317,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k5_subset_1 @ A @ B @ C )
                = ( a_3_1_domain_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2457]) ).

thf(1345,axiom,
    ! [A: $i,B: $i] :
      ( ( k1_funct_2 @ A @ B )
      = ( k4_card_3 @ ( k2_funcop_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_card_3) ).

thf(8942,plain,
    ! [A: $i,B: $i] :
      ( ( k1_funct_2 @ A @ B )
      = ( k4_card_3 @ ( k2_funcop_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).

thf(1526,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( m1_realset1 @ C @ A @ B )
          <=> ! [D: $i] :
                ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
               => ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_realset1) ).

thf(9790,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( ( m1_realset1 @ C @ A @ B )
             => ! [D: $i] :
                  ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
                 => ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) )
            & ( ! [D: $i] :
                  ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
                 => ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) )
             => ( m1_realset1 @ C @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1526]) ).

thf(403,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) ) )
     => ( ( B
          = ( k2_funcop_1 @ ( k1_tarski @ ( k4_tarski @ A @ A ) ) @ A ) )
        & ( v1_setwiseo @ B @ ( k1_tarski @ A ) )
        & ( v1_binop_1 @ B @ ( k1_tarski @ A ) )
        & ( v2_binop_1 @ B @ ( k1_tarski @ A ) )
        & ( v3_binop_1 @ B @ ( k1_tarski @ A ) )
        & ( v5_monoid_0 @ B @ ( k1_tarski @ A ) )
        & ( v8_monoid_0 @ B @ ( k1_tarski @ A ) )
        & ( v9_monoid_0 @ B @ ( k1_tarski @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_monoid_0) ).

thf(4757,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) ) )
     => ( ( B
          = ( k2_funcop_1 @ ( k1_tarski @ ( k4_tarski @ A @ A ) ) @ A ) )
        & ( v1_setwiseo @ B @ ( k1_tarski @ A ) )
        & ( v1_binop_1 @ B @ ( k1_tarski @ A ) )
        & ( v2_binop_1 @ B @ ( k1_tarski @ A ) )
        & ( v3_binop_1 @ B @ ( k1_tarski @ A ) )
        & ( v5_monoid_0 @ B @ ( k1_tarski @ A ) )
        & ( v8_monoid_0 @ B @ ( k1_tarski @ A ) )
        & ( v9_monoid_0 @ B @ ( k1_tarski @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(1798,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
            & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
         => ( ! [F: $i,G: $i] :
                ( ( ( r2_hidden @ F @ A )
                  & ( r2_hidden @ G @ B ) )
               => ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
                  = ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) )
           => ( D = E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_funct_2) ).

thf(11152,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
            & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
         => ( ! [F: $i,G: $i] :
                ( ( ( r2_hidden @ F @ A )
                  & ( r2_hidden @ G @ B ) )
               => ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
                  = ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) )
           => ( D = E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1798]) ).

thf(444,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( r2_hidden @ A @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
        & ! [F: $i,G: $i,H: $i,I: $i] :
            ~ ( ( r2_hidden @ F @ B )
              & ( r2_hidden @ G @ C )
              & ( r2_hidden @ H @ D )
              & ( r2_hidden @ I @ E )
              & ( A
                = ( k4_mcart_1 @ F @ G @ H @ I ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_mcart_1) ).

thf(4947,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( r2_hidden @ A @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
        & ! [F: $i,G: $i,H: $i,I: $i] :
            ~ ( ( r2_hidden @ F @ B )
              & ( r2_hidden @ G @ C )
              & ( r2_hidden @ H @ D )
              & ( r2_hidden @ I @ E )
              & ( A
                = ( k4_mcart_1 @ F @ G @ H @ I ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(171,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k2_funct_4 @ B ) ) )
          & ! [C: $i,D: $i] :
              ( A
             != ( k4_tarski @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funct_6) ).

thf(3556,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ~ ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k2_funct_4 @ B ) ) )
          & ! [C: $i,D: $i] :
              ( A
             != ( k4_tarski @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(2256,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ( ( A != k1_xboole_0 )
                   => ( m1_subset_1 @ ( k2_enumset1 @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_subset_1) ).

thf(13536,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ( ( A != k1_xboole_0 )
                   => ( m1_subset_1 @ ( k2_enumset1 @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2256]) ).

thf(2361,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ( r3_zfrefle1 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_zfrefle1) ).

thf(13924,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ( r3_zfrefle1 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2361]) ).

thf(176,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( k5_funcop_1 @ A @ B @ C )
            = ( k5_relat_1 @ ( k13_funct_3 @ ( k2_funcop_1 @ ( k1_relat_1 @ C ) @ B ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funcop_1) ).

thf(3578,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( k5_funcop_1 @ A @ B @ C )
            = ( k5_relat_1 @ ( k13_funct_3 @ ( k2_funcop_1 @ ( k1_relat_1 @ C ) @ B ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(2330,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] : ( m2_card_fil @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_card_fil) ).

thf(13799,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] : ( m2_card_fil @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2330]) ).

thf(1818,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( C
              = ( k1_cantor_1 @ A @ B ) )
          <=> ! [D: $i] :
                ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
               => ( ( r2_hidden @ D @ C )
                <=> ? [E: $i] :
                      ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
                      & ( r1_tarski @ E @ B )
                      & ( D
                        = ( k5_setfam_1 @ A @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_cantor_1) ).

thf(11249,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( ( C
                = ( k1_cantor_1 @ A @ B ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                 => ( ( ( r2_hidden @ D @ C )
                     => ? [E: $i] :
                          ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
                          & ( r1_tarski @ E @ B )
                          & ( D
                            = ( k5_setfam_1 @ A @ E ) ) ) )
                    & ( ? [E: $i] :
                          ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
                          & ( r1_tarski @ E @ B )
                          & ( D
                            = ( k5_setfam_1 @ A @ E ) ) )
                     => ( r2_hidden @ D @ C ) ) ) ) )
            & ( ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                 => ( ( ( r2_hidden @ D @ C )
                     => ? [E: $i] :
                          ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
                          & ( r1_tarski @ E @ B )
                          & ( D
                            = ( k5_setfam_1 @ A @ E ) ) ) )
                    & ( ? [E: $i] :
                          ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
                          & ( r1_tarski @ E @ B )
                          & ( D
                            = ( k5_setfam_1 @ A @ E ) ) )
                     => ( r2_hidden @ D @ C ) ) ) )
             => ( C
                = ( k1_cantor_1 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1818]) ).

thf(1521,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) )
                 => ( ( A
                      = ( k7_mcart_1 @ B @ C @ D @ E ) )
                  <=> ! [F: $i] :
                        ( ( m1_subset_1 @ F @ B )
                       => ! [G: $i] :
                            ( ( m1_subset_1 @ G @ C )
                           => ! [H: $i] :
                                ( ( m1_subset_1 @ H @ D )
                               => ( ( E
                                    = ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
                                 => ( A = H ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_domain_1) ).

thf(9758,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) )
                 => ( ( ( A
                        = ( k7_mcart_1 @ B @ C @ D @ E ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ C )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ D )
                                 => ( ( E
                                      = ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
                                   => ( A = H ) ) ) ) ) )
                    & ( ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ C )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ D )
                                 => ( ( E
                                      = ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
                                   => ( A = H ) ) ) ) )
                     => ( A
                        = ( k7_mcart_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521]) ).

thf(856,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ( ( k5_relat_1 @ ( k6_partfun1 @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_functor0) ).

thf(6708,plain,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ( ( k5_relat_1 @ ( k6_partfun1 @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(1628,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i] :
                  ~ ( ( ( r2_hidden @ C @ A )
                      | ( r2_hidden @ D @ A ) )
                    & ( B
                      = ( k4_tarski @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_mcart_1) ).

thf(10247,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i] :
                  ~ ( ( ( r2_hidden @ C @ A )
                      | ( r2_hidden @ D @ A ) )
                    & ( B
                      = ( k4_tarski @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1628]) ).

thf(2537,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ ( k1_subset_1 @ A ) )
      & ( m1_subset_1 @ ( k1_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_subset_1) ).

thf(14681,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ ( k1_subset_1 @ A ) )
      & ( m1_subset_1 @ ( k1_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2537]) ).

thf(1487,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ B @ C ) )
     => ( r1_tarski @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).

thf(9539,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ B @ C ) )
     => ( r1_tarski @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487]) ).

thf(592,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k9_relat_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).

thf(5534,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k9_relat_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(1044,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ( ( k4_zfmisc_1 @ A @ B @ C @ D )
                    = ( a_4_0_domain_1 @ A @ B @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_domain_1) ).

thf(7625,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ( ( k4_zfmisc_1 @ A @ B @ C @ D )
                    = ( a_4_0_domain_1 @ A @ B @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).

thf(2075,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( ( v1_funct_1 @ ( k2_funct_3 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k2_funct_3 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) )
        & ( m2_relset_1 @ ( k2_funct_3 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_3) ).

thf(12692,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( ( v1_funct_1 @ ( k2_funct_3 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k2_funct_3 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) )
        & ( m2_relset_1 @ ( k2_funct_3 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2075]) ).

thf(2115,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_card_fil @ C @ B )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( r2_hidden @ A @ ( a_3_0_card_fil @ B @ C @ D ) )
      <=> ? [E: $i] :
            ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
            & ( A = E )
            & ? [F: $i] :
                ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
                & ( r2_hidden @ F @ ( a_3_1_card_fil @ B @ C @ D ) )
                & ( r1_tarski @ F @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_card_fil) ).

thf(12881,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_card_fil @ C @ B )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( ( r2_hidden @ A @ ( a_3_0_card_fil @ B @ C @ D ) )
         => ? [E: $i] :
              ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
              & ( A = E )
              & ? [F: $i] :
                  ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
                  & ( r2_hidden @ F @ ( a_3_1_card_fil @ B @ C @ D ) )
                  & ( r1_tarski @ F @ E ) ) ) )
        & ( ? [E: $i] :
              ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
              & ( A = E )
              & ? [F: $i] :
                  ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
                  & ( r2_hidden @ F @ ( a_3_1_card_fil @ B @ C @ D ) )
                  & ( r1_tarski @ F @ E ) ) )
         => ( r2_hidden @ A @ ( a_3_0_card_fil @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2115]) ).

thf(1955,axiom,
    ! [A: $i] :
    ? [B: $i] : ( m1_pboole @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_pboole) ).

thf(12025,plain,
    ! [A: $i] :
    ? [B: $i] : ( m1_pboole @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1955]) ).

thf(2553,axiom,
    m1_subset_1 @ k2_zfrefle1 @ ( k1_zfmisc_1 @ k9_zf_lang ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfrefle1) ).

thf(14735,plain,
    m1_subset_1 @ k2_zfrefle1 @ ( k1_zfmisc_1 @ k9_zf_lang ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2553]) ).

thf(1024,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ! [D: $i] :
                  ( ( v1_relat_1 @ D )
                 => ( ( ( r1_tarski @ A @ B )
                      & ( r1_tarski @ C @ D ) )
                   => ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_relat_1) ).

thf(7545,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ! [D: $i] :
                  ( ( v1_relat_1 @ D )
                 => ( ( ( r1_tarski @ A @ B )
                      & ( r1_tarski @ C @ D ) )
                   => ( r1_tarski @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).

thf(2208,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( C
              = ( k7_setfam_1 @ A @ B ) )
          <=> ! [D: $i] :
                ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
               => ( ( r2_hidden @ D @ C )
                <=> ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).

thf(13359,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( ( C
                = ( k7_setfam_1 @ A @ B ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                 => ( ( ( r2_hidden @ D @ C )
                     => ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B ) )
                    & ( ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B )
                     => ( r2_hidden @ D @ C ) ) ) ) )
            & ( ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                 => ( ( ( r2_hidden @ D @ C )
                     => ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B ) )
                    & ( ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B )
                     => ( r2_hidden @ D @ C ) ) ) )
             => ( C
                = ( k7_setfam_1 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2208]) ).

thf(340,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( ( v2_funct_1 @ D )
          & ( r2_hidden @ C @ A ) )
       => ( ( B = k1_xboole_0 )
          | ( ( k1_funct_1 @ ( k2_funct_1 @ D ) @ ( k1_funct_1 @ D @ C ) )
            = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_funct_2) ).

thf(4402,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( ( v2_funct_1 @ D )
          & ( r2_hidden @ C @ A ) )
       => ( ( B = k1_xboole_0 )
          | ( ( k1_funct_1 @ ( k2_funct_1 @ D ) @ ( k1_funct_1 @ D @ C ) )
            = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(1456,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k3_xboole_0 @ B @ C ) )
     => ( ( k1_funct_7 @ A @ B )
        = ( k1_funct_7 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_funct_7) ).

thf(9423,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k3_xboole_0 @ B @ C ) )
     => ( ( k1_funct_7 @ A @ B )
        = ( k1_funct_7 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456]) ).

thf(2426,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ( ( r2_subset_1 @ A @ B )
       => ( r2_subset_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r2_subset_1) ).

thf(14167,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ( ( r2_subset_1 @ A @ B )
       => ( r2_subset_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2426]) ).

thf(716,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ? [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) )
          & ( v1_xboole_0 @ C )
          & ( v1_relat_1 @ C )
          & ( v1_funct_1 @ C )
          & ( v2_funct_1 @ C )
          & ( v1_finset_1 @ C )
          & ( v1_fraenkel @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_closure2) ).

thf(6096,plain,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ? [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) )
          & ( v1_xboole_0 @ C )
          & ( v1_relat_1 @ C )
          & ( v1_funct_1 @ C )
          & ( v2_funct_1 @ C )
          & ( v1_finset_1 @ C )
          & ( v1_fraenkel @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(779,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
         => ( ( k10_setwiseo @ A @ A @ B @ ( k11_setwiseo @ A ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_setwiseo) ).

thf(6392,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
         => ( ( k10_setwiseo @ A @ A @ B @ ( k11_setwiseo @ A ) )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(706,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v2_funct_1 @ B )
       => ( v2_funct_1 @ ( k7_relat_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_funct_1) ).

thf(6060,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v2_funct_1 @ B )
       => ( v2_funct_1 @ ( k7_relat_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(2585,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( r1_filter_2 @ A @ B @ C )
      <=> ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).

thf(14894,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( ( r1_filter_2 @ A @ B @ C )
         => ( B = C ) )
        & ( ( B = C )
         => ( r1_filter_2 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2585]) ).

thf(1895,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_sysrel) ).

thf(11670,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1895]) ).

thf(1319,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ? [C: $i] :
            ( ( m1_subset_1 @ C @ A )
            & ( r3_binop_1 @ A @ C @ B ) )
       => ! [C: $i] :
            ( ( m1_subset_1 @ C @ A )
           => ( ( C
                = ( k3_binop_1 @ A @ B ) )
            <=> ( r3_binop_1 @ A @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_binop_1) ).

thf(8847,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ? [C: $i] :
            ( ( m1_subset_1 @ C @ A )
            & ( r3_binop_1 @ A @ C @ B ) )
       => ! [C: $i] :
            ( ( m1_subset_1 @ C @ A )
           => ( ( ( C
                  = ( k3_binop_1 @ A @ B ) )
               => ( r3_binop_1 @ A @ C @ B ) )
              & ( ( r3_binop_1 @ A @ C @ B )
               => ( C
                  = ( k3_binop_1 @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).

thf(1106,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ! [E: $i] :
              ( ( ( v1_funct_1 @ E )
                & ( m2_relset_1 @ E @ A @ B ) )
             => ( ( ( r1_partfun1 @ C @ E )
                  & ( r1_partfun1 @ D @ E )
                  & ( v1_partfun1 @ E @ A @ B ) )
               => ( r1_partfun1 @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_partfun1) ).

thf(7891,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ! [E: $i] :
              ( ( ( v1_funct_1 @ E )
                & ( m2_relset_1 @ E @ A @ B ) )
             => ( ( ( r1_partfun1 @ C @ E )
                  & ( r1_partfun1 @ D @ E )
                  & ( v1_partfun1 @ E @ A @ B ) )
               => ( r1_partfun1 @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).

thf(285,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( m2_finseq_1 @ ( k11_finseq_1 @ B @ C @ D ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_finseq_2) ).

thf(4104,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( m2_finseq_1 @ ( k11_finseq_1 @ B @ C @ D ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(1711,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ! [D: $i] :
            ( ( r2_hidden @ D @ C )
           => ( r1_tarski @ B @ D ) )
       => ( ( C = k1_xboole_0 )
          | ( r1_tarski @ B @ ( k8_setfam_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_mssubfam) ).

thf(10615,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ! [D: $i] :
            ( ( r2_hidden @ D @ C )
           => ( r1_tarski @ B @ D ) )
       => ( ( C = k1_xboole_0 )
          | ( r1_tarski @ B @ ( k8_setfam_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1711]) ).

thf(1186,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( ~ ( r1_xboole_0 @ A @ B )
          & ! [C: $i] :
              ~ ( ( r2_hidden @ C @ A )
                & ( r2_hidden @ C @ B ) ) )
      & ~ ( ? [C: $i] :
              ( ( r2_hidden @ C @ A )
              & ( r2_hidden @ C @ B ) )
          & ( r1_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).

thf(8226,plain,
    ! [A: $i,B: $i] :
      ( ~ ( ~ ( r1_xboole_0 @ A @ B )
          & ! [C: $i] :
              ~ ( ( r2_hidden @ C @ A )
                & ( r2_hidden @ C @ B ) ) )
      & ~ ( ? [C: $i] :
              ( ( r2_hidden @ C @ A )
              & ( r2_hidden @ C @ B ) )
          & ( r1_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).

thf(33,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( k1_relat_1 @ ( k4_funct_4 @ A @ B @ C @ D ) )
        = ( k2_tarski @ A @ B ) )
      & ( r1_tarski @ ( k2_relat_1 @ ( k4_funct_4 @ A @ B @ C @ D ) ) @ ( k2_tarski @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funct_4) ).

thf(2741,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( k1_relat_1 @ ( k4_funct_4 @ A @ B @ C @ D ) )
        = ( k2_tarski @ A @ B ) )
      & ( r1_tarski @ ( k2_relat_1 @ ( k4_funct_4 @ A @ B @ C @ D ) ) @ ( k2_tarski @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(1504,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k5_enumset1 @ A @ A @ B @ C @ D @ E @ F )
      = ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_enumset1) ).

thf(9613,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k5_enumset1 @ A @ A @ B @ C @ D @ E @ F )
      = ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504]) ).

thf(2217,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) )
     => ( D
        = ( k9_funct_2 @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_2) ).

thf(13411,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) )
     => ( D
        = ( k9_funct_2 @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2217]) ).

thf(1878,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ~ ( v1_xboole_0 @ D )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) ) )
     => ~ ( v1_xboole_0 @ ( k9_relat_1 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_waybel_2) ).

thf(11602,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ~ ( v1_xboole_0 @ D )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) ) )
     => ~ ( v1_xboole_0 @ ( k9_relat_1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1878]) ).

thf(1161,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( r1_tarski @ B @ C )
           => ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t157_relat_1) ).

thf(8136,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( r1_tarski @ B @ C )
           => ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k9_relat_1 @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).

thf(2342,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ B )
     => ( ( v1_xboole_0 @ B )
        | ( r2_hidden @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

thf(13853,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ B )
     => ( ( v1_xboole_0 @ B )
        | ( r2_hidden @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2342]) ).

thf(2060,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H )
      = ( k2_xboole_0 @ ( k1_enumset1 @ A @ B @ C ) @ ( k3_enumset1 @ D @ E @ F @ G @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_enumset1) ).

thf(12571,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H )
      = ( k2_xboole_0 @ ( k1_enumset1 @ A @ B @ C ) @ ( k3_enumset1 @ D @ E @ F @ G @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2060]) ).

thf(540,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v3_monoid_0 @ B @ A )
          <=> ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ? [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                        & ( ( k2_binop_1 @ A @ A @ A @ B @ E @ C )
                          = D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_monoid_0) ).

thf(5330,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( v3_monoid_0 @ B @ A )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ? [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                          & ( ( k2_binop_1 @ A @ A @ A @ B @ E @ C )
                            = D ) ) ) ) )
            & ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ? [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                          & ( ( k2_binop_1 @ A @ A @ A @ B @ E @ C )
                            = D ) ) ) )
             => ( v3_monoid_0 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(1247,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_membered @ A )
        & ( v1_membered @ B ) )
     => ( v1_membered @ ( k2_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc22_membered) ).

thf(8518,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_membered @ A )
        & ( v1_membered @ B ) )
     => ( v1_membered @ ( k2_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).

thf(1062,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_eqrel_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
             => ( ( k3_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ C )
                = ( k3_tarski @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_borsuk_1) ).

thf(7686,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_eqrel_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
             => ( ( k3_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ C )
                = ( k3_tarski @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).

thf(1143,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
        = ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ A @ C ) ) )
      & ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
        = ( k2_tarski @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_zfmisc_1) ).

thf(8073,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
        = ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ A @ C ) ) )
      & ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
        = ( k2_tarski @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).

thf(1166,axiom,
    ! [A: $i] :
      ( ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
      & ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_partfun1) ).

thf(8155,plain,
    ! [A: $i] :
      ( ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
      & ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).

thf(1258,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( v1_yellow18 @ D @ A @ B @ C )
      <=> ( v2_funct_1 @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_v1_yellow18) ).

thf(8562,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( ( v1_yellow18 @ D @ A @ B @ C )
         => ( v2_funct_1 @ D ) )
        & ( ( v2_funct_1 @ D )
         => ( v1_yellow18 @ D @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).

thf(656,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ ( k3_cqc_lang @ A @ B ) )
      & ( v1_relat_1 @ ( k3_cqc_lang @ A @ B ) )
      & ( v1_funct_1 @ ( k3_cqc_lang @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_7) ).

thf(5798,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ ( k3_cqc_lang @ A @ B ) )
      & ( v1_relat_1 @ ( k3_cqc_lang @ A @ B ) )
      & ( v1_funct_1 @ ( k3_cqc_lang @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(203,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k1_relat_1 @ B ) )
        & ( r1_tarski @ ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k2_relat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funct_1) ).

thf(3704,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k1_relat_1 @ B ) )
        & ( r1_tarski @ ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k2_relat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(1331,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( v1_relat_1 @ E )
     => ( ( ( r1_tarski @ E @ ( k2_zfmisc_1 @ A @ B ) )
          & ( A
            = ( k2_xboole_0 @ C @ D ) ) )
       => ( E
          = ( k2_xboole_0 @ ( k7_relat_1 @ E @ C ) @ ( k7_relat_1 @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_sysrel) ).

thf(8884,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( v1_relat_1 @ E )
     => ( ( ( r1_tarski @ E @ ( k2_zfmisc_1 @ A @ B ) )
          & ( A
            = ( k2_xboole_0 @ C @ D ) ) )
       => ( E
          = ( k2_xboole_0 @ ( k7_relat_1 @ E @ C ) @ ( k7_relat_1 @ E @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).

thf(2576,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( B
            = ( k3_tarski @ ( a_2_0_relset_2 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_relset_2) ).

thf(14855,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( B
            = ( k3_tarski @ ( a_2_0_relset_2 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2576]) ).

thf(2097,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_enumset1 @ C @ D @ E ) @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_qc_lang1) ).

thf(12796,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_enumset1 @ C @ D @ E ) @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2097]) ).

thf(1162,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ( r1_xboole_0 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_mcart_1) ).

thf(8138,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ( r1_xboole_0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).

thf(2374,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A ) )
     => ( ( k4_setwiseo @ A @ B @ C @ D )
        = ( k1_enumset1 @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_setwiseo) ).

thf(13981,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A ) )
     => ( ( k4_setwiseo @ A @ B @ C @ D )
        = ( k1_enumset1 @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2374]) ).

thf(1189,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
                 => ( ( k10_setwiseo @ A @ B @ ( k5_setwiseo @ A @ E @ ( k2_setwiseo @ A @ D ) ) @ C )
                    = ( k5_setwiseo @ B @ ( k10_setwiseo @ A @ B @ E @ C ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_setwiseo) ).

thf(8238,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
                 => ( ( k10_setwiseo @ A @ B @ ( k5_setwiseo @ A @ E @ ( k2_setwiseo @ A @ D ) ) @ C )
                    = ( k5_setwiseo @ B @ ( k10_setwiseo @ A @ B @ E @ C ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).

thf(414,axiom,
    ( ( v1_funct_1 @ k33_binop_2 )
    & ( v1_funct_2 @ k33_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( v1_binop_1 @ k33_binop_2 @ k1_numbers )
    & ( v2_binop_1 @ k33_binop_2 @ k1_numbers )
    & ( v1_setwiseo @ k33_binop_2 @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_binop_2) ).

thf(4808,plain,
    ( ( v1_funct_1 @ k33_binop_2 )
    & ( v1_funct_2 @ k33_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( v1_binop_1 @ k33_binop_2 @ k1_numbers )
    & ( v2_binop_1 @ k33_binop_2 @ k1_numbers )
    & ( v1_setwiseo @ k33_binop_2 @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(1215,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
     => ( ( A != k1_xboole_0 )
       => ( ( k5_partfun1 @ A @ k1_xboole_0 @ B )
          = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t172_partfun1) ).

thf(8354,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
     => ( ( A != k1_xboole_0 )
       => ( ( k5_partfun1 @ A @ k1_xboole_0 @ B )
          = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).

thf(2473,axiom,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s4_filter_1 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f2_s4_filter_1 )
           => ( p1_s4_filter_1 @ ( k1_domain_1 @ f1_s4_filter_1 @ f2_s4_filter_1 @ A @ B ) ) ) )
   => ! [A: $i] :
        ( ( m1_subset_1 @ A @ ( k2_zfmisc_1 @ f1_s4_filter_1 @ f2_s4_filter_1 ) )
       => ( p1_s4_filter_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_filter_1) ).

thf(14380,plain,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s4_filter_1 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f2_s4_filter_1 )
           => ( p1_s4_filter_1 @ ( k1_domain_1 @ f1_s4_filter_1 @ f2_s4_filter_1 @ A @ B ) ) ) )
   => ! [A: $i] :
        ( ( m1_subset_1 @ A @ ( k2_zfmisc_1 @ f1_s4_filter_1 @ f2_s4_filter_1 ) )
       => ( p1_s4_filter_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2473]) ).

thf(843,axiom,
    ! [A: $i,B: $i] :
      ( ( k3_tarski @ ( k2_tarski @ A @ B ) )
      = ( k2_xboole_0 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_zfmisc_1) ).

thf(6656,plain,
    ! [A: $i,B: $i] :
      ( ( k3_tarski @ ( k2_tarski @ A @ B ) )
      = ( k2_xboole_0 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).

thf(1531,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ B ) )
     => ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_binop_1) ).

thf(9814,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ B ) )
     => ( m1_subset_1 @ ( k2_binop_1 @ A @ B @ C @ D @ E @ F ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1531]) ).

thf(1238,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( r1_partfun1 @ ( k7_relat_1 @ B @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_partfun1) ).

thf(8471,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( r1_partfun1 @ ( k7_relat_1 @ B @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).

thf(202,axiom,
    ( ( v1_funct_1 @ k33_binop_2 )
    & ( v1_funct_2 @ k33_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( v1_binop_1 @ k33_binop_2 @ k1_numbers )
    & ( v2_binop_1 @ k33_binop_2 @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_binop_2) ).

thf(3699,plain,
    ( ( v1_funct_1 @ k33_binop_2 )
    & ( v1_funct_2 @ k33_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( v1_binop_1 @ k33_binop_2 @ k1_numbers )
    & ( v2_binop_1 @ k33_binop_2 @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(1762,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ A @ ( k2_ens_1 @ A ) )
            & ( m2_relset_1 @ B @ A @ ( k2_ens_1 @ A ) ) )
         => ( ( B
              = ( k11_ens_1 @ A ) )
          <=> ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ( ( k8_funct_2 @ A @ ( k2_ens_1 @ A ) @ B @ C )
                  = ( k5_ens_1 @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_ens_1) ).

thf(10962,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ A @ ( k2_ens_1 @ A ) )
            & ( m2_relset_1 @ B @ A @ ( k2_ens_1 @ A ) ) )
         => ( ( ( B
                = ( k11_ens_1 @ A ) )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ( ( k8_funct_2 @ A @ ( k2_ens_1 @ A ) @ B @ C )
                    = ( k5_ens_1 @ A @ C ) ) ) )
            & ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ( ( k8_funct_2 @ A @ ( k2_ens_1 @ A ) @ B @ C )
                    = ( k5_ens_1 @ A @ C ) ) )
             => ( B
                = ( k11_ens_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1762]) ).

thf(971,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ? [C: $i] :
              ( ( m1_card_fil @ C @ A )
              & ( r1_tarski @ B @ C )
              & ( v3_card_fil @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_card_fil) ).

thf(7281,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ? [C: $i] :
              ( ( m1_card_fil @ C @ A )
              & ( r1_tarski @ B @ C )
              & ( v3_card_fil @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(1090,axiom,
    ! [A: $i,B: $i] :
      ( ( k15_funct_3 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) )
      = ( k6_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_funct_3) ).

thf(7799,plain,
    ! [A: $i,B: $i] :
      ( ( k15_funct_3 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) )
      = ( k6_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).

thf(237,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( ( ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
              = k1_xboole_0 )
            & ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) )
         => ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k2_relat_1 @ B ) ) ) )
            = k1_xboole_0 ) )
        & ( ( ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ B )
              = k1_xboole_0 )
            & ( r1_tarski @ ( k1_relat_1 @ B ) @ A ) )
         => ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
            = k1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_sysrel) ).

thf(3909,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( ( ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
              = k1_xboole_0 )
            & ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) )
         => ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k2_relat_1 @ B ) ) ) )
            = k1_xboole_0 ) )
        & ( ( ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ B )
              = k1_xboole_0 )
            & ( r1_tarski @ ( k1_relat_1 @ B ) @ A ) )
         => ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
            = k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(1473,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v1_setwiseo @ B @ A )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ( ( ( k2_binop_1 @ A @ A @ A @ B @ ( k3_binop_1 @ A @ B ) @ C )
                    = C )
                  & ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k3_binop_1 @ A @ B ) )
                    = C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_setwiseo) ).

thf(9493,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v1_setwiseo @ B @ A )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ( ( ( k2_binop_1 @ A @ A @ A @ B @ ( k3_binop_1 @ A @ B ) @ C )
                    = C )
                  & ( ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k3_binop_1 @ A @ B ) )
                    = C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473]) ).

thf(786,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ ( k5_finsub_1 @ B ) )
                & ( m2_relset_1 @ D @ A @ ( k5_finsub_1 @ B ) ) )
             => ( ( k10_setwiseo @ A @ B @ C @ D )
                = ( k7_setwiseo @ A @ ( k5_finsub_1 @ B ) @ ( k9_setwiseo @ B ) @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_setwiseo) ).

thf(6413,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ ( k5_finsub_1 @ B ) )
                & ( m2_relset_1 @ D @ A @ ( k5_finsub_1 @ B ) ) )
             => ( ( k10_setwiseo @ A @ B @ C @ D )
                = ( k7_setwiseo @ A @ ( k5_finsub_1 @ B ) @ ( k9_setwiseo @ B ) @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(2109,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( m1_cantor_1 @ B @ ( g1_pre_topc @ A @ ( k1_cantor_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_cantor_1) ).

thf(12863,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( m1_cantor_1 @ B @ ( g1_pre_topc @ A @ ( k1_cantor_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2109]) ).

thf(982,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( ( ( k5_relat_1 @ ( k2_xboole_0 @ A @ B ) @ C )
                  = ( k2_xboole_0 @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) )
                & ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
                  = ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_sysrel) ).

thf(7329,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( ( ( k5_relat_1 @ ( k2_xboole_0 @ A @ B ) @ C )
                  = ( k2_xboole_0 @ ( k5_relat_1 @ A @ C ) @ ( k5_relat_1 @ B @ C ) ) )
                & ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
                  = ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).

thf(2131,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ! [B: $i] :
            ( ( m1_subset_1 @ B @ A )
           => ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
       => ~ ( v1_realset1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_realset1) ).

thf(12987,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ! [B: $i] :
            ( ( m1_subset_1 @ B @ A )
           => ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
       => ~ ( v1_realset1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2131]) ).

thf(446,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k2_xboole_0 @ ( k1_tarski @ A ) @ B ) @ B )
     => ( r2_hidden @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_zfmisc_1) ).

thf(4957,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k2_xboole_0 @ ( k1_tarski @ A ) @ B ) @ B )
     => ( r2_hidden @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(948,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k5_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc17_finset_1) ).

thf(7142,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k5_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).

thf(218,axiom,
    ! [A: $i] :
      ( ( ( k1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
        = k1_xboole_0 )
      & ( ( k2_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funcop_1) ).

thf(3831,plain,
    ! [A: $i] :
      ( ( ( k1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
        = k1_xboole_0 )
      & ( ( k2_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
        = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(49,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ( ( ( v1_binop_1 @ C @ B )
                          & ( v2_binop_1 @ C @ B ) )
                       => ( ( ( D = k1_xboole_0 )
                            & ~ ( v1_setwiseo @ C @ B ) )
                          | ! [F: $i] :
                              ( ( m1_subset_1 @ F @ B )
                             => ( ( F
                                  = ( k7_setwiseo @ A @ B @ C @ D @ E ) )
                              <=> ? [G: $i] :
                                    ( ( v1_funct_1 @ G )
                                    & ( v1_funct_2 @ G @ ( k5_finsub_1 @ A ) @ B )
                                    & ( m2_relset_1 @ G @ ( k5_finsub_1 @ A ) @ B )
                                    & ( F
                                      = ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ D ) )
                                    & ! [H: $i] :
                                        ( ( m1_subset_1 @ H @ B )
                                       => ( ( r3_binop_1 @ B @ H @ C )
                                         => ( ( k1_funct_1 @ G @ k1_xboole_0 )
                                            = H ) ) )
                                    & ! [H: $i] :
                                        ( ( m1_subset_1 @ H @ A )
                                       => ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k2_setwiseo @ A @ H ) )
                                          = ( k8_funct_2 @ A @ B @ E @ H ) ) )
                                    & ! [H: $i] :
                                        ( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
                                       => ( ( r1_tarski @ H @ D )
                                         => ( ( H = k1_xboole_0 )
                                            | ! [I: $i] :
                                                ( ( m1_subset_1 @ I @ A )
                                               => ( ( r2_hidden @ I @ ( k6_setwiseo @ A @ D @ H ) )
                                                 => ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k5_setwiseo @ A @ H @ ( k2_setwiseo @ A @ I ) ) )
                                                    = ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ H ) @ ( k8_funct_2 @ A @ B @ E @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_setwiseo) ).

thf(2840,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ( ( ( v1_binop_1 @ C @ B )
                          & ( v2_binop_1 @ C @ B ) )
                       => ( ( ( D = k1_xboole_0 )
                            & ~ ( v1_setwiseo @ C @ B ) )
                          | ! [F: $i] :
                              ( ( m1_subset_1 @ F @ B )
                             => ( ( ( F
                                    = ( k7_setwiseo @ A @ B @ C @ D @ E ) )
                                 => ? [G: $i] :
                                      ( ( v1_funct_1 @ G )
                                      & ( v1_funct_2 @ G @ ( k5_finsub_1 @ A ) @ B )
                                      & ( m2_relset_1 @ G @ ( k5_finsub_1 @ A ) @ B )
                                      & ( F
                                        = ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ D ) )
                                      & ! [H: $i] :
                                          ( ( m1_subset_1 @ H @ B )
                                         => ( ( r3_binop_1 @ B @ H @ C )
                                           => ( ( k1_funct_1 @ G @ k1_xboole_0 )
                                              = H ) ) )
                                      & ! [H: $i] :
                                          ( ( m1_subset_1 @ H @ A )
                                         => ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k2_setwiseo @ A @ H ) )
                                            = ( k8_funct_2 @ A @ B @ E @ H ) ) )
                                      & ! [H: $i] :
                                          ( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
                                         => ( ( r1_tarski @ H @ D )
                                           => ( ( H = k1_xboole_0 )
                                              | ! [I: $i] :
                                                  ( ( m1_subset_1 @ I @ A )
                                                 => ( ( r2_hidden @ I @ ( k6_setwiseo @ A @ D @ H ) )
                                                   => ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k5_setwiseo @ A @ H @ ( k2_setwiseo @ A @ I ) ) )
                                                      = ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ H ) @ ( k8_funct_2 @ A @ B @ E @ I ) ) ) ) ) ) ) ) ) )
                                & ( ? [G: $i] :
                                      ( ( v1_funct_1 @ G )
                                      & ( v1_funct_2 @ G @ ( k5_finsub_1 @ A ) @ B )
                                      & ( m2_relset_1 @ G @ ( k5_finsub_1 @ A ) @ B )
                                      & ( F
                                        = ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ D ) )
                                      & ! [H: $i] :
                                          ( ( m1_subset_1 @ H @ B )
                                         => ( ( r3_binop_1 @ B @ H @ C )
                                           => ( ( k1_funct_1 @ G @ k1_xboole_0 )
                                              = H ) ) )
                                      & ! [H: $i] :
                                          ( ( m1_subset_1 @ H @ A )
                                         => ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k2_setwiseo @ A @ H ) )
                                            = ( k8_funct_2 @ A @ B @ E @ H ) ) )
                                      & ! [H: $i] :
                                          ( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
                                         => ( ( r1_tarski @ H @ D )
                                           => ( ( H = k1_xboole_0 )
                                              | ! [I: $i] :
                                                  ( ( m1_subset_1 @ I @ A )
                                                 => ( ( r2_hidden @ I @ ( k6_setwiseo @ A @ D @ H ) )
                                                   => ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k5_setwiseo @ A @ H @ ( k2_setwiseo @ A @ I ) ) )
                                                      = ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ H ) @ ( k8_funct_2 @ A @ B @ E @ I ) ) ) ) ) ) ) ) )
                                 => ( F
                                    = ( k7_setwiseo @ A @ B @ C @ D @ E ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(160,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
                      & ( r1_tarski @ ( k2_relat_1 @ D ) @ ( k1_relat_1 @ B ) )
                      & ( r1_partfun1 @ A @ B ) )
                   => ( ( k5_relat_1 @ ( k1_funct_4 @ C @ D ) @ ( k1_funct_4 @ A @ B ) )
                      = ( k1_funct_4 @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ D @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_4) ).

thf(3482,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_relat_1 @ A ) )
                      & ( r1_tarski @ ( k2_relat_1 @ D ) @ ( k1_relat_1 @ B ) )
                      & ( r1_partfun1 @ A @ B ) )
                   => ( ( k5_relat_1 @ ( k1_funct_4 @ C @ D ) @ ( k1_funct_4 @ A @ B ) )
                      = ( k1_funct_4 @ ( k5_relat_1 @ C @ A ) @ ( k5_relat_1 @ D @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(472,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( v6_ordinal1 @ A )
       => ( ( k2_zfmisc_1 @ ( k3_tarski @ A ) @ ( k3_tarski @ A ) )
          = ( k3_tarski @ ( a_1_0_lattice5 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_lattice5) ).

thf(5053,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( v6_ordinal1 @ A )
       => ( ( k2_zfmisc_1 @ ( k3_tarski @ A ) @ ( k3_tarski @ A ) )
          = ( k3_tarski @ ( a_1_0_lattice5 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(507,axiom,
    ! [A: $i,B: $i] :
      ( ( v2_membered @ B )
     => ( ( r1_tarski @ A @ B )
       => ( v2_membered @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_membered) ).

thf(5221,plain,
    ! [A: $i,B: $i] :
      ( ( v2_membered @ B )
     => ( ( r1_tarski @ A @ B )
       => ( v2_membered @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(151,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) )
             => ! [D: $i] :
                  ( ( m1_pboole @ D @ ( k2_zfmisc_1 @ A @ B ) )
                 => ( ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                           => ( ( k1_binop_1 @ C @ E @ F )
                              = ( k1_binop_1 @ D @ E @ F ) ) ) )
                   => ( r6_pboole @ ( k2_zfmisc_1 @ A @ B ) @ D @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_altcat_1) ).

thf(3413,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) )
             => ! [D: $i] :
                  ( ( m1_pboole @ D @ ( k2_zfmisc_1 @ A @ B ) )
                 => ( ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                           => ( ( k1_binop_1 @ C @ E @ F )
                              = ( k1_binop_1 @ D @ E @ F ) ) ) )
                   => ( r6_pboole @ ( k2_zfmisc_1 @ A @ B ) @ D @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(2459,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k10_classes2 @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_classes2) ).

thf(14327,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k10_classes2 @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2459]) ).

thf(1689,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) )
             => ( m1_subset_1 @ ( k7_subset_1 @ ( k1_closure2 @ A @ B ) @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_closure2) ).

thf(10529,plain,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) )
             => ( m1_subset_1 @ ( k7_subset_1 @ ( k1_closure2 @ A @ B ) @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1689]) ).

thf(2135,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i,D: $i] :
          ( ( ( g2_lattices @ A @ B )
            = ( g2_lattices @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g2_lattices) ).

thf(13006,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i,D: $i] :
          ( ( ( g2_lattices @ A @ B )
            = ( g2_lattices @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2135]) ).

thf(869,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_membered @ A )
        & ( v1_membered @ B ) )
     => ( v1_membered @ ( k5_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc42_membered) ).

thf(6801,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_membered @ A )
        & ( v1_membered @ B ) )
     => ( v1_membered @ ( k5_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(2178,axiom,
    ! [A: $i] :
      ( ( k1_orders_1 @ A )
      = ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_orders_1) ).

thf(13222,plain,
    ! [A: $i] :
      ( ( k1_orders_1 @ A )
      = ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2178]) ).

thf(914,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ A )
     => ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_realset1) ).

thf(6995,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ A )
     => ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).

thf(458,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D ) )
     => ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_xboole_1) ).

thf(5006,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D ) )
     => ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(928,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ A @ C )
            & ( m2_relset_1 @ E @ A @ C ) )
         => ~ ( ( ( B = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ( ( C = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ~ ( ( ( k5_relat_1 @ ( k13_funct_3 @ D @ E ) @ ( k9_funct_3 @ B @ C ) )
                    = D )
                  & ( ( k5_relat_1 @ ( k13_funct_3 @ D @ E ) @ ( k10_funct_3 @ B @ C ) )
                    = E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_funct_3) ).

thf(7065,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ A @ C )
            & ( m2_relset_1 @ E @ A @ C ) )
         => ~ ( ( ( B = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ( ( C = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ~ ( ( ( k5_relat_1 @ ( k13_funct_3 @ D @ E ) @ ( k9_funct_3 @ B @ C ) )
                    = D )
                  & ( ( k5_relat_1 @ ( k13_funct_3 @ D @ E ) @ ( k10_funct_3 @ B @ C ) )
                    = E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).

thf(226,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
          & ! [C: $i] :
              ~ ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_relat_1) ).

thf(3862,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
          & ! [C: $i] :
              ~ ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(1934,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( k4_tarski @ A @ B )
        = ( k4_tarski @ C @ D ) )
     => ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).

thf(11884,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( k4_tarski @ A @ B )
        = ( k4_tarski @ C @ D ) )
     => ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1934]) ).

thf(2518,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ( m1_subset_1 @ ( a_3_8_domain_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_domain_1) ).

thf(14629,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ( m1_subset_1 @ ( a_3_8_domain_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2518]) ).

thf(738,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ B )
                        & ( m2_relset_1 @ E @ B @ B ) )
                     => ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
                        = ( k6_funcop_1 @ B @ A @ C @ D @ ( k7_funct_2 @ A @ B @ B @ D @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funcop_1) ).

thf(6195,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ B )
                        & ( m2_relset_1 @ E @ B @ B ) )
                     => ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
                        = ( k6_funcop_1 @ B @ A @ C @ D @ ( k7_funct_2 @ A @ B @ B @ D @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(287,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( ( k1_relat_1 @ A )
                = ( k1_relat_1 @ B ) )
              & ! [C: $i] :
                  ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
                 => ( r1_tarski @ ( k1_funct_1 @ A @ C ) @ ( k1_funct_1 @ B @ C ) ) ) )
           => ( r1_tarski @ ( k4_card_3 @ A ) @ ( k4_card_3 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_card_3) ).

thf(4108,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( ( k1_relat_1 @ A )
                = ( k1_relat_1 @ B ) )
              & ! [C: $i] :
                  ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
                 => ( r1_tarski @ ( k1_funct_1 @ A @ C ) @ ( k1_funct_1 @ B @ C ) ) ) )
           => ( r1_tarski @ ( k4_card_3 @ A ) @ ( k4_card_3 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(803,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A != B )
     => ( ( r1_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ D ) )
        & ( r1_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ D @ ( k1_tarski @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_zfmisc_1) ).

thf(6477,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A != B )
     => ( ( r1_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ D ) )
        & ( r1_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ D @ ( k1_tarski @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(2356,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).

thf(13904,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2356]) ).

thf(2165,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( r2_hidden @ A @ ( k2_cantor_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_cantor_1) ).

thf(13173,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( r2_hidden @ A @ ( k2_cantor_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2165]) ).

thf(830,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
        & ( v1_finset_1 @ ( k2_tarski @ A @ B ) )
        & ( v1_fraenkel @ ( k2_tarski @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_closure2) ).

thf(6603,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
        & ( v1_finset_1 @ ( k2_tarski @ A @ B ) )
        & ( v1_fraenkel @ ( k2_tarski @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(1267,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ C )
      = ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_xboole_1) ).

thf(8604,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ C )
      = ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).

thf(2046,axiom,
    ( ( v1_funct_1 @ k7_metric_1 )
    & ( v1_funct_2 @ k7_metric_1 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( m2_relset_1 @ k7_metric_1 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_metric_1) ).

thf(12506,plain,
    ( ( v1_funct_1 @ k7_metric_1 )
    & ( v1_funct_2 @ k7_metric_1 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( m2_relset_1 @ k7_metric_1 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2046]) ).

thf(353,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( v2_funct_1 @ B ) )
           => ( ( k2_funct_1 @ ( k5_relat_1 @ A @ B ) )
              = ( k5_relat_1 @ ( k2_funct_1 @ B ) @ ( k2_funct_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_1) ).

thf(4544,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( v2_funct_1 @ B ) )
           => ( ( k2_funct_1 @ ( k5_relat_1 @ A @ B ) )
              = ( k5_relat_1 @ ( k2_funct_1 @ B ) @ ( k2_funct_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(1210,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i,C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( C
              = ( k7_relat_1 @ A @ B ) )
          <=> ! [D: $i,E: $i] :
                ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
              <=> ( ( r2_hidden @ D @ B )
                  & ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).

thf(8319,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i,C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( ( C
                = ( k7_relat_1 @ A @ B ) )
             => ! [D: $i,E: $i] :
                  ( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
                   => ( ( r2_hidden @ D @ B )
                      & ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) ) )
                  & ( ( ( r2_hidden @ D @ B )
                      & ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) )
                   => ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) )
            & ( ! [D: $i,E: $i] :
                  ( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
                   => ( ( r2_hidden @ D @ B )
                      & ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) ) )
                  & ( ( ( r2_hidden @ D @ B )
                      & ( r2_hidden @ ( k4_tarski @ D @ E ) @ A ) )
                   => ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
             => ( C
                = ( k7_relat_1 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).

thf(1411,axiom,
    ! [A: $i] :
      ( ! [B: $i] :
          ( ( r2_hidden @ B @ A )
         => ( v2_membered @ B ) )
     => ( v2_membered @ ( k3_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_membered) ).

thf(9244,plain,
    ! [A: $i] :
      ( ! [B: $i] :
          ( ( r2_hidden @ B @ A )
         => ( v2_membered @ B ) )
     => ( v2_membered @ ( k3_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411]) ).

thf(1342,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m2_realset1 @ C @ A @ B )
         => ( ( k3_realset1 @ A @ B @ C )
            = ( k1_realset1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_realset1) ).

thf(8931,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m2_realset1 @ C @ A @ B )
         => ( ( k3_realset1 @ A @ B @ C )
            = ( k1_realset1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342]) ).

thf(2337,axiom,
    ? [A: $i] :
      ( ( v1_funct_1 @ A )
      & ( v1_funct_2 @ A @ ( k3_zfmisc_1 @ f1_s4_multop_1 @ f2_s4_multop_1 @ f3_s4_multop_1 ) @ f4_s4_multop_1 )
      & ( m2_relset_1 @ A @ ( k3_zfmisc_1 @ f1_s4_multop_1 @ f2_s4_multop_1 @ f3_s4_multop_1 ) @ f4_s4_multop_1 )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s4_multop_1 )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ f2_s4_multop_1 )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ f3_s4_multop_1 )
                 => ( ( k2_multop_1 @ f1_s4_multop_1 @ f2_s4_multop_1 @ f3_s4_multop_1 @ f4_s4_multop_1 @ A @ B @ C @ D )
                    = ( f5_s4_multop_1 @ B @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_multop_1) ).

thf(13825,plain,
    ? [A: $i] :
      ( ( v1_funct_1 @ A )
      & ( v1_funct_2 @ A @ ( k3_zfmisc_1 @ f1_s4_multop_1 @ f2_s4_multop_1 @ f3_s4_multop_1 ) @ f4_s4_multop_1 )
      & ( m2_relset_1 @ A @ ( k3_zfmisc_1 @ f1_s4_multop_1 @ f2_s4_multop_1 @ f3_s4_multop_1 ) @ f4_s4_multop_1 )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s4_multop_1 )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ f2_s4_multop_1 )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ f3_s4_multop_1 )
                 => ( ( k2_multop_1 @ f1_s4_multop_1 @ f2_s4_multop_1 @ f3_s4_multop_1 @ f4_s4_multop_1 @ A @ B @ C @ D )
                    = ( f5_s4_multop_1 @ B @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2337]) ).

thf(1358,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v2_membered @ A )
        & ( v2_membered @ B ) )
     => ( ( v1_membered @ ( k5_xboole_0 @ A @ B ) )
        & ( v2_membered @ ( k5_xboole_0 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc43_membered) ).

thf(8984,plain,
    ! [A: $i,B: $i] :
      ( ( ( v2_membered @ A )
        & ( v2_membered @ B ) )
     => ( ( v1_membered @ ( k5_xboole_0 @ A @ B ) )
        & ( v2_membered @ ( k5_xboole_0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).

thf(1130,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( v1_fraenkel @ ( k4_card_3 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_card_3) ).

thf(8016,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( v1_fraenkel @ ( k4_card_3 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).

thf(1605,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( v1_funct_1 @ ( k1_nattra_1 @ A @ B @ C @ D ) )
        & ( v1_funct_2 @ ( k1_nattra_1 @ A @ B @ C @ D ) @ D @ B )
        & ( m2_relset_1 @ ( k1_nattra_1 @ A @ B @ C @ D ) @ D @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_nattra_1) ).

thf(10152,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( v1_funct_1 @ ( k1_nattra_1 @ A @ B @ C @ D ) )
        & ( v1_funct_2 @ ( k1_nattra_1 @ A @ B @ C @ D ) @ D @ B )
        & ( m2_relset_1 @ ( k1_nattra_1 @ A @ B @ C @ D ) @ D @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1605]) ).

thf(1666,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ B @ A )
     => ( ( m2_relset_1 @ C @ B @ k1_xboole_0 )
       => ( C = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_relset_1) ).

thf(10445,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ B @ A )
     => ( ( m2_relset_1 @ C @ B @ k1_xboole_0 )
       => ( C = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1666]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( ( k2_relat_1 @ A )
                = ( k1_relat_1 @ B ) )
              & ( ( k5_relat_1 @ A @ B )
                = A ) )
           => ( B
              = ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_1) ).

thf(2724,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( ( k2_relat_1 @ A )
                = ( k1_relat_1 @ B ) )
              & ( ( k5_relat_1 @ A @ B )
                = A ) )
           => ( B
              = ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(440,axiom,
    ! [A: $i] :
      ( ~ ( v1_finset_1 @ A )
     => ? [B: $i] :
          ( ( m1_card_fil @ B @ A )
          & ~ ( v1_xboole_0 @ B )
          & ~ ( v2_card_fil @ B @ A )
          & ( v3_card_fil @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_card_fil) ).

thf(4930,plain,
    ! [A: $i] :
      ( ~ ( v1_finset_1 @ A )
     => ? [B: $i] :
          ( ( m1_card_fil @ B @ A )
          & ~ ( v1_xboole_0 @ B )
          & ~ ( v2_card_fil @ B @ A )
          & ( v3_card_fil @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(1662,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v5_grcat_1 @ A ) )
     => ? [B: $i] : ( m3_grcat_1 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_grcat_1) ).

thf(10434,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v5_grcat_1 @ A ) )
     => ? [B: $i] : ( m3_grcat_1 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1662]) ).

thf(82,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( v2_funct_2 @ ( k1_functor0 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C )
       => ( v2_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_functor0) ).

thf(3119,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( v2_funct_2 @ ( k1_functor0 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C )
       => ( v2_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(212,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ B @ ( k2_zfmisc_1 @ A @ A ) )
       => ( ( ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) )
            = ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
          & ( ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k2_relat_1 @ B ) ) )
            = ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_sysrel) ).

thf(3746,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ B @ ( k2_zfmisc_1 @ A @ A ) )
       => ( ( ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) )
            = ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
          & ( ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k2_relat_1 @ B ) ) )
            = ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(1573,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).

thf(10021,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1573]) ).

thf(2479,axiom,
    m1_subset_1 @ k3_qc_lang1 @ ( k1_zfmisc_1 @ k1_qc_lang1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_qc_lang1) ).

thf(14413,plain,
    m1_subset_1 @ k3_qc_lang1 @ ( k1_zfmisc_1 @ k1_qc_lang1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2479]) ).

thf(2455,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) ) )
     => ( ( k13_mcart_1 @ A @ B @ C @ D @ E @ F )
        = ( k3_zfmisc_1 @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k13_mcart_1) ).

thf(14312,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) ) )
     => ( ( k13_mcart_1 @ A @ B @ C @ D @ E @ F )
        = ( k3_zfmisc_1 @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2455]) ).

thf(897,axiom,
    ? [A: $i] :
      ( ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).

thf(6919,plain,
    ? [A: $i] :
      ( ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).

thf(1805,axiom,
    ( ( v1_funct_1 @ k31_binop_2 )
    & ( v1_funct_2 @ k31_binop_2 @ k1_numbers @ k1_numbers )
    & ( m2_relset_1 @ k31_binop_2 @ k1_numbers @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k31_binop_2) ).

thf(11189,plain,
    ( ( v1_funct_1 @ k31_binop_2 )
    & ( v1_funct_2 @ k31_binop_2 @ k1_numbers @ k1_numbers )
    & ( m2_relset_1 @ k31_binop_2 @ k1_numbers @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1805]) ).

thf(1309,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
                         => ( ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) @ ( k16_funct_3 @ A @ C @ B @ C @ D @ ( k6_partfun1 @ C ) ) @ ( k12_mcart_1 @ A @ C @ E @ F ) )
                            = ( k12_mcart_1 @ B @ C @ ( k2_funct_2 @ A @ B @ D @ E ) @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_borsuk_1) ).

thf(8800,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
                         => ( ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) @ ( k16_funct_3 @ A @ C @ B @ C @ D @ ( k6_partfun1 @ C ) ) @ ( k12_mcart_1 @ A @ C @ E @ F ) )
                            = ( k12_mcart_1 @ B @ C @ ( k2_funct_2 @ A @ B @ D @ E ) @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).

thf(2231,axiom,
    v1_xboole_0 @ k1_xboole_0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(13458,plain,
    v1_xboole_0 @ k1_xboole_0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2231]) ).

thf(2312,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( r2_hidden @ A @ ( a_2_1_domain_1 @ B @ C ) )
      <=> ? [D: $i] :
            ( ( m1_subset_1 @ D @ B )
            & ( A = D )
            & ( r2_hidden @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_domain_1) ).

thf(13735,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( ( r2_hidden @ A @ ( a_2_1_domain_1 @ B @ C ) )
         => ? [D: $i] :
              ( ( m1_subset_1 @ D @ B )
              & ( A = D )
              & ( r2_hidden @ D @ C ) ) )
        & ( ? [D: $i] :
              ( ( m1_subset_1 @ D @ B )
              & ( A = D )
              & ( r2_hidden @ D @ C ) )
         => ( r2_hidden @ A @ ( a_2_1_domain_1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2312]) ).

thf(723,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_relat_1 @ ( k1_funct_4 @ A @ B ) )
        & ( v1_funct_1 @ ( k1_funct_4 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_4) ).

thf(6128,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_relat_1 @ ( k1_funct_4 @ A @ B ) )
        & ( v1_funct_1 @ ( k1_funct_4 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(1502,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ B @ D @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_enumset1) ).

thf(9603,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ B @ D @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1502]) ).

thf(1092,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ~ ( ( r2_hidden @ C @ B )
          & ( ( k2_relat_1 @ D )
            = B )
          & ! [E: $i] :
              ~ ( ( r2_hidden @ E @ A )
                & ( ( k1_funct_1 @ D @ E )
                  = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_2) ).

thf(7809,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ~ ( ( r2_hidden @ C @ B )
          & ( ( k2_relat_1 @ D )
            = B )
          & ! [E: $i] :
              ~ ( ( r2_hidden @ E @ A )
                & ( ( k1_funct_1 @ D @ E )
                  = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).

thf(95,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( ( k1_funct_5 @ ( k1_relat_1 @ A ) )
          = ( k2_funct_5 @ ( k1_relat_1 @ ( k2_funct_4 @ A ) ) ) )
        & ( ( k2_funct_5 @ ( k1_relat_1 @ A ) )
          = ( k1_funct_5 @ ( k1_relat_1 @ ( k2_funct_4 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funct_5) ).

thf(3176,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( ( k1_funct_5 @ ( k1_relat_1 @ A ) )
          = ( k2_funct_5 @ ( k1_relat_1 @ ( k2_funct_4 @ A ) ) ) )
        & ( ( k2_funct_5 @ ( k1_relat_1 @ A ) )
          = ( k1_funct_5 @ ( k1_relat_1 @ ( k2_funct_4 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(1522,axiom,
    ! [A: $i] :
      ( ~ ( ~ ( v1_realset1 @ A )
          & ! [B: $i,C: $i] :
              ~ ( ( r2_hidden @ B @ A )
                & ( r2_hidden @ C @ A )
                & ( B != C ) ) )
      & ~ ( ? [B: $i,C: $i] :
              ( ( r2_hidden @ B @ A )
              & ( r2_hidden @ C @ A )
              & ( B != C ) )
          & ( v1_realset1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_realset1) ).

thf(9772,plain,
    ! [A: $i] :
      ( ~ ( ~ ( v1_realset1 @ A )
          & ! [B: $i,C: $i] :
              ~ ( ( r2_hidden @ B @ A )
                & ( r2_hidden @ C @ A )
                & ( B != C ) ) )
      & ~ ( ? [B: $i,C: $i] :
              ( ( r2_hidden @ B @ A )
              & ( r2_hidden @ C @ A )
              & ( B != C ) )
          & ( v1_realset1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1522]) ).

thf(317,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
      <=> ! [B: $i,C: $i] :
            ( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
              & ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
              & ( ( k1_funct_1 @ A @ B )
                = ( k1_funct_1 @ A @ C ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).

thf(4291,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( ( v2_funct_1 @ A )
         => ! [B: $i,C: $i] :
              ( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
                & ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
                & ( ( k1_funct_1 @ A @ B )
                  = ( k1_funct_1 @ A @ C ) ) )
             => ( B = C ) ) )
        & ( ! [B: $i,C: $i] :
              ( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
                & ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
                & ( ( k1_funct_1 @ A @ B )
                  = ( k1_funct_1 @ A @ C ) ) )
             => ( B = C ) )
         => ( v2_funct_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(1172,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
      = ( k2_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_xboole_1) ).

thf(8176,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
      = ( k2_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).

thf(2089,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ( ( A != k1_xboole_0 )
       => ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_subset_1) ).

thf(12768,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ( ( A != k1_xboole_0 )
       => ( m1_subset_1 @ ( k1_tarski @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2089]) ).

thf(907,axiom,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ? [B: $i] : ( m4_realset1 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m4_realset1) ).

thf(6967,plain,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ? [B: $i] : ( m4_realset1 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(2253,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_realset1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( v1_tex_2 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tex_2) ).

thf(13527,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_realset1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( v1_tex_2 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2253]) ).

thf(2291,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m2_finseq_1 @ C @ B )
             => ( m2_finseq_1 @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finseq_2) ).

thf(13661,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m2_finseq_1 @ C @ B )
             => ( m2_finseq_1 @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2291]) ).

thf(609,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( ( v1_relat_1 @ D )
                & ( v1_funct_1 @ D ) )
             => ! [E: $i] :
                  ( ( ( k7_relat_1 @ A @ C )
                    = ( k7_relat_1 @ B @ C ) )
                 => ( ( k7_relat_1 @ ( k4_funcop_1 @ D @ A @ E ) @ C )
                    = ( k7_relat_1 @ ( k4_funcop_1 @ D @ B @ E ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_funcop_1) ).

thf(5588,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( ( v1_relat_1 @ D )
                & ( v1_funct_1 @ D ) )
             => ! [E: $i] :
                  ( ( ( k7_relat_1 @ A @ C )
                    = ( k7_relat_1 @ B @ C ) )
                 => ( ( k7_relat_1 @ ( k4_funcop_1 @ D @ A @ E ) @ C )
                    = ( k7_relat_1 @ ( k4_funcop_1 @ D @ B @ E ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(326,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
       => ( ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_relat_1) ).

thf(4333,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
       => ( ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(2325,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k4_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_subset_1) ).

thf(13790,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k4_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2325]) ).

thf(381,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( k1_relat_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) )
        = ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_1) ).

thf(4653,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( k1_relat_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) )
        = ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(2588,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ( ( k15_ens_1 @ A @ B )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_ens_1) ).

thf(14914,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ( ( k15_ens_1 @ A @ B )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2588]) ).

thf(933,axiom,
    ! [A: $i,B: $i] : ( v1_fraenkel @ ( k1_funct_2 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_fraenkel) ).

thf(7091,plain,
    ! [A: $i,B: $i] : ( v1_fraenkel @ ( k1_funct_2 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).

thf(1255,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
                = ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_relat_1) ).

thf(8544,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( ( k5_relat_1 @ A @ ( k2_xboole_0 @ B @ C ) )
                = ( k2_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).

thf(126,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
            = k1_xboole_0 )
         => ( ( k1_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
            = ( k4_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ ( k6_relat_1 @ A ) ) ) ) )
        & ( ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ ( k6_relat_1 @ A ) )
            = k1_xboole_0 )
         => ( ( k2_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
            = ( k4_xboole_0 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ ( k6_relat_1 @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_sysrel) ).

thf(3311,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
            = k1_xboole_0 )
         => ( ( k1_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
            = ( k4_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ ( k6_relat_1 @ A ) ) ) ) )
        & ( ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ ( k6_relat_1 @ A ) )
            = k1_xboole_0 )
         => ( ( k2_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
            = ( k4_xboole_0 @ ( k2_relat_1 @ B ) @ ( k2_relat_1 @ ( k6_relat_1 @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(1982,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
        & ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
        & ~ ( r2_hidden @ k1_xboole_0 @ ( k1_tarski @ A ) )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
               => ( ( ( ( r2_hidden @ B @ ( k1_tarski @ A ) )
                      & ( r2_hidden @ C @ ( k1_tarski @ A ) ) )
                   => ( r2_hidden @ ( k5_subset_1 @ A @ B @ C ) @ ( k1_tarski @ A ) ) )
                  & ( ( ( r2_hidden @ B @ ( k1_tarski @ A ) )
                      & ( r1_tarski @ B @ C ) )
                   => ( r2_hidden @ C @ ( k1_tarski @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_card_fil) ).

thf(12151,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
        & ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
        & ~ ( r2_hidden @ k1_xboole_0 @ ( k1_tarski @ A ) )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
               => ( ( ( ( r2_hidden @ B @ ( k1_tarski @ A ) )
                      & ( r2_hidden @ C @ ( k1_tarski @ A ) ) )
                   => ( r2_hidden @ ( k5_subset_1 @ A @ B @ C ) @ ( k1_tarski @ A ) ) )
                  & ( ( ( r2_hidden @ B @ ( k1_tarski @ A ) )
                      & ( r1_tarski @ B @ C ) )
                   => ( r2_hidden @ C @ ( k1_tarski @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1982]) ).

thf(1315,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ A ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_xboole_1) ).

thf(8835,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ A ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).

thf(2284,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( B
          = ( k2_tarski @ k1_xboole_0 @ A ) )
       => ( ( ( k1_cantor_1 @ A @ B )
            = B )
          & ( ( k2_cantor_1 @ A @ B )
            = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_yellow_9) ).

thf(13635,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( B
          = ( k2_tarski @ k1_xboole_0 @ A ) )
       => ( ( ( k1_cantor_1 @ A @ B )
            = B )
          & ( ( k2_cantor_1 @ A @ B )
            = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2284]) ).

thf(2575,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( r2_hidden @ A @ ( a_3_7_domain_1 @ B @ C @ D ) )
      <=> ? [E: $i] :
            ( ( m1_subset_1 @ E @ B )
            & ( A = E )
            & ~ ( ( r2_hidden @ E @ C )
              <=> ( r2_hidden @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_7_domain_1) ).

thf(14841,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( ( r2_hidden @ A @ ( a_3_7_domain_1 @ B @ C @ D ) )
         => ? [E: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( A = E )
              & ~ ( ( ( r2_hidden @ E @ C )
                   => ( r2_hidden @ E @ D ) )
                  & ( ( r2_hidden @ E @ D )
                   => ( r2_hidden @ E @ C ) ) ) ) )
        & ( ? [E: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( A = E )
              & ~ ( ( ( r2_hidden @ E @ C )
                   => ( r2_hidden @ E @ D ) )
                  & ( ( r2_hidden @ E @ D )
                   => ( r2_hidden @ E @ C ) ) ) )
         => ( r2_hidden @ A @ ( a_3_7_domain_1 @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2575]) ).

thf(498,axiom,
    ! [A: $i] :
      ( ( k7_relat_1 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_relat_1) ).

thf(5166,plain,
    ! [A: $i] :
      ( ( k7_relat_1 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(791,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m1_relset_1 @ D @ A @ B )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ C )
        & ( m1_relset_1 @ E @ A @ C ) )
     => ( ( k14_funct_3 @ A @ B @ C @ D @ E )
        = ( k13_funct_3 @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k14_funct_3) ).

thf(6428,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m1_relset_1 @ D @ A @ B )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ C )
        & ( m1_relset_1 @ E @ A @ C ) )
     => ( ( k14_funct_3 @ A @ B @ C @ D @ E )
        = ( k13_funct_3 @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(315,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( v2_funct_1 @ C )
          & ( ( k2_relat_1 @ C )
            = B ) )
       => ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
          & ( v1_funct_2 @ ( k2_funct_1 @ C ) @ B @ A )
          & ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_funct_2) ).

thf(4276,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( v2_funct_1 @ C )
          & ( ( k2_relat_1 @ C )
            = B ) )
       => ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
          & ( v1_funct_2 @ ( k2_funct_1 @ C ) @ B @ A )
          & ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(2120,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( G
        = ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) )
    <=> ! [H: $i] :
          ( ( r2_hidden @ H @ G )
        <=> ~ ( ( H != A )
              & ( H != B )
              & ( H != C )
              & ( H != D )
              & ( H != E )
              & ( H != F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_enumset1) ).

thf(12906,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( G
          = ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) )
       => ! [H: $i] :
            ( ( ( r2_hidden @ H @ G )
             => ~ ( ( H != A )
                  & ( H != B )
                  & ( H != C )
                  & ( H != D )
                  & ( H != E )
                  & ( H != F ) ) )
            & ( ~ ( ( H != A )
                  & ( H != B )
                  & ( H != C )
                  & ( H != D )
                  & ( H != E )
                  & ( H != F ) )
             => ( r2_hidden @ H @ G ) ) ) )
      & ( ! [H: $i] :
            ( ( ( r2_hidden @ H @ G )
             => ~ ( ( H != A )
                  & ( H != B )
                  & ( H != C )
                  & ( H != D )
                  & ( H != E )
                  & ( H != F ) ) )
            & ( ~ ( ( H != A )
                  & ( H != B )
                  & ( H != C )
                  & ( H != D )
                  & ( H != E )
                  & ( H != F ) )
             => ( r2_hidden @ H @ G ) ) )
       => ( G
          = ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2120]) ).

thf(1324,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ B @ A )
        & ( m1_relset_1 @ D @ B @ A )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ B @ A )
        & ( m1_relset_1 @ E @ B @ A ) )
     => ( ( k6_funcop_1 @ A @ B @ C @ D @ E )
        = ( k3_funcop_1 @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_funcop_1) ).

thf(8864,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ B @ A )
        & ( m1_relset_1 @ D @ B @ A )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ B @ A )
        & ( m1_relset_1 @ E @ B @ A ) )
     => ( ( k6_funcop_1 @ A @ B @ C @ D @ E )
        = ( k3_funcop_1 @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).

thf(2295,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k7_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).

thf(13682,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k7_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2295]) ).

thf(1046,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_finset_1 @ A )
     => ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finset_1) ).

thf(7631,plain,
    ! [A: $i,B: $i] :
      ( ( v1_finset_1 @ A )
     => ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).

thf(221,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
       => ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finset_1) ).

thf(3846,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
       => ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(1451,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ A @ C )
        & ! [D: $i] :
            ( ( ( r1_tarski @ D @ B )
              & ( r1_tarski @ D @ C ) )
           => ( r1_tarski @ D @ A ) ) )
     => ( A
        = ( k3_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_xboole_1) ).

thf(9397,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ A @ C )
        & ! [D: $i] :
            ( ( ( r1_tarski @ D @ B )
              & ( r1_tarski @ D @ C ) )
           => ( r1_tarski @ D @ A ) ) )
     => ( A
        = ( k3_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).

thf(501,axiom,
    ! [A: $i,B: $i] :
      ( ( k5_enumset1 @ A @ A @ A @ A @ A @ A @ B )
      = ( k2_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_enumset1) ).

thf(5181,plain,
    ! [A: $i,B: $i] :
      ( ( k5_enumset1 @ A @ A @ A @ A @ A @ A @ B )
      = ( k2_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(2194,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_card_fil @ C @ A )
             => ~ ( ( r2_hidden @ B @ C )
                  & ( r2_hidden @ ( k1_card_fil @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_card_fil) ).

thf(13291,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_card_fil @ C @ A )
             => ~ ( ( r2_hidden @ B @ C )
                  & ( r2_hidden @ ( k1_card_fil @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2194]) ).

thf(925,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ~ ( ( r2_hidden @ C @ ( k9_relat_1 @ D @ A ) )
          & ! [E: $i] :
              ( ( m1_subset_1 @ E @ A )
             => ~ ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ D ) )
                  & ( C
                    = ( k1_funct_1 @ D @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_partfun1) ).

thf(7054,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ~ ( ( r2_hidden @ C @ ( k9_relat_1 @ D @ A ) )
          & ! [E: $i] :
              ( ( m1_subset_1 @ E @ A )
             => ~ ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ D ) )
                  & ( C
                    = ( k1_funct_1 @ D @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).

thf(580,axiom,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ( r1_tarski @ A @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_membered) ).

thf(5496,plain,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ( r1_tarski @ A @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(2199,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r1_tarski @ ( k2_funcop_1 @ A @ B ) @ ( k2_funcop_1 @ C @ D ) )
     => ( ( A = k1_xboole_0 )
        | ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_funct_4) ).

thf(13308,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r1_tarski @ ( k2_funcop_1 @ A @ B ) @ ( k2_funcop_1 @ C @ D ) )
     => ( ( A = k1_xboole_0 )
        | ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2199]) ).

thf(190,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k4_relat_1 @ ( k2_xboole_0 @ A @ B ) )
            = ( k2_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_relat_1) ).

thf(3622,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k4_relat_1 @ ( k2_xboole_0 @ A @ B ) )
            = ( k2_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(631,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_finset_1) ).

thf(5705,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(1194,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( v1_xboole_0 @ C )
     => ~ ( ( r1_tarski @ C @ A )
          & ( r1_tarski @ C @ B )
          & ( r1_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_xboole_1) ).

thf(8251,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( v1_xboole_0 @ C )
     => ~ ( ( r1_tarski @ C @ A )
          & ( r1_tarski @ C @ B )
          & ( r1_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).

thf(829,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( k3_mcart_1 @ A @ B @ C )
        = ( k3_mcart_1 @ D @ E @ F ) )
     => ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_mcart_1) ).

thf(6593,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( k3_mcart_1 @ A @ B @ C )
        = ( k3_mcart_1 @ D @ E @ F ) )
     => ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(396,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( r1_partfun1 @ B @ C )
              & ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
           => ( ( k1_funct_1 @ ( k1_funct_4 @ B @ C ) @ A )
              = ( k1_funct_1 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_4) ).

thf(4721,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( r1_partfun1 @ B @ C )
              & ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
           => ( ( k1_funct_1 @ ( k1_funct_4 @ B @ C ) @ A )
              = ( k1_funct_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(2076,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( ( k14_domain_1 @ A @ B @ C @ D )
        = ( k17_mcart_1 @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k14_domain_1) ).

thf(12696,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( ( k14_domain_1 @ A @ B @ C @ D )
        = ( k17_mcart_1 @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2076]) ).

thf(1653,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
             => ( ( ( r1_tarski @ B @ C )
                  & ( r1_xboole_0 @ D @ C ) )
               => ( r1_tarski @ B @ ( k3_subset_1 @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_subset_1) ).

thf(10391,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
             => ( ( ( r1_tarski @ B @ C )
                  & ( r1_xboole_0 @ D @ C ) )
               => ( r1_tarski @ B @ ( k3_subset_1 @ A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1653]) ).

thf(2161,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k3_pre_circ @ A @ B @ C )
        = ( k7_relat_1 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_pre_circ) ).

thf(13154,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k3_pre_circ @ A @ B @ C )
        = ( k7_relat_1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2161]) ).

thf(840,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( r1_tarski @ ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).

thf(6642,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( r1_tarski @ ( k2_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).

thf(845,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_membered @ A )
     => ( v1_membered @ ( k3_xboole_0 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc28_membered) ).

thf(6661,plain,
    ! [A: $i,B: $i] :
      ( ( v1_membered @ A )
     => ( v1_membered @ ( k3_xboole_0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(2511,axiom,
    ? [A: $i] :
      ( ( m2_relset_1 @ A @ f1_s2_relset_1 @ f2_s2_relset_1 )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s2_relset_1 )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ f2_s2_relset_1 )
             => ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
              <=> ( p1_s2_relset_1 @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_relset_1) ).

thf(14598,plain,
    ? [A: $i] :
      ( ( m2_relset_1 @ A @ f1_s2_relset_1 @ f2_s2_relset_1 )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s2_relset_1 )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ f2_s2_relset_1 )
             => ( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
                 => ( p1_s2_relset_1 @ B @ C ) )
                & ( ( p1_s2_relset_1 @ B @ C )
                 => ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2511]) ).

thf(653,axiom,
    ! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).

thf(5791,plain,
    ! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(1457,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( ( v1_funct_1 @ G )
                                & ( v1_funct_2 @ G @ ( k2_zfmisc_1 @ A @ B ) @ C )
                                & ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                             => ! [H: $i] :
                                  ( ( m2_finseq_1 @ H @ A )
                                 => ( ( H
                                      = ( k10_finseq_1 @ D @ E ) )
                                   => ( ( k4_funcop_1 @ G @ H @ F )
                                      = ( k10_finseq_1 @ ( k2_binop_1 @ A @ B @ C @ G @ D @ F ) @ ( k2_binop_1 @ A @ B @ C @ G @ E @ F ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t101_finseq_2) ).

thf(9426,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( ( v1_funct_1 @ G )
                                & ( v1_funct_2 @ G @ ( k2_zfmisc_1 @ A @ B ) @ C )
                                & ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                             => ! [H: $i] :
                                  ( ( m2_finseq_1 @ H @ A )
                                 => ( ( H
                                      = ( k10_finseq_1 @ D @ E ) )
                                   => ( ( k4_funcop_1 @ G @ H @ F )
                                      = ( k10_finseq_1 @ ( k2_binop_1 @ A @ B @ C @ G @ D @ F ) @ ( k2_binop_1 @ A @ B @ C @ G @ E @ F ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457]) ).

thf(2421,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( ( k1_relset_2 @ A @ B @ C )
        = ( k1_relset_2 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k1_relset_2) ).

thf(14153,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( ( k1_relset_2 @ A @ B @ C )
        = ( k1_relset_2 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2421]) ).

thf(619,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
                     => ( ( ( ( k5_mcart_1 @ A @ B @ C @ D )
                            = ( k5_mcart_1 @ A @ B @ C @ E ) )
                          & ( ( k6_mcart_1 @ A @ B @ C @ D )
                            = ( k6_mcart_1 @ A @ B @ C @ E ) )
                          & ( ( k7_mcart_1 @ A @ B @ C @ D )
                            = ( k7_mcart_1 @ A @ B @ C @ E ) ) )
                       => ( D = E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_domain_1) ).

thf(5620,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
                     => ( ( ( ( k5_mcart_1 @ A @ B @ C @ D )
                            = ( k5_mcart_1 @ A @ B @ C @ E ) )
                          & ( ( k6_mcart_1 @ A @ B @ C @ D )
                            = ( k6_mcart_1 @ A @ B @ C @ E ) )
                          & ( ( k7_mcart_1 @ A @ B @ C @ D )
                            = ( k7_mcart_1 @ A @ B @ C @ E ) ) )
                       => ( D = E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(182,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( ( k2_funct_1 @ ( k2_funct_1 @ A ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funct_1) ).

thf(3596,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( ( k2_funct_1 @ ( k2_funct_1 @ A ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(442,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G )
      = ( k2_xboole_0 @ ( k3_enumset1 @ A @ B @ C @ D @ E ) @ ( k2_tarski @ F @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_enumset1) ).

thf(4938,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G )
      = ( k2_xboole_0 @ ( k3_enumset1 @ A @ B @ C @ D @ E ) @ ( k2_tarski @ F @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(1712,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m1_relset_1 @ E @ A @ B )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ C @ D )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( ( r4_nattra_1 @ A @ B @ C @ D @ E @ F )
       => ( r4_nattra_1 @ A @ B @ C @ D @ F @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r4_nattra_1) ).

thf(10620,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m1_relset_1 @ E @ A @ B )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ C @ D )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( ( r4_nattra_1 @ A @ B @ C @ D @ E @ F )
       => ( r4_nattra_1 @ A @ B @ C @ D @ F @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1712]) ).

thf(520,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_mcart_1 @ A @ B @ C @ D )
      = ( k4_tarski @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_mcart_1) ).

thf(5263,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_mcart_1 @ A @ B @ C @ D )
      = ( k4_tarski @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(1039,axiom,
    ! [A: $i] :
      ( ( k5_xboole_0 @ A @ A )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_xboole_1) ).

thf(7604,plain,
    ! [A: $i] :
      ( ( k5_xboole_0 @ A @ A )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).

thf(1815,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ A )
         => ( ( k2_relset_2 @ A @ B @ C @ D )
            = ( k10_relset_1 @ A @ B @ C @ ( k1_tarski @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_2) ).

thf(11229,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ A )
         => ( ( k2_relset_2 @ A @ B @ C @ D )
            = ( k10_relset_1 @ A @ B @ C @ ( k1_tarski @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1815]) ).

thf(1887,axiom,
    ! [A: $i] :
      ( ( v1_funct_1 @ k1_xboole_0 )
      & ( v1_funct_2 @ k1_xboole_0 @ A @ k1_xboole_0 )
      & ( m2_relset_1 @ k1_xboole_0 @ A @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_functor0) ).

thf(11642,plain,
    ! [A: $i] :
      ( ( v1_funct_1 @ k1_xboole_0 )
      & ( v1_funct_2 @ k1_xboole_0 @ A @ k1_xboole_0 )
      & ( m2_relset_1 @ k1_xboole_0 @ A @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1887]) ).

thf(2410,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ? [C: $i] : ( m3_realset1 @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_realset1) ).

thf(14110,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ? [C: $i] : ( m3_realset1 @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2410]) ).

thf(1139,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ A )
                    & ( m2_relset_1 @ D @ A @ A ) )
                 => ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ D @ ( k6_partfun1 @ A ) ) @ C )
                    = ( k2_binop_1 @ A @ A @ A @ B @ ( k8_funct_2 @ A @ A @ D @ C ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funcop_1) ).

thf(8053,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ A )
                    & ( m2_relset_1 @ D @ A @ A ) )
                 => ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ D @ ( k6_partfun1 @ A ) ) @ C )
                    = ( k2_binop_1 @ A @ A @ A @ B @ ( k8_funct_2 @ A @ A @ D @ C ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).

thf(1159,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ ( k5_xboole_0 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_xboole_1) ).

thf(8132,plain,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ ( k5_xboole_0 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).

thf(1391,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k4_xboole_0 @ A @ B )
        = k1_xboole_0 )
    <=> ( r1_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).

thf(9100,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( k4_xboole_0 @ A @ B )
          = k1_xboole_0 )
       => ( r1_tarski @ A @ B ) )
      & ( ( r1_tarski @ A @ B )
       => ( ( k4_xboole_0 @ A @ B )
          = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391]) ).

thf(1116,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( ( C
                  = ( k5_relat_1 @ A @ B ) )
              <=> ! [D: $i,E: $i] :
                    ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
                  <=> ? [F: $i] :
                        ( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
                        & ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).

thf(7930,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( ( ( C
                    = ( k5_relat_1 @ A @ B ) )
                 => ! [D: $i,E: $i] :
                      ( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
                       => ? [F: $i] :
                            ( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
                            & ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) ) )
                      & ( ? [F: $i] :
                            ( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
                            & ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) )
                       => ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) )
                & ( ! [D: $i,E: $i] :
                      ( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
                       => ? [F: $i] :
                            ( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
                            & ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) ) )
                      & ( ? [F: $i] :
                            ( ( r2_hidden @ ( k4_tarski @ D @ F ) @ A )
                            & ( r2_hidden @ ( k4_tarski @ F @ E ) @ B ) )
                       => ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
                 => ( C
                    = ( k5_relat_1 @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).

thf(1893,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k1_finsub_1 @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_finsub_1) ).

thf(11666,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k1_finsub_1 @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1893]) ).

thf(270,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_funct_3 @ B ) ) )
       => ( ( k1_funct_1 @ ( k1_funct_3 @ B ) @ A )
          = ( k9_relat_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_3) ).

thf(4054,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k1_funct_3 @ B ) ) )
       => ( ( k1_funct_1 @ ( k1_funct_3 @ B ) @ A )
          = ( k9_relat_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(156,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
             => ! [D: $i] :
                  ( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
                 => ( ( ( k4_finseq_2 @ C @ A )
                      = ( k4_finseq_2 @ D @ B ) )
                   => ( C = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_pralg_1) ).

thf(3428,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
             => ! [D: $i] :
                  ( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
                 => ( ( ( k4_finseq_2 @ C @ A )
                      = ( k4_finseq_2 @ D @ B ) )
                   => ( C = D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(1725,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( v1_funct_1 @ ( k6_funct_3 @ A @ B ) )
        & ( v1_funct_2 @ ( k6_funct_3 @ A @ B ) @ B @ A )
        & ( m2_relset_1 @ ( k6_funct_3 @ A @ B ) @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_funct_3) ).

thf(10688,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( v1_funct_1 @ ( k6_funct_3 @ A @ B ) )
        & ( v1_funct_2 @ ( k6_funct_3 @ A @ B ) @ B @ A )
        & ( m2_relset_1 @ ( k6_funct_3 @ A @ B ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1725]) ).

thf(1007,axiom,
    ! [A: $i,B: $i] :
      ( ( k3_xboole_0 @ A @ B )
      = ( k3_xboole_0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

thf(7480,plain,
    ! [A: $i,B: $i] :
      ( ( k3_xboole_0 @ A @ B )
      = ( k3_xboole_0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).

thf(1388,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( k3_funct_2 @ A @ B @ C @ ( k2_funct_2 @ A @ B @ C @ A ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funct_2) ).

thf(9085,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( k3_funct_2 @ A @ B @ C @ ( k2_funct_2 @ A @ B @ C @ A ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388]) ).

thf(780,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( v1_classes2 @ B ) )
         => ( ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) )
            & ( v1_classes2 @ ( k2_xboole_0 @ A @ B ) )
            & ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
            & ( v1_classes2 @ ( k3_xboole_0 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_classes2) ).

thf(6395,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( v1_classes2 @ B ) )
         => ( ~ ( v1_xboole_0 @ ( k2_xboole_0 @ A @ B ) )
            & ( v1_classes2 @ ( k2_xboole_0 @ A @ B ) )
            & ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
            & ( v1_classes2 @ ( k3_xboole_0 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(1213,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_2) ).

thf(8346,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).

thf(2549,axiom,
    ? [A: $i] :
      ( ( v1_funct_1 @ A )
      & ( v1_funct_2 @ A @ f1_s10_funct_2 @ f2_s10_funct_2 )
      & ( m2_relset_1 @ A @ f1_s10_funct_2 @ f2_s10_funct_2 )
      & ( ( k8_funct_2 @ f1_s10_funct_2 @ f2_s10_funct_2 @ A @ f3_s10_funct_2 )
        = f4_s10_funct_2 )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s10_funct_2 )
         => ( ( B != f3_s10_funct_2 )
           => ( ( k8_funct_2 @ f1_s10_funct_2 @ f2_s10_funct_2 @ A @ B )
              = ( f5_s10_funct_2 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s10_funct_2) ).

thf(14719,plain,
    ? [A: $i] :
      ( ( v1_funct_1 @ A )
      & ( v1_funct_2 @ A @ f1_s10_funct_2 @ f2_s10_funct_2 )
      & ( m2_relset_1 @ A @ f1_s10_funct_2 @ f2_s10_funct_2 )
      & ( ( k8_funct_2 @ f1_s10_funct_2 @ f2_s10_funct_2 @ A @ f3_s10_funct_2 )
        = f4_s10_funct_2 )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s10_funct_2 )
         => ( ( B != f3_s10_funct_2 )
           => ( ( k8_funct_2 @ f1_s10_funct_2 @ f2_s10_funct_2 @ A @ B )
              = ( f5_s10_funct_2 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2549]) ).

thf(2408,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( k3_subset_1 @ A @ B )
            = ( a_2_2_domain_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_domain_1) ).

thf(14104,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( k3_subset_1 @ A @ B )
            = ( a_2_2_domain_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2408]) ).

thf(926,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ( ( k1_funct_4 @ D @ ( k2_partfun1 @ A @ B @ D @ C ) )
                = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_lattice2) ).

thf(7059,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ( ( k1_funct_4 @ D @ ( k2_partfun1 @ A @ B @ D @ C ) )
                = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).

thf(2169,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_setfam_1 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( ~ ( v1_xboole_0 @ ( k4_card_3 @ C ) )
        & ( v1_fraenkel @ ( k4_card_3 @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_card_3) ).

thf(13184,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_setfam_1 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( ~ ( v1_xboole_0 @ ( k4_card_3 @ C ) )
        & ( v1_fraenkel @ ( k4_card_3 @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2169]) ).

thf(997,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( m1_subset_1 @ B @ ( u1_cat_1 @ ( k12_ens_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_ens_1) ).

thf(7404,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( m1_subset_1 @ B @ ( u1_cat_1 @ ( k12_ens_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).

thf(1626,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_eqrel_1 @ B @ A )
     => ! [C: $i,D: $i,E: $i] :
          ( ( ( r2_hidden @ C @ D )
            & ( r2_hidden @ D @ B )
            & ( r2_hidden @ C @ E )
            & ( r2_hidden @ E @ B ) )
         => ( D = E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_pua2mss1) ).

thf(10239,plain,
    ! [A: $i,B: $i] :
      ( ( m1_eqrel_1 @ B @ A )
     => ! [C: $i,D: $i,E: $i] :
          ( ( ( r2_hidden @ C @ D )
            & ( r2_hidden @ D @ B )
            & ( r2_hidden @ C @ E )
            & ( r2_hidden @ E @ B ) )
         => ( D = E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1626]) ).

thf(976,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_finset_1 @ B )
     => ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_finset_1) ).

thf(7313,plain,
    ! [A: $i,B: $i] :
      ( ( v1_finset_1 @ B )
     => ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).

thf(757,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ( ( v2_funct_1 @ B )
      <=> ! [C: $i,D: $i] :
            ( ( ( r2_hidden @ C @ A )
              & ( r2_hidden @ D @ A )
              & ( ( k1_funct_1 @ B @ C )
                = ( k1_funct_1 @ B @ D ) ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_funct_2) ).

thf(6275,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ( ( ( v2_funct_1 @ B )
         => ! [C: $i,D: $i] :
              ( ( ( r2_hidden @ C @ A )
                & ( r2_hidden @ D @ A )
                & ( ( k1_funct_1 @ B @ C )
                  = ( k1_funct_1 @ B @ D ) ) )
             => ( C = D ) ) )
        & ( ! [C: $i,D: $i] :
              ( ( ( r2_hidden @ C @ A )
                & ( r2_hidden @ D @ A )
                & ( ( k1_funct_1 @ B @ C )
                  = ( k1_funct_1 @ B @ D ) ) )
             => ( C = D ) )
         => ( v2_funct_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(415,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ~ ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k3_tarski @ A ) )
          & ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ~ ( ( ( k1_relat_1 @ C )
                    = ( k1_relat_1 @ B ) )
                  & ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
                  & ( r2_hidden @ B @ ( k4_card_3 @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_pua2mss1) ).

thf(4814,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ~ ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k3_tarski @ A ) )
          & ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ~ ( ( ( k1_relat_1 @ C )
                    = ( k1_relat_1 @ B ) )
                  & ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
                  & ( r2_hidden @ B @ ( k4_card_3 @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(55,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m2_finseq_1 @ ( k12_finseq_1 @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_finseq_1) ).

thf(2978,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m2_finseq_1 @ ( k12_finseq_1 @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(1449,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_xboole_0 @ A @ D )
        & ( r1_xboole_0 @ B @ D )
        & ( r1_xboole_0 @ C @ D ) )
     => ( r1_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_xboole_1) ).

thf(9392,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_xboole_0 @ A @ D )
        & ( r1_xboole_0 @ B @ D )
        & ( r1_xboole_0 @ C @ D ) )
     => ( r1_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( B
              = ( k2_funct_4 @ A ) )
          <=> ( ! [C: $i] :
                  ( ( r2_hidden @ C @ ( k1_relat_1 @ B ) )
                <=> ? [D: $i,E: $i] :
                      ( ( C
                        = ( k4_tarski @ E @ D ) )
                      & ( r2_hidden @ ( k4_tarski @ D @ E ) @ ( k1_relat_1 @ A ) ) ) )
              & ! [C: $i,D: $i] :
                  ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( k1_relat_1 @ A ) )
                 => ( ( k1_funct_1 @ B @ ( k4_tarski @ D @ C ) )
                    = ( k1_funct_1 @ A @ ( k4_tarski @ C @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funct_4) ).

thf(2649,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( B
                = ( k2_funct_4 @ A ) )
             => ( ! [C: $i] :
                    ( ( ( r2_hidden @ C @ ( k1_relat_1 @ B ) )
                     => ? [D: $i,E: $i] :
                          ( ( C
                            = ( k4_tarski @ E @ D ) )
                          & ( r2_hidden @ ( k4_tarski @ D @ E ) @ ( k1_relat_1 @ A ) ) ) )
                    & ( ? [D: $i,E: $i] :
                          ( ( C
                            = ( k4_tarski @ E @ D ) )
                          & ( r2_hidden @ ( k4_tarski @ D @ E ) @ ( k1_relat_1 @ A ) ) )
                     => ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) )
                & ! [C: $i,D: $i] :
                    ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( k1_relat_1 @ A ) )
                   => ( ( k1_funct_1 @ B @ ( k4_tarski @ D @ C ) )
                      = ( k1_funct_1 @ A @ ( k4_tarski @ C @ D ) ) ) ) ) )
            & ( ( ! [C: $i] :
                    ( ( ( r2_hidden @ C @ ( k1_relat_1 @ B ) )
                     => ? [D: $i,E: $i] :
                          ( ( C
                            = ( k4_tarski @ E @ D ) )
                          & ( r2_hidden @ ( k4_tarski @ D @ E ) @ ( k1_relat_1 @ A ) ) ) )
                    & ( ? [D: $i,E: $i] :
                          ( ( C
                            = ( k4_tarski @ E @ D ) )
                          & ( r2_hidden @ ( k4_tarski @ D @ E ) @ ( k1_relat_1 @ A ) ) )
                     => ( r2_hidden @ C @ ( k1_relat_1 @ B ) ) ) )
                & ! [C: $i,D: $i] :
                    ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( k1_relat_1 @ A ) )
                   => ( ( k1_funct_1 @ B @ ( k4_tarski @ D @ C ) )
                      = ( k1_funct_1 @ A @ ( k4_tarski @ C @ D ) ) ) ) )
             => ( B
                = ( k2_funct_4 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(1647,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ~ ( ( B != k1_xboole_0 )
          & ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ~ ( r2_hidden @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_subset_1) ).

thf(10353,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ~ ( ( B != k1_xboole_0 )
          & ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ~ ( r2_hidden @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1647]) ).

thf(2257,axiom,
    ( ( ( v1_finset_1 @ f3_s22_fraenkel )
      & ( v1_finset_1 @ f4_s22_fraenkel ) )
   => ( v1_finset_1 @ a_0_39_fraenkel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s22_fraenkel) ).

thf(13539,plain,
    ( ( ( v1_finset_1 @ f3_s22_fraenkel )
      & ( v1_finset_1 @ f4_s22_fraenkel ) )
   => ( v1_finset_1 @ a_0_39_fraenkel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2257]) ).

thf(1150,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
         => ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t168_partfun1) ).

thf(8100,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
         => ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).

thf(48,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
          <=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
              & ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ ( k1_relat_1 @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).

thf(2836,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
             => ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
                & ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ ( k1_relat_1 @ B ) ) ) )
            & ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
                & ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ ( k1_relat_1 @ B ) ) )
             => ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(741,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
      & ( v1_relat_1 @ C )
      & ( v1_funct_1 @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).

thf(6207,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
      & ( v1_relat_1 @ C )
      & ( v1_funct_1 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(2465,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ( r1_tarski @ ( k2_ens_1 @ B ) @ ( k2_ens_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ens_1) ).

thf(14352,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ( r1_tarski @ ( k2_ens_1 @ B ) @ ( k2_ens_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2465]) ).

thf(1310,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
        = ( k7_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_relat_1) ).

thf(8803,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
        = ( k7_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).

thf(575,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( k7_relat_1 @ ( k7_relat_1 @ B @ A ) @ A )
        = ( k7_relat_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t101_relat_1) ).

thf(5479,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( k7_relat_1 @ ( k7_relat_1 @ B @ A ) @ A )
        = ( k7_relat_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(111,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ ( k1_funct_4 @ A @ B ) ) )
            & ( r1_tarski @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ ( k1_funct_4 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funct_4) ).

thf(3242,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ ( k1_funct_4 @ A @ B ) ) )
            & ( r1_tarski @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ ( k1_funct_4 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(1402,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_enumset1) ).

thf(9200,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402]) ).

thf(1914,axiom,
    ! [A: $i,B: $i,C: $i] : ( v1_finset_1 @ ( k1_enumset1 @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_finset_1) ).

thf(11742,plain,
    ! [A: $i,B: $i,C: $i] : ( v1_finset_1 @ ( k1_enumset1 @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1914]) ).

thf(605,axiom,
    ! [A: $i] : ( v2_funct_1 @ ( k6_relat_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_1) ).

thf(5576,plain,
    ! [A: $i] : ( v2_funct_1 @ ( k6_relat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(667,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k2_relat_1 @ ( k2_xboole_0 @ A @ B ) )
            = ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_relat_1) ).

thf(5850,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k2_relat_1 @ ( k2_xboole_0 @ A @ B ) )
            = ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(725,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( r1_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_3) ).

thf(6134,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( r1_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(2026,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_enumset1 @ A @ B @ C )
      = ( k1_enumset1 @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_enumset1) ).

thf(12410,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_enumset1 @ A @ B @ C )
      = ( k1_enumset1 @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2026]) ).

thf(1184,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( r2_hidden @ A @ B )
     => ( r1_xboole_0 @ ( k1_tarski @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_zfmisc_1) ).

thf(8219,plain,
    ! [A: $i,B: $i] :
      ( ~ ( r2_hidden @ A @ B )
     => ( r1_xboole_0 @ ( k1_tarski @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).

thf(1129,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
                    & ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
                 => ( ( k9_funcop_1 @ A @ C @ B @ ( k10_funcop_1 @ A @ B @ C @ D ) )
                    = ( k4_relat_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funcop_1) ).

thf(8013,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
                    & ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
                 => ( ( k9_funcop_1 @ A @ C @ B @ ( k10_funcop_1 @ A @ B @ C @ D ) )
                    = ( k4_relat_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).

thf(2108,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( m2_realset1 @ C @ A @ B )
          <=> ! [D: $i] :
                ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
               => ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_realset1) ).

thf(12859,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( m2_realset1 @ C @ A @ B )
             => ! [D: $i] :
                  ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
                 => ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
            & ( ! [D: $i] :
                  ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
                 => ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) )
             => ( m2_realset1 @ C @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2108]) ).

thf(1921,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ? [C: $i] :
          ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
          & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
          & ! [D: $i] :
              ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
             => ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_realset1) ).

thf(11828,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ? [C: $i] :
          ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
          & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
          & ! [D: $i] :
              ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ B @ B ) )
             => ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1921]) ).

thf(1442,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ ( k2_tarski @ B @ C ) )
    <=> ~ ( ( A != k1_xboole_0 )
          & ( A
           != ( k1_tarski @ B ) )
          & ( A
           != ( k1_tarski @ C ) )
          & ( A
           != ( k2_tarski @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_zfmisc_1) ).

thf(9348,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ ( k2_tarski @ B @ C ) )
       => ~ ( ( A != k1_xboole_0 )
            & ( A
             != ( k1_tarski @ B ) )
            & ( A
             != ( k1_tarski @ C ) )
            & ( A
             != ( k2_tarski @ B @ C ) ) ) )
      & ( ~ ( ( A != k1_xboole_0 )
            & ( A
             != ( k1_tarski @ B ) )
            & ( A
             != ( k1_tarski @ C ) )
            & ( A
             != ( k2_tarski @ B @ C ) ) )
       => ( r1_tarski @ A @ ( k2_tarski @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442]) ).

thf(985,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
        = ( k1_tarski @ A ) )
    <=> ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).

thf(7340,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
          = ( k1_tarski @ A ) )
       => ( A != B ) )
      & ( ( A != B )
       => ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
          = ( k1_tarski @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).

thf(1368,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
        = ( k2_tarski @ A @ B ) )
    <=> ( ~ ( r2_hidden @ A @ C )
        & ~ ( r2_hidden @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).

thf(9012,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
          = ( k2_tarski @ A @ B ) )
       => ( ~ ( r2_hidden @ A @ C )
          & ~ ( r2_hidden @ B @ C ) ) )
      & ( ( ~ ( r2_hidden @ A @ C )
          & ~ ( r2_hidden @ B @ C ) )
       => ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
          = ( k2_tarski @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368]) ).

thf(1236,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
     => ( ( k9_relat_1 @ C @ B )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_partfun1) ).

thf(8442,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
     => ( ( k9_relat_1 @ C @ B )
        = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).

thf(1105,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ B @ C )
            & ( m2_relset_1 @ E @ B @ C ) )
         => ( ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
              & ( ( k2_relat_1 @ D )
                = B ) )
           => ( ( ( C = k1_xboole_0 )
                & ( B != k1_xboole_0 ) )
              | ( ( v2_funct_1 @ D )
                & ( v2_funct_1 @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_funct_2) ).

thf(7878,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ B @ C )
            & ( m2_relset_1 @ E @ B @ C ) )
         => ( ( ( v2_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
              & ( ( k2_relat_1 @ D )
                = B ) )
           => ( ( ( C = k1_xboole_0 )
                & ( B != k1_xboole_0 ) )
              | ( ( v2_funct_1 @ D )
                & ( v2_funct_1 @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).

thf(2566,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
     => ~ ( v1_xboole_0 @ ( k2_funct_5 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_yellow_3) ).

thf(14784,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
     => ~ ( v1_xboole_0 @ ( k2_funct_5 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2566]) ).

thf(1333,axiom,
    ! [A: $i,B: $i] :
      ( ( v2_membered @ A )
     => ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
        & ( v2_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc29_membered) ).

thf(8891,plain,
    ! [A: $i,B: $i] :
      ( ( v2_membered @ A )
     => ( ( v1_membered @ ( k3_xboole_0 @ A @ B ) )
        & ( v2_membered @ ( k3_xboole_0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).

thf(2570,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ( m1_subset_1 @ ( a_4_2_domain_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_domain_1) ).

thf(14799,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ( m1_subset_1 @ ( a_4_2_domain_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2570]) ).

thf(551,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( k12_ens_1 @ A )
        = ( g1_cat_1 @ A @ ( k2_ens_1 @ A ) @ ( k8_ens_1 @ A ) @ ( k9_ens_1 @ A ) @ ( k10_ens_1 @ A ) @ ( k11_ens_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_ens_1) ).

thf(5374,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( k12_ens_1 @ A )
        = ( g1_cat_1 @ A @ ( k2_ens_1 @ A ) @ ( k8_ens_1 @ A ) @ ( k9_ens_1 @ A ) @ ( k10_ens_1 @ A ) @ ( k11_ens_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(700,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( k7_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
        = ( k3_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_relat_1) ).

thf(6033,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( k7_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
        = ( k3_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(2528,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) ) )
     => ? [C: $i] : ( m1_triang_1 @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_triang_1) ).

thf(14655,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) ) )
     => ? [C: $i] : ( m1_triang_1 @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2528]) ).

thf(916,axiom,
    ! [A: $i,B: $i] :
      ( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_xboole_1) ).

thf(7014,plain,
    ! [A: $i,B: $i] :
      ( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(2030,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( ( k15_domain_1 @ A @ B @ C @ D )
        = ( k18_mcart_1 @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k15_domain_1) ).

thf(12429,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( ( k15_domain_1 @ A @ B @ C @ D )
        = ( k18_mcart_1 @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2030]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
     => ( m1_subset_1 @ ( k6_setwiseo @ A @ B @ C ) @ ( k5_finsub_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setwiseo) ).

thf(2598,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
     => ( m1_subset_1 @ ( k6_setwiseo @ A @ B @ C ) @ ( k5_finsub_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(137,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
      <=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k1_relat_1 @ ( k2_funct_4 @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funct_4) ).

thf(3354,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
         => ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k1_relat_1 @ ( k2_funct_4 @ C ) ) ) )
        & ( ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k1_relat_1 @ ( k2_funct_4 @ C ) ) )
         => ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(2401,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ( r2_zfrefle1 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r2_zfrefle1) ).

thf(14067,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ( r2_zfrefle1 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2401]) ).

thf(553,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( k2_xboole_0 @ A @ B ) )
    <=> ! [D: $i] :
          ( ( r2_hidden @ D @ C )
        <=> ( ( r2_hidden @ D @ A )
            | ( r2_hidden @ D @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).

thf(5380,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C
          = ( k2_xboole_0 @ A @ B ) )
       => ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ( ( r2_hidden @ D @ A )
                | ( r2_hidden @ D @ B ) ) )
            & ( ( ( r2_hidden @ D @ A )
                | ( r2_hidden @ D @ B ) )
             => ( r2_hidden @ D @ C ) ) ) )
      & ( ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ( ( r2_hidden @ D @ A )
                | ( r2_hidden @ D @ B ) ) )
            & ( ( ( r2_hidden @ D @ A )
                | ( r2_hidden @ D @ B ) )
             => ( r2_hidden @ D @ C ) ) )
       => ( C
          = ( k2_xboole_0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(2021,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( r2_hidden @ D @ B )
               => ( r1_tarski @ C @ D ) )
           => ( r1_tarski @ C @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_mssubfam) ).

thf(12378,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( r2_hidden @ D @ B )
               => ( r1_tarski @ C @ D ) )
           => ( r1_tarski @ C @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2021]) ).

thf(1986,axiom,
    ! [A: $i] : ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finsub_1) ).

thf(12164,plain,
    ! [A: $i] : ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1986]) ).

thf(1474,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ A @ B )
      = ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_xboole_1) ).

thf(9498,plain,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ A @ B )
      = ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474]) ).

thf(512,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_subset_1) ).

thf(5234,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(2526,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( v1_xboole_0 @ ( k7_setfam_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_setfam_1) ).

thf(14649,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( v1_xboole_0 @ ( k7_setfam_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2526]) ).

thf(581,axiom,
    ! [A: $i] :
      ( ? [B: $i,C: $i] :
          ( A
          = ( k4_tarski @ B @ C ) )
     => ! [B: $i] :
          ( ( B
            = ( k2_mcart_1 @ A ) )
        <=> ! [C: $i,D: $i] :
              ( ( A
                = ( k4_tarski @ C @ D ) )
             => ( B = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_mcart_1) ).

thf(5498,plain,
    ! [A: $i] :
      ( ? [B: $i,C: $i] :
          ( A
          = ( k4_tarski @ B @ C ) )
     => ! [B: $i] :
          ( ( ( B
              = ( k2_mcart_1 @ A ) )
           => ! [C: $i,D: $i] :
                ( ( A
                  = ( k4_tarski @ C @ D ) )
               => ( B = D ) ) )
          & ( ! [C: $i,D: $i] :
                ( ( A
                  = ( k4_tarski @ C @ D ) )
               => ( B = D ) )
           => ( B
              = ( k2_mcart_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(1857,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( r2_hidden @ A @ ( a_1_0_lattice5 @ B ) )
      <=> ? [C: $i] :
            ( ( m1_subset_1 @ C @ B )
            & ( A
              = ( k2_zfmisc_1 @ C @ C ) )
            & ( r2_hidden @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_lattice5) ).

thf(11474,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( ( r2_hidden @ A @ ( a_1_0_lattice5 @ B ) )
         => ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A
                = ( k2_zfmisc_1 @ C @ C ) )
              & ( r2_hidden @ C @ B ) ) )
        & ( ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A
                = ( k2_zfmisc_1 @ C @ C ) )
              & ( r2_hidden @ C @ B ) )
         => ( r2_hidden @ A @ ( a_1_0_lattice5 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1857]) ).

thf(1495,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ( ( ( r3_binop_1 @ A @ C @ B )
                  & ( r3_binop_1 @ A @ D @ B ) )
               => ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_binop_1) ).

thf(9581,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ( ( ( r3_binop_1 @ A @ C @ B )
                  & ( r3_binop_1 @ A @ D @ B ) )
               => ( C = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1495]) ).

thf(742,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) )
      = ( k2_tarski @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_mcart_1) ).

thf(6211,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) )
      = ( k2_tarski @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(2057,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ D )
        & ( r2_hidden @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_ordinal1) ).

thf(12558,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ D )
        & ( r2_hidden @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2057]) ).

thf(306,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k9_finseq_1 @ A )
     != ( k10_finseq_1 @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_finseq_3) ).

thf(4237,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k9_finseq_1 @ A )
     != ( k10_finseq_1 @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(1507,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E
        = ( k2_enumset1 @ A @ B @ C @ D ) )
    <=> ! [F: $i] :
          ( ( r2_hidden @ F @ E )
        <=> ~ ( ( F != A )
              & ( F != B )
              & ( F != C )
              & ( F != D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_enumset1) ).

thf(9630,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E
          = ( k2_enumset1 @ A @ B @ C @ D ) )
       => ! [F: $i] :
            ( ( ( r2_hidden @ F @ E )
             => ~ ( ( F != A )
                  & ( F != B )
                  & ( F != C )
                  & ( F != D ) ) )
            & ( ~ ( ( F != A )
                  & ( F != B )
                  & ( F != C )
                  & ( F != D ) )
             => ( r2_hidden @ F @ E ) ) ) )
      & ( ! [F: $i] :
            ( ( ( r2_hidden @ F @ E )
             => ~ ( ( F != A )
                  & ( F != B )
                  & ( F != C )
                  & ( F != D ) ) )
            & ( ~ ( ( F != A )
                  & ( F != B )
                  & ( F != C )
                  & ( F != D ) )
             => ( r2_hidden @ F @ E ) ) )
       => ( E
          = ( k2_enumset1 @ A @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1507]) ).

thf(148,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ B ) )
      <=> ? [D: $i] :
            ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
            & ( r2_hidden @ ( k4_tarski @ D @ A ) @ C )
            & ( r2_hidden @ D @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).

thf(3390,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( ( r2_hidden @ A @ ( k9_relat_1 @ C @ B ) )
         => ? [D: $i] :
              ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
              & ( r2_hidden @ ( k4_tarski @ D @ A ) @ C )
              & ( r2_hidden @ D @ B ) ) )
        & ( ? [D: $i] :
              ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
              & ( r2_hidden @ ( k4_tarski @ D @ A ) @ C )
              & ( r2_hidden @ D @ B ) )
         => ( r2_hidden @ A @ ( k9_relat_1 @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(1011,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_xboole_1) ).

thf(7495,plain,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).

thf(1686,axiom,
    ? [A: $i] :
      ~ ( v2_setfam_1 @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_setfam_1) ).

thf(10518,plain,
    ? [A: $i] :
      ~ ( v2_setfam_1 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1686]) ).

thf(2494,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
     => ( m1_subset_1 @ ( k17_domain_1 @ A @ B @ C @ D ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_domain_1) ).

thf(14494,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
     => ( m1_subset_1 @ ( k17_domain_1 @ A @ B @ C @ D ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2494]) ).

thf(2209,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( r1_tarski @ ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) ) @ ( k3_subset_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_subset_1) ).

thf(13376,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( r1_tarski @ ( k3_subset_1 @ A @ ( k4_subset_1 @ A @ B @ C ) ) @ ( k3_subset_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2209]) ).

thf(1379,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ C @ B ) )
     => ( ( k2_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_zfmisc_1) ).

thf(9053,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ C @ B ) )
     => ( ( k2_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379]) ).

thf(1235,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) )
      = ( k1_tarski @ ( k4_mcart_1 @ A @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_mcart_1) ).

thf(8439,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) @ ( k1_tarski @ D ) )
      = ( k1_tarski @ ( k4_mcart_1 @ A @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).

thf(1804,axiom,
    ! [A: $i] :
      ( ( v1_setfam_1 @ A )
    <=> ~ ( r2_hidden @ k1_xboole_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_setfam_1) ).

thf(11184,plain,
    ! [A: $i] :
      ( ( ( v1_setfam_1 @ A )
       => ~ ( r2_hidden @ k1_xboole_0 @ A ) )
      & ( ~ ( r2_hidden @ k1_xboole_0 @ A )
       => ( v1_setfam_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1804]) ).

thf(1334,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
    <=> ! [B: $i] :
          ~ ( ( r2_hidden @ B @ A )
            & ! [C: $i,D: $i] :
                ( B
               != ( k4_tarski @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).

thf(8896,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
       => ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i] :
                  ( B
                 != ( k4_tarski @ C @ D ) ) ) )
      & ( ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i] :
                  ( B
                 != ( k4_tarski @ C @ D ) ) )
       => ( v1_relat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).

thf(993,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( ( v1_xboole_0 @ ( k2_relat_1 @ A ) )
        & ( v1_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).

thf(7385,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( ( v1_xboole_0 @ ( k2_relat_1 @ A ) )
        & ( v1_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).

thf(1596,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( v1_funct_1 @ ( k9_relset_1 @ A @ B @ C @ D ) )
        & ( m2_relset_1 @ ( k9_relset_1 @ A @ B @ C @ D ) @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_partfun1) ).

thf(10122,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( v1_funct_1 @ ( k9_relset_1 @ A @ B @ C @ D ) )
        & ( m2_relset_1 @ ( k9_relset_1 @ A @ B @ C @ D ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1596]) ).

thf(2294,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ k9_zf_lang ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ k9_zf_lang ) )
             => ( ( ( r1_zfrefle1 @ A @ B )
                  & ( r1_zfrefle1 @ A @ C ) )
               => ( r1_zfrefle1 @ A @ ( k4_subset_1 @ k9_zf_lang @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_zfrefle1) ).

thf(13680,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ k9_zf_lang ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ k9_zf_lang ) )
             => ( ( ( r1_zfrefle1 @ A @ B )
                  & ( r1_zfrefle1 @ A @ C ) )
               => ( r1_zfrefle1 @ A @ ( k4_subset_1 @ k9_zf_lang @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2294]) ).

thf(1664,axiom,
    ! [A: $i] :
    ? [B: $i] : ( m2_finseq_1 @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_finseq_1) ).

thf(10438,plain,
    ! [A: $i] :
    ? [B: $i] : ( m2_finseq_1 @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1664]) ).

thf(2189,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ B )
        & ( m1_subset_1 @ G @ C )
        & ( m1_subset_1 @ H @ D ) )
     => ( m1_subset_1 @ ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_domain_1) ).

thf(13277,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ B )
        & ( m1_subset_1 @ G @ C )
        & ( m1_subset_1 @ H @ D ) )
     => ( m1_subset_1 @ ( k5_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2189]) ).

thf(1748,axiom,
    ( ~ ( v1_xboole_0 @ k5_urysohn1 )
    & ( v1_membered @ k5_urysohn1 )
    & ( v2_membered @ k5_urysohn1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_urysohn1) ).

thf(10879,plain,
    ( ~ ( v1_xboole_0 @ k5_urysohn1 )
    & ( v1_membered @ k5_urysohn1 )
    & ( v2_membered @ k5_urysohn1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1748]) ).

thf(304,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k2_tarski @ B @ C ) @ D ) )
     => ( ( ( ( k1_mcart_1 @ A )
            = B )
          | ( ( k1_mcart_1 @ A )
            = C ) )
        & ( r2_hidden @ ( k2_mcart_1 @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_mcart_1) ).

thf(4231,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k2_tarski @ B @ C ) @ D ) )
     => ( ( ( ( k1_mcart_1 @ A )
            = B )
          | ( ( k1_mcart_1 @ A )
            = C ) )
        & ( r2_hidden @ ( k2_mcart_1 @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(2244,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k5_classes2 @ A @ B @ C )
        = ( k2_tarski @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_classes2) ).

thf(13500,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k5_classes2 @ A @ B @ C )
        = ( k2_tarski @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2244]) ).

thf(931,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ C )
        & ( v4_finsub_1 @ C ) )
     => ( ( ( m1_subset_1 @ A @ C )
          & ( m1_subset_1 @ B @ C ) )
       => ( m1_subset_1 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finsub_1) ).

thf(7086,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ C )
        & ( v4_finsub_1 @ C ) )
     => ( ( ( m1_subset_1 @ A @ C )
          & ( m1_subset_1 @ B @ C ) )
       => ( m1_subset_1 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(2499,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
     => ( m1_subset_1 @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relset_2) ).

thf(14526,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
     => ( m1_subset_1 @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2499]) ).

thf(1113,axiom,
    ! [A: $i,B: $i] :
      ( ( k1_funct_2 @ A @ ( k1_tarski @ B ) )
      = ( k1_tarski @ ( k2_funcop_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_5) ).

thf(7913,plain,
    ! [A: $i,B: $i] :
      ( ( k1_funct_2 @ A @ ( k1_tarski @ B ) )
      = ( k1_tarski @ ( k2_funcop_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).

thf(533,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
        = ( k1_tarski @ A ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_zfmisc_1) ).

thf(5305,plain,
    ! [A: $i,B: $i] :
      ( ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
        = ( k1_tarski @ A ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(2164,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ C )
                    & ( m2_relset_1 @ D @ B @ C ) )
                 => ( ( ( C = k1_xboole_0 )
                     => ( B = k1_xboole_0 ) )
                   => ( r2_hidden @ ( k1_domain_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k1_domain_1 @ A @ A @ B @ C ) @ D ) @ ( k2_ens_1 @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_ens_1) ).

thf(13167,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ C )
                    & ( m2_relset_1 @ D @ B @ C ) )
                 => ( ( ( C = k1_xboole_0 )
                     => ( B = k1_xboole_0 ) )
                   => ( r2_hidden @ ( k1_domain_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k1_domain_1 @ A @ A @ B @ C ) @ D ) @ ( k2_ens_1 @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2164]) ).

thf(893,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( r2_hidden @ A @ B )
     => ( ( k4_xboole_0 @ ( k2_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_zfmisc_1) ).

thf(6908,plain,
    ! [A: $i,B: $i] :
      ( ~ ( r2_hidden @ A @ B )
     => ( ( k4_xboole_0 @ ( k2_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k1_tarski @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(2365,axiom,
    ? [A: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s3_subset_1 ) )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s3_subset_1 )
         => ( ( r2_hidden @ B @ A )
          <=> ( p1_s3_subset_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_subset_1) ).

thf(13943,plain,
    ? [A: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s3_subset_1 ) )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s3_subset_1 )
         => ( ( ( r2_hidden @ B @ A )
             => ( p1_s3_subset_1 @ B ) )
            & ( ( p1_s3_subset_1 @ B )
             => ( r2_hidden @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2365]) ).

thf(1639,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( r2_hidden @ ( k4_tarski @ ( k4_tarski @ C @ D ) @ B ) @ ( k2_ens_1 @ A ) )
             => ( ( ( D = k1_xboole_0 )
                 => ( C = k1_xboole_0 ) )
                & ( v1_funct_1 @ B )
                & ( v1_funct_2 @ B @ C @ D )
                & ( m2_relset_1 @ B @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ens_1) ).

thf(10302,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( r2_hidden @ ( k4_tarski @ ( k4_tarski @ C @ D ) @ B ) @ ( k2_ens_1 @ A ) )
             => ( ( ( D = k1_xboole_0 )
                 => ( C = k1_xboole_0 ) )
                & ( v1_funct_1 @ B )
                & ( v1_funct_2 @ B @ C @ D )
                & ( m2_relset_1 @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1639]) ).

thf(150,axiom,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k5_numbers )
     => ( ~ ( v1_xboole_0 @ ( k3_urysohn1 @ A ) )
        & ( v1_membered @ ( k3_urysohn1 @ A ) )
        & ( v2_membered @ ( k3_urysohn1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_urysohn1) ).

thf(3409,plain,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k5_numbers )
     => ( ~ ( v1_xboole_0 @ ( k3_urysohn1 @ A ) )
        & ( v1_membered @ ( k3_urysohn1 @ A ) )
        & ( v2_membered @ ( k3_urysohn1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(1922,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ A )
                     => ! [G: $i] :
                          ( ( m1_subset_1 @ G @ A )
                         => ! [H: $i] :
                              ( ( m1_subset_1 @ H @ A )
                             => ( ( A != k1_xboole_0 )
                               => ( m1_subset_1 @ ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_subset_1) ).

thf(11833,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ A )
                     => ! [G: $i] :
                          ( ( m1_subset_1 @ G @ A )
                         => ! [H: $i] :
                              ( ( m1_subset_1 @ H @ A )
                             => ( ( A != k1_xboole_0 )
                               => ( m1_subset_1 @ ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1922]) ).

thf(200,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_relat_1 @ E )
        & ( v1_funct_1 @ E ) )
     => ! [F: $i] :
          ( ( ( v1_relat_1 @ F )
            & ( v1_funct_1 @ F ) )
         => ( ( r2_hidden @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) @ ( k1_relat_1 @ ( k3_funct_4 @ E @ F ) ) )
          <=> ( ( r2_hidden @ ( k4_tarski @ A @ C ) @ ( k1_relat_1 @ E ) )
              & ( r2_hidden @ ( k4_tarski @ B @ D ) @ ( k1_relat_1 @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_4) ).

thf(3692,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_relat_1 @ E )
        & ( v1_funct_1 @ E ) )
     => ! [F: $i] :
          ( ( ( v1_relat_1 @ F )
            & ( v1_funct_1 @ F ) )
         => ( ( ( r2_hidden @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) @ ( k1_relat_1 @ ( k3_funct_4 @ E @ F ) ) )
             => ( ( r2_hidden @ ( k4_tarski @ A @ C ) @ ( k1_relat_1 @ E ) )
                & ( r2_hidden @ ( k4_tarski @ B @ D ) @ ( k1_relat_1 @ F ) ) ) )
            & ( ( ( r2_hidden @ ( k4_tarski @ A @ C ) @ ( k1_relat_1 @ E ) )
                & ( r2_hidden @ ( k4_tarski @ B @ D ) @ ( k1_relat_1 @ F ) ) )
             => ( r2_hidden @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) @ ( k1_relat_1 @ ( k3_funct_4 @ E @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(1714,axiom,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ k1_numbers @ k1_numbers )
        & ( m2_relset_1 @ A @ k1_numbers @ k1_numbers ) )
     => ( ( A = k32_binop_2 )
      <=> ! [B: $i] :
            ( ( m1_subset_1 @ B @ k1_numbers )
           => ( ( k8_funct_2 @ k1_numbers @ k1_numbers @ A @ B )
              = ( k8_binop_2 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_binop_2) ).

thf(10629,plain,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ k1_numbers @ k1_numbers )
        & ( m2_relset_1 @ A @ k1_numbers @ k1_numbers ) )
     => ( ( ( A = k32_binop_2 )
         => ! [B: $i] :
              ( ( m1_subset_1 @ B @ k1_numbers )
             => ( ( k8_funct_2 @ k1_numbers @ k1_numbers @ A @ B )
                = ( k8_binop_2 @ B ) ) ) )
        & ( ! [B: $i] :
              ( ( m1_subset_1 @ B @ k1_numbers )
             => ( ( k8_funct_2 @ k1_numbers @ k1_numbers @ A @ B )
                = ( k8_binop_2 @ B ) ) )
         => ( A = k32_binop_2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1714]) ).

thf(2520,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( C
              = ( a_2_0_cantor_1 @ A @ B ) )
           => ( ( k8_setfam_1 @ A @ C )
              = ( k8_setfam_1 @ A @ ( k5_setfam_1 @ ( k1_zfmisc_1 @ A ) @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_cantor_1) ).

thf(14634,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( C
              = ( a_2_0_cantor_1 @ A @ B ) )
           => ( ( k8_setfam_1 @ A @ C )
              = ( k8_setfam_1 @ A @ ( k5_setfam_1 @ ( k1_zfmisc_1 @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2520]) ).

thf(2007,axiom,
    ! [A: $i] :
      ( ( k6_lattice5 @ A )
      = ( k2_xboole_0 @ A @ ( k1_enumset1 @ ( k1_tarski @ A ) @ ( k1_tarski @ ( k1_tarski @ A ) ) @ ( k1_tarski @ ( k1_tarski @ ( k1_tarski @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_lattice5) ).

thf(12310,plain,
    ! [A: $i] :
      ( ( k6_lattice5 @ A )
      = ( k2_xboole_0 @ A @ ( k1_enumset1 @ ( k1_tarski @ A ) @ ( k1_tarski @ ( k1_tarski @ A ) ) @ ( k1_tarski @ ( k1_tarski @ ( k1_tarski @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2007]) ).

thf(2310,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_realset1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ~ ( v1_xboole_0 @ B )
           => ( ~ ( v1_xboole_0 @ B )
              & ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_tex_2) ).

thf(13731,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_realset1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ~ ( v1_xboole_0 @ B )
           => ( ~ ( v1_xboole_0 @ B )
              & ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2310]) ).

thf(2414,axiom,
    ! [A: $i] : ( m1_subset_1 @ ( k8_subset_1 @ A ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_subset_1) ).

thf(14125,plain,
    ! [A: $i] : ( m1_subset_1 @ ( k8_subset_1 @ A ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2414]) ).

thf(1147,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A != B )
     => ( ( k2_relat_1 @ ( k4_funct_4 @ A @ B @ C @ D ) )
        = ( k2_tarski @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_4) ).

thf(8090,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A != B )
     => ( ( k2_relat_1 @ ( k4_funct_4 @ A @ B @ C @ D ) )
        = ( k2_tarski @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).

thf(1705,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k11_classes2 @ A @ B @ C )
        = ( k2_zfmisc_1 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k11_classes2) ).

thf(10588,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k11_classes2 @ A @ B @ C )
        = ( k2_zfmisc_1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1705]) ).

thf(1500,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( k12_mcart_1 @ A @ B @ C @ D )
        = ( k2_zfmisc_1 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k12_mcart_1) ).

thf(9598,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( k12_mcart_1 @ A @ B @ C @ D )
        = ( k2_zfmisc_1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1500]) ).

thf(2332,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
        & ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) ) )
     => ( ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H )
        = ( k4_zfmisc_1 @ E @ F @ G @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k14_mcart_1) ).

thf(13804,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
        & ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) ) )
     => ( ( k14_mcart_1 @ A @ B @ C @ D @ E @ F @ G @ H )
        = ( k4_zfmisc_1 @ E @ F @ G @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2332]) ).

thf(1882,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ A @ C )
       => ( ( v1_funct_1 @ D )
          & ( m2_relset_1 @ D @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_partfun1) ).

thf(11610,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ A @ C )
       => ( ( v1_funct_1 @ D )
          & ( m2_relset_1 @ D @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1882]) ).

thf(2272,axiom,
    ! [A: $i] :
      ( ( v1_funct_1 @ ( k9_setwiseo @ A ) )
      & ( v1_funct_2 @ ( k9_setwiseo @ A ) @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) )
      & ( m2_relset_1 @ ( k9_setwiseo @ A ) @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_setwiseo) ).

thf(13591,plain,
    ! [A: $i] :
      ( ( v1_funct_1 @ ( k9_setwiseo @ A ) )
      & ( v1_funct_2 @ ( k9_setwiseo @ A ) @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) )
      & ( m2_relset_1 @ ( k9_setwiseo @ A ) @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2272]) ).

thf(1612,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ( ( k10_setwiseo @ A @ B @ ( k2_setwiseo @ A @ D ) @ C )
                = ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_setwiseo) ).

thf(10180,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ( ( k10_setwiseo @ A @ B @ ( k2_setwiseo @ A @ D ) @ C )
                = ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1612]) ).

thf(1163,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ! [B: $i,C: $i] :
            ( ( k9_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) )
            = ( k4_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
       => ( v2_funct_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_funct_1) ).

thf(8144,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ! [B: $i,C: $i] :
            ( ( k9_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) )
            = ( k4_xboole_0 @ ( k9_relat_1 @ A @ B ) @ ( k9_relat_1 @ A @ C ) ) )
       => ( v2_funct_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).

thf(549,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ A )
                    & ( m2_relset_1 @ D @ A @ A ) )
                 => ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ D ) @ C )
                    = ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k8_funct_2 @ A @ A @ D @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funcop_1) ).

thf(5369,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ A )
                    & ( m2_relset_1 @ D @ A @ A ) )
                 => ( ( k8_funct_2 @ A @ A @ ( k6_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ D ) @ C )
                    = ( k2_binop_1 @ A @ A @ A @ B @ C @ ( k8_funct_2 @ A @ A @ D @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(2335,axiom,
    m1_subset_1 @ a_0_0_domain_1 @ ( k1_zfmisc_1 @ f1_s7_domain_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s7_domain_1) ).

thf(13822,plain,
    m1_subset_1 @ a_0_0_domain_1 @ ( k1_zfmisc_1 @ f1_s7_domain_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2335]) ).

thf(1094,axiom,
    m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_numbers) ).

thf(7826,plain,
    m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).

thf(2299,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
     => ? [D: $i] : ( m1_nat_lat @ D @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_nat_lat) ).

thf(13693,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
     => ? [D: $i] : ( m1_nat_lat @ D @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2299]) ).

thf(463,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
     != k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_zfmisc_1) ).

thf(5026,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
     != k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(275,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( ( k4_relset_1 @ A @ B @ C )
        = ( k1_relat_1 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).

thf(4069,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( ( k4_relset_1 @ A @ B @ C )
        = ( k1_relat_1 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(2203,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( r2_hidden @ A @ ( a_1_2_ens_1 @ B ) )
      <=> ? [C: $i,D: $i] :
            ( ( m1_subset_1 @ C @ B )
            & ( m1_subset_1 @ D @ B )
            & ( A
              = ( k7_ens_1 @ B @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_2_ens_1) ).

thf(13340,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( ( r2_hidden @ A @ ( a_1_2_ens_1 @ B ) )
         => ? [C: $i,D: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( m1_subset_1 @ D @ B )
              & ( A
                = ( k7_ens_1 @ B @ C @ D ) ) ) )
        & ( ? [C: $i,D: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( m1_subset_1 @ D @ B )
              & ( A
                = ( k7_ens_1 @ B @ C @ D ) ) )
         => ( r2_hidden @ A @ ( a_1_2_ens_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2203]) ).

thf(240,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ C ) )
     => ( ( ( k1_mcart_1 @ A )
          = B )
        & ( r2_hidden @ ( k2_mcart_1 @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_mcart_1) ).

thf(3920,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ C ) )
     => ( ( ( k1_mcart_1 @ A )
          = B )
        & ( r2_hidden @ ( k2_mcart_1 @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(2241,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( v1_classes2 @ B ) )
         => ~ ( ~ ( r2_hidden @ A @ B )
              & ( A != B )
              & ~ ( r2_hidden @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_classes2) ).

thf(13490,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( v1_classes2 @ B ) )
         => ~ ( ~ ( r2_hidden @ A @ B )
              & ( A != B )
              & ~ ( r2_hidden @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2241]) ).

thf(2069,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
          ( ( ( g2_quantal1 @ A @ B @ C @ D @ E )
            = ( g2_quantal1 @ F @ G @ H @ I @ J ) )
         => ( ( A = F )
            & ( B = G )
            & ( C = H )
            & ( D = I )
            & ( E = J ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g2_quantal1) ).

thf(12641,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
          ( ( ( g2_quantal1 @ A @ B @ C @ D @ E )
            = ( g2_quantal1 @ F @ G @ H @ I @ J ) )
         => ( ( A = F )
            & ( B = G )
            & ( C = H )
            & ( D = I )
            & ( E = J ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2069]) ).

thf(814,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ ( k1_realset1 @ A @ B ) )
        & ( v1_funct_1 @ ( k1_realset1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_realset1) ).

thf(6533,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ ( k1_realset1 @ A @ B ) )
        & ( v1_funct_1 @ ( k1_realset1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(2305,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( m1_subset_1 @ ( a_2_3_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_domain_1) ).

thf(13714,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( m1_subset_1 @ ( a_2_3_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2305]) ).

thf(2437,axiom,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s3_filter_1 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s3_filter_1 )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ f1_s3_filter_1 )
               => ( p1_s3_filter_1 @ ( k2_filter_1 @ f1_s3_filter_1 @ f2_s3_filter_1 @ A ) @ ( k2_filter_1 @ f1_s3_filter_1 @ f2_s3_filter_1 @ B ) @ ( k2_filter_1 @ f1_s3_filter_1 @ f2_s3_filter_1 @ C ) ) ) ) )
   => ! [A: $i] :
        ( ( m2_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s3_filter_1 ) @ ( k8_eqrel_1 @ f1_s3_filter_1 @ f2_s3_filter_1 ) )
       => ! [B: $i] :
            ( ( m2_subset_1 @ B @ ( k1_zfmisc_1 @ f1_s3_filter_1 ) @ ( k8_eqrel_1 @ f1_s3_filter_1 @ f2_s3_filter_1 ) )
           => ! [C: $i] :
                ( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ f1_s3_filter_1 ) @ ( k8_eqrel_1 @ f1_s3_filter_1 @ f2_s3_filter_1 ) )
               => ( p1_s3_filter_1 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_filter_1) ).

thf(14216,plain,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s3_filter_1 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s3_filter_1 )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ f1_s3_filter_1 )
               => ( p1_s3_filter_1 @ ( k2_filter_1 @ f1_s3_filter_1 @ f2_s3_filter_1 @ A ) @ ( k2_filter_1 @ f1_s3_filter_1 @ f2_s3_filter_1 @ B ) @ ( k2_filter_1 @ f1_s3_filter_1 @ f2_s3_filter_1 @ C ) ) ) ) )
   => ! [A: $i] :
        ( ( m2_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s3_filter_1 ) @ ( k8_eqrel_1 @ f1_s3_filter_1 @ f2_s3_filter_1 ) )
       => ! [B: $i] :
            ( ( m2_subset_1 @ B @ ( k1_zfmisc_1 @ f1_s3_filter_1 ) @ ( k8_eqrel_1 @ f1_s3_filter_1 @ f2_s3_filter_1 ) )
           => ! [C: $i] :
                ( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ f1_s3_filter_1 ) @ ( k8_eqrel_1 @ f1_s3_filter_1 @ f2_s3_filter_1 ) )
               => ( p1_s3_filter_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2437]) ).

thf(1942,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_eqrel_1 @ D @ B )
        & ( m1_eqrel_1 @ E @ C ) )
     => ( ( r2_hidden @ A @ ( a_4_0_pua2mss1 @ B @ C @ D @ E ) )
      <=> ? [F: $i,G: $i] :
            ( ( m2_subset_1 @ F @ ( k1_zfmisc_1 @ B ) @ D )
            & ( m2_subset_1 @ G @ ( k1_zfmisc_1 @ C ) @ E )
            & ( A
              = ( k12_mcart_1 @ B @ C @ F @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_0_pua2mss1) ).

thf(11940,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_eqrel_1 @ D @ B )
        & ( m1_eqrel_1 @ E @ C ) )
     => ( ( ( r2_hidden @ A @ ( a_4_0_pua2mss1 @ B @ C @ D @ E ) )
         => ? [F: $i,G: $i] :
              ( ( m2_subset_1 @ F @ ( k1_zfmisc_1 @ B ) @ D )
              & ( m2_subset_1 @ G @ ( k1_zfmisc_1 @ C ) @ E )
              & ( A
                = ( k12_mcart_1 @ B @ C @ F @ G ) ) ) )
        & ( ? [F: $i,G: $i] :
              ( ( m2_subset_1 @ F @ ( k1_zfmisc_1 @ B ) @ D )
              & ( m2_subset_1 @ G @ ( k1_zfmisc_1 @ C ) @ E )
              & ( A
                = ( k12_mcart_1 @ B @ C @ F @ G ) ) )
         => ( r2_hidden @ A @ ( a_4_0_pua2mss1 @ B @ C @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1942]) ).

thf(1739,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( m1_subset_1 @ ( k2_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_2) ).

thf(10819,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( m1_subset_1 @ ( k2_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1739]) ).

thf(842,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
        = k1_xboole_0 )
    <=> ( ( r2_hidden @ A @ C )
        & ( r2_hidden @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).

thf(6647,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
          = k1_xboole_0 )
       => ( ( r2_hidden @ A @ C )
          & ( r2_hidden @ B @ C ) ) )
      & ( ( ( r2_hidden @ A @ C )
          & ( r2_hidden @ B @ C ) )
       => ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
          = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(516,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
        & ( v1_setfam_1 @ ( k2_tarski @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_setfam_1) ).

thf(5249,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
        & ( v1_setfam_1 @ ( k2_tarski @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(2379,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k2_cantor_1 @ A @ B )
        = ( k2_cantor_1 @ A @ ( k2_cantor_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_cantor_1) ).

thf(14003,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k2_cantor_1 @ A @ B )
        = ( k2_cantor_1 @ A @ ( k2_cantor_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2379]) ).

thf(351,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k7_relat_1 @ C @ B ) ) )
      <=> ( ( r2_hidden @ A @ B )
          & ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).

thf(4535,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k7_relat_1 @ C @ B ) ) )
         => ( ( r2_hidden @ A @ B )
            & ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) ) )
        & ( ( ( r2_hidden @ A @ B )
            & ( r2_hidden @ A @ ( k1_relat_1 @ C ) ) )
         => ( r2_hidden @ A @ ( k1_relat_1 @ ( k7_relat_1 @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(1171,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_cat_1 @ ( k12_ens_1 @ A ) ) )
         => ( m1_subset_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ens_1) ).

thf(8174,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_cat_1 @ ( k12_ens_1 @ A ) ) )
         => ( m1_subset_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).

thf(1486,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i,D: $i] :
          ( ( ( g1_group_1 @ A @ B )
            = ( g1_group_1 @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_group_1) ).

thf(9534,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i,D: $i] :
          ( ( ( g1_group_1 @ A @ B )
            = ( g1_group_1 @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486]) ).

thf(488,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).

thf(5112,plain,
    ! [A: $i] :
      ( ( k2_xboole_0 @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(235,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k4_relat_1 @ ( k4_xboole_0 @ A @ B ) )
            = ( k4_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_relat_1) ).

thf(3903,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k4_relat_1 @ ( k4_xboole_0 @ A @ B ) )
            = ( k4_xboole_0 @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(599,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( v1_relat_1 @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).

thf(5557,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( v1_relat_1 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(2529,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ A )
          & ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_classes2) ).

thf(14657,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ A )
          & ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2529]) ).

thf(918,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( v2_funct_1 @ ( k2_funct_4 @ ( k15_funct_3 @ A @ B ) ) )
           => ( v2_funct_1 @ ( k15_funct_3 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_functor0) ).

thf(7020,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( v2_funct_1 @ ( k2_funct_4 @ ( k15_funct_3 @ A @ B ) ) )
           => ( v2_funct_1 @ ( k15_funct_3 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).

thf(2246,axiom,
    ! [A: $i] :
    ? [B: $i] : ( m1_eqrel_1 @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).

thf(13507,plain,
    ! [A: $i] :
    ? [B: $i] : ( m1_eqrel_1 @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2246]) ).

thf(2149,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ B )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ! [F: $i] :
                      ( ( ( v1_funct_1 @ F )
                        & ( v1_funct_2 @ F @ A @ C )
                        & ( m2_relset_1 @ F @ A @ C ) )
                     => ! [G: $i] :
                          ( ( ( v1_funct_1 @ G )
                            & ( v1_funct_2 @ G @ A @ C )
                            & ( m2_relset_1 @ G @ A @ C ) )
                         => ( ( ( k14_funct_3 @ A @ B @ C @ D @ F )
                              = ( k14_funct_3 @ A @ B @ C @ E @ G ) )
                           => ( ( D = E )
                              & ( F = G ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_funct_3) ).

thf(13103,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ B )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ! [F: $i] :
                      ( ( ( v1_funct_1 @ F )
                        & ( v1_funct_2 @ F @ A @ C )
                        & ( m2_relset_1 @ F @ A @ C ) )
                     => ! [G: $i] :
                          ( ( ( v1_funct_1 @ G )
                            & ( v1_funct_2 @ G @ A @ C )
                            & ( m2_relset_1 @ G @ A @ C ) )
                         => ( ( ( k14_funct_3 @ A @ B @ C @ D @ F )
                              = ( k14_funct_3 @ A @ B @ C @ E @ G ) )
                           => ( ( D = E )
                              & ( F = G ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2149]) ).

thf(1468,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( k2_relat_1 @ ( k15_funct_3 @ A @ B ) )
            = ( k2_zfmisc_1 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_funct_3) ).

thf(9468,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( k2_relat_1 @ ( k15_funct_3 @ A @ B ) )
            = ( k2_zfmisc_1 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468]) ).

thf(1316,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( k9_relat_1 @ B @ ( k6_partfun1 @ A ) )
        = ( k9_relat_1 @ ( k2_funct_4 @ B ) @ ( k6_partfun1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_functor0) ).

thf(8839,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( k9_relat_1 @ B @ ( k6_partfun1 @ A ) )
        = ( k9_relat_1 @ ( k2_funct_4 @ B ) @ ( k6_partfun1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).

thf(173,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ( ( ( v3_binop_1 @ C @ A )
                      & ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A )
                      & ( v1_setwiseo @ C @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
                           => ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ E @ F ) @ D )
                              = ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ E @ D ) @ ( k7_setwiseo @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_setwiseo) ).

thf(3563,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ( ( ( v3_binop_1 @ C @ A )
                      & ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A )
                      & ( v1_setwiseo @ C @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
                           => ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ E @ F ) @ D )
                              = ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ E @ D ) @ ( k7_setwiseo @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(2001,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
         => ( ( m2_card_fil @ B @ A )
          <=> ( ~ ( r2_hidden @ A @ B )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                     => ( ( ( ( r2_hidden @ C @ B )
                            & ( r2_hidden @ D @ B ) )
                         => ( r2_hidden @ ( k4_subset_1 @ A @ C @ D ) @ B ) )
                        & ( ( ( r2_hidden @ C @ B )
                            & ( r1_tarski @ D @ C ) )
                         => ( r2_hidden @ D @ B ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_card_fil) ).

thf(12282,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
         => ( ( ( m2_card_fil @ B @ A )
             => ( ~ ( r2_hidden @ A @ B )
                & ! [C: $i] :
                    ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                   => ! [D: $i] :
                        ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                       => ( ( ( ( r2_hidden @ C @ B )
                              & ( r2_hidden @ D @ B ) )
                           => ( r2_hidden @ ( k4_subset_1 @ A @ C @ D ) @ B ) )
                          & ( ( ( r2_hidden @ C @ B )
                              & ( r1_tarski @ D @ C ) )
                           => ( r2_hidden @ D @ B ) ) ) ) ) ) )
            & ( ( ~ ( r2_hidden @ A @ B )
                & ! [C: $i] :
                    ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                   => ! [D: $i] :
                        ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                       => ( ( ( ( r2_hidden @ C @ B )
                              & ( r2_hidden @ D @ B ) )
                           => ( r2_hidden @ ( k4_subset_1 @ A @ C @ D ) @ B ) )
                          & ( ( ( r2_hidden @ C @ B )
                              & ( r1_tarski @ D @ C ) )
                           => ( r2_hidden @ D @ B ) ) ) ) ) )
             => ( m2_card_fil @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2001]) ).

thf(1192,axiom,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k1_numbers )
     => ( m1_subset_1 @ ( k8_binop_2 @ A ) @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_binop_2) ).

thf(8247,plain,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k1_numbers )
     => ( m1_subset_1 @ ( k8_binop_2 @ A ) @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).

thf(1242,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k4_xboole_0 @ A @ ( k2_tarski @ B @ C ) )
        = k1_xboole_0 )
    <=> ~ ( ( A != k1_xboole_0 )
          & ( A
           != ( k1_tarski @ B ) )
          & ( A
           != ( k1_tarski @ C ) )
          & ( A
           != ( k2_tarski @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_zfmisc_1) ).

thf(8482,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( k4_xboole_0 @ A @ ( k2_tarski @ B @ C ) )
          = k1_xboole_0 )
       => ~ ( ( A != k1_xboole_0 )
            & ( A
             != ( k1_tarski @ B ) )
            & ( A
             != ( k1_tarski @ C ) )
            & ( A
             != ( k2_tarski @ B @ C ) ) ) )
      & ( ~ ( ( A != k1_xboole_0 )
            & ( A
             != ( k1_tarski @ B ) )
            & ( A
             != ( k1_tarski @ C ) )
            & ( A
             != ( k2_tarski @ B @ C ) ) )
       => ( ( k4_xboole_0 @ A @ ( k2_tarski @ B @ C ) )
          = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).

thf(1390,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i] :
                  ( ( ( r2_hidden @ C @ D )
                    & ( r2_hidden @ D @ B ) )
                 => ( r1_xboole_0 @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_mcart_1) ).

thf(9094,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i] :
                  ( ( ( r2_hidden @ C @ D )
                    & ( r2_hidden @ D @ B ) )
                 => ( r1_xboole_0 @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390]) ).

thf(924,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_relat_1 @ D )
        & ( v1_funct_1 @ D ) )
     => ! [E: $i] :
          ( ( ( v1_relat_1 @ E )
            & ( v1_funct_1 @ E ) )
         => ( ( ( r2_hidden @ D @ ( k1_funct_2 @ A @ B ) )
              & ( r2_hidden @ E @ ( k1_funct_2 @ B @ C ) ) )
           => ( r2_hidden @ ( k5_relat_1 @ D @ E ) @ ( k1_funct_2 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_altcat_1) ).

thf(7052,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_relat_1 @ D )
        & ( v1_funct_1 @ D ) )
     => ! [E: $i] :
          ( ( ( v1_relat_1 @ E )
            & ( v1_funct_1 @ E ) )
         => ( ( ( r2_hidden @ D @ ( k1_funct_2 @ A @ B ) )
              & ( r2_hidden @ E @ ( k1_funct_2 @ B @ C ) ) )
           => ( r2_hidden @ ( k5_relat_1 @ D @ E ) @ ( k1_funct_2 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).

thf(481,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( ( k1_relset_2 @ A @ B @ C )
        = ( k3_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_relset_2) ).

thf(5090,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( ( k1_relset_2 @ A @ B @ C )
        = ( k3_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(1069,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( ( k5_relset_1 @ A @ B @ C )
        = ( k2_relat_1 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).

thf(7721,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( ( k5_relset_1 @ A @ B @ C )
        = ( k2_relat_1 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).

thf(1245,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( k1_funct_4 @ A @ k1_xboole_0 )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_4) ).

thf(8512,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( k1_funct_4 @ A @ k1_xboole_0 )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).

thf(278,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( r1_tarski @ ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).

thf(4081,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( r1_tarski @ ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(2080,axiom,
    ! [A: $i] : ( m2_finseq_1 @ k1_xboole_0 @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finseq_1) ).

thf(12736,plain,
    ! [A: $i] : ( m2_finseq_1 @ k1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2080]) ).

thf(2381,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( r2_hidden @ A @ ( a_1_3_domain_1 @ B ) )
      <=> ? [C: $i] :
            ( ( m1_subset_1 @ C @ B )
            & ( A = C )
            & ( p1_s5_domain_1 @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_3_domain_1) ).

thf(14008,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( ( r2_hidden @ A @ ( a_1_3_domain_1 @ B ) )
         => ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A = C )
              & ( p1_s5_domain_1 @ C ) ) )
        & ( ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A = C )
              & ( p1_s5_domain_1 @ C ) )
         => ( r2_hidden @ A @ ( a_1_3_domain_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2381]) ).

thf(2116,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_realset1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_realset1) ).

thf(12891,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_realset1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2116]) ).

thf(1144,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_membered @ A )
     => ( v1_membered @ ( k3_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc27_membered) ).

thf(8080,plain,
    ! [A: $i,B: $i] :
      ( ( v1_membered @ A )
     => ( v1_membered @ ( k3_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).

thf(94,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v1_setwiseo @ B @ A )
          <=> ( r3_binop_1 @ A @ ( k3_binop_1 @ A @ B ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_setwiseo) ).

thf(3173,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( v1_setwiseo @ B @ A )
             => ( r3_binop_1 @ A @ ( k3_binop_1 @ A @ B ) @ B ) )
            & ( ( r3_binop_1 @ A @ ( k3_binop_1 @ A @ B ) @ B )
             => ( v1_setwiseo @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(1420,axiom,
    ! [A: $i,B: $i] :
      ( ( k3_enumset1 @ A @ A @ A @ A @ B )
      = ( k2_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_enumset1) ).

thf(9269,plain,
    ! [A: $i,B: $i] :
      ( ( k3_enumset1 @ A @ A @ A @ A @ B )
      = ( k2_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1420]) ).

thf(1651,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( v1_funct_1 @ G )
        & ( v1_funct_2 @ G @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ! [H: $i] :
          ( ( ( v1_funct_1 @ H )
            & ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ D @ E ) @ F )
            & ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ D @ E ) @ F ) )
         => ~ ( ( C != k1_xboole_0 )
              & ( F != k1_xboole_0 )
              & ~ ( ( v1_funct_1 @ ( k3_funct_4 @ G @ H ) )
                  & ( v1_funct_2 @ ( k3_funct_4 @ G @ H ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ E ) ) @ ( k2_zfmisc_1 @ C @ F ) )
                  & ( m2_relset_1 @ ( k3_funct_4 @ G @ H ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ E ) ) @ ( k2_zfmisc_1 @ C @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funct_4) ).

thf(10377,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ( v1_funct_1 @ G )
        & ( v1_funct_2 @ G @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ! [H: $i] :
          ( ( ( v1_funct_1 @ H )
            & ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ D @ E ) @ F )
            & ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ D @ E ) @ F ) )
         => ~ ( ( C != k1_xboole_0 )
              & ( F != k1_xboole_0 )
              & ~ ( ( v1_funct_1 @ ( k3_funct_4 @ G @ H ) )
                  & ( v1_funct_2 @ ( k3_funct_4 @ G @ H ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ E ) ) @ ( k2_zfmisc_1 @ C @ F ) )
                  & ( m2_relset_1 @ ( k3_funct_4 @ G @ H ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ D ) @ ( k2_zfmisc_1 @ B @ E ) ) @ ( k2_zfmisc_1 @ C @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1651]) ).

thf(225,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v1_finset_1 @ A )
      & ( v1_finseq_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc8_finseq_1) ).

thf(3856,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v1_finset_1 @ A )
      & ( v1_finseq_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(1230,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( r1_tarski @ ( k2_relat_1 @ ( k3_funct_4 @ A @ B ) ) @ ( k2_zfmisc_1 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_4) ).

thf(8422,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( r1_tarski @ ( k2_relat_1 @ ( k3_funct_4 @ A @ B ) ) @ ( k2_zfmisc_1 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).

thf(1366,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ ( k2_xboole_0 @ A @ B ) @ C )
     => ( r1_tarski @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_xboole_1) ).

thf(9008,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ ( k2_xboole_0 @ A @ B ) @ C )
     => ( r1_tarski @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).

thf(1340,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( ( k10_relset_1 @ A @ B @ C @ D )
        = ( k9_relat_1 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_relset_1) ).

thf(8923,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( ( k10_relset_1 @ A @ B @ C @ D )
        = ( k9_relat_1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).

thf(563,axiom,
    ! [A: $i] : ( r2_hidden @ ( k6_relat_1 @ A ) @ ( k1_funct_2 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_altcat_1) ).

thf(5434,plain,
    ! [A: $i] : ( r2_hidden @ ( k6_relat_1 @ A ) @ ( k1_funct_2 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(687,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_xboole_0 @ ( k15_funct_3 @ B @ A ) )
        & ( v1_relat_1 @ ( k15_funct_3 @ B @ A ) )
        & ( v1_funct_1 @ ( k15_funct_3 @ B @ A ) )
        & ( v2_funct_1 @ ( k15_funct_3 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_functor0) ).

thf(5964,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_xboole_0 @ ( k15_funct_3 @ B @ A ) )
        & ( v1_relat_1 @ ( k15_funct_3 @ B @ A ) )
        & ( v1_funct_1 @ ( k15_funct_3 @ B @ A ) )
        & ( v2_funct_1 @ ( k15_funct_3 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(2317,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_realset1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( ~ ( v1_xboole_0 @ B )
              & ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) )
           => ( ~ ( v1_xboole_0 @ B )
              & ~ ( v1_realset1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_tex_2) ).

thf(13772,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_realset1 @ A ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( ~ ( v1_xboole_0 @ B )
              & ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) )
           => ( ~ ( v1_xboole_0 @ B )
              & ~ ( v1_realset1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2317]) ).

thf(1349,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ( ( ( ( k1_relat_1 @ C )
                = ( k1_relat_1 @ D ) )
              & ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
              & ( r1_tarski @ ( k2_relat_1 @ D ) @ B ) )
           => ( ( ( k5_relat_1 @ ( k13_funct_3 @ C @ D ) @ ( k9_funct_3 @ A @ B ) )
                = C )
              & ( ( k5_relat_1 @ ( k13_funct_3 @ C @ D ) @ ( k10_funct_3 @ A @ B ) )
                = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_3) ).

thf(8955,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ( ( ( ( k1_relat_1 @ C )
                = ( k1_relat_1 @ D ) )
              & ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
              & ( r1_tarski @ ( k2_relat_1 @ D ) @ B ) )
           => ( ( ( k5_relat_1 @ ( k13_funct_3 @ C @ D ) @ ( k9_funct_3 @ A @ B ) )
                = C )
              & ( ( k5_relat_1 @ ( k13_funct_3 @ C @ D ) @ ( k10_funct_3 @ A @ B ) )
                = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).

thf(1399,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k1_funct_2 @ A @ B ) @ ( k4_partfun1 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_funct_2) ).

thf(9169,plain,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k1_funct_2 @ A @ B ) @ ( k4_partfun1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399]) ).

thf(1400,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ A )
        & ( m2_relset_1 @ C @ A @ A ) )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ( ( r2_hidden @ B @ A )
           => ( ( k1_funct_1 @ ( k5_relat_1 @ C @ D ) @ B )
              = ( k1_funct_1 @ D @ ( k1_funct_1 @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_2) ).

thf(9171,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ A )
        & ( m2_relset_1 @ C @ A @ A ) )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ( ( r2_hidden @ B @ A )
           => ( ( k1_funct_1 @ ( k5_relat_1 @ C @ D ) @ B )
              = ( k1_funct_1 @ D @ ( k1_funct_1 @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400]) ).

thf(1198,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) ) @ B )
        & ( r1_tarski @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_relat_1) ).

thf(8262,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) ) @ B )
        & ( r1_tarski @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).

thf(558,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ~ ( r1_xboole_0 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
     => ( ~ ( r1_xboole_0 @ A @ E )
        & ~ ( r1_xboole_0 @ B @ F )
        & ~ ( r1_xboole_0 @ C @ G )
        & ~ ( r1_xboole_0 @ D @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_mcart_1) ).

thf(5419,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ~ ( r1_xboole_0 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
     => ( ~ ( r1_xboole_0 @ A @ E )
        & ~ ( r1_xboole_0 @ B @ F )
        & ~ ( r1_xboole_0 @ C @ G )
        & ~ ( r1_xboole_0 @ D @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(1807,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ A )
                        & ( m2_relset_1 @ E @ B @ A ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ( ! [G: $i] :
                                ( ( m1_subset_1 @ G @ B )
                               => ( ( k8_funct_2 @ B @ A @ D @ G )
                                  = ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ E @ G ) @ F ) ) )
                           => ( D
                              = ( k7_funcop_1 @ A @ B @ C @ E @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funcop_1) ).

thf(11196,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ A )
                        & ( m2_relset_1 @ E @ B @ A ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ( ! [G: $i] :
                                ( ( m1_subset_1 @ G @ B )
                               => ( ( k8_funct_2 @ B @ A @ D @ G )
                                  = ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ E @ G ) @ F ) ) )
                           => ( D
                              = ( k7_funcop_1 @ A @ B @ C @ E @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1807]) ).

thf(1760,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ B )
      <=> ( B
          = ( k2_subset_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_subset_1) ).

thf(10951,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ B )
         => ( B
            = ( k2_subset_1 @ A ) ) )
        & ( ( B
            = ( k2_subset_1 @ A ) )
         => ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1760]) ).

thf(679,axiom,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
        & ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) )
     => ( ( A = k36_binop_2 )
      <=> ! [B: $i] :
            ( ( m1_subset_1 @ B @ k1_numbers )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ k1_numbers )
               => ( ( k2_binop_1 @ k1_numbers @ k1_numbers @ k1_numbers @ A @ B @ C )
                  = ( k12_binop_2 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_binop_2) ).

thf(5930,plain,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
        & ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) )
     => ( ( ( A = k36_binop_2 )
         => ! [B: $i] :
              ( ( m1_subset_1 @ B @ k1_numbers )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ k1_numbers )
                 => ( ( k2_binop_1 @ k1_numbers @ k1_numbers @ k1_numbers @ A @ B @ C )
                    = ( k12_binop_2 @ B @ C ) ) ) ) )
        & ( ! [B: $i] :
              ( ( m1_subset_1 @ B @ k1_numbers )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ k1_numbers )
                 => ( ( k2_binop_1 @ k1_numbers @ k1_numbers @ k1_numbers @ A @ B @ C )
                    = ( k12_binop_2 @ B @ C ) ) ) )
         => ( A = k36_binop_2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(1346,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) ) )
     => ( m1_subset_1 @ ( k4_ens_1 @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_ens_1) ).

thf(8945,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) ) )
     => ( m1_subset_1 @ ( k4_ens_1 @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).

thf(1424,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
      = ( k2_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_xboole_1) ).

thf(9284,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C )
      = ( k2_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424]) ).

thf(2156,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_eqrel_1 @ B @ A ) )
     => ( ( v1_funct_1 @ ( k2_borsuk_1 @ A @ B ) )
        & ( v1_funct_2 @ ( k2_borsuk_1 @ A @ B ) @ A @ B )
        & ( m2_relset_1 @ ( k2_borsuk_1 @ A @ B ) @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_borsuk_1) ).

thf(13137,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_eqrel_1 @ B @ A ) )
     => ( ( v1_funct_1 @ ( k2_borsuk_1 @ A @ B ) )
        & ( v1_funct_2 @ ( k2_borsuk_1 @ A @ B ) @ A @ B )
        & ( m2_relset_1 @ ( k2_borsuk_1 @ A @ B ) @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2156]) ).

thf(2349,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
        & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) )
     => ( m2_relset_1 @ ( k9_relset_2 @ A @ B @ C @ D @ E ) @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relset_2) ).

thf(13879,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
        & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) )
     => ( m2_relset_1 @ ( k9_relset_2 @ A @ B @ C @ D @ E ) @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2349]) ).

thf(265,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v1_binop_1 @ B @ A )
          <=> ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
                      = ( k2_binop_1 @ A @ A @ A @ B @ D @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_binop_1) ).

thf(4036,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( v1_binop_1 @ B @ A )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
                        = ( k2_binop_1 @ A @ A @ A @ B @ D @ C ) ) ) ) )
            & ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
                        = ( k2_binop_1 @ A @ A @ A @ B @ D @ C ) ) ) )
             => ( v1_binop_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(2469,axiom,
    ! [A: $i] :
      ( ( r2_hidden @ A @ a_0_0_group_5 )
    <=> ? [B: $i,C: $i,D: $i] :
          ( ( m1_subset_1 @ B @ f1_s1_group_5 )
          & ( m1_subset_1 @ C @ f2_s1_group_5 )
          & ( m1_subset_1 @ D @ f3_s1_group_5 )
          & ( A
            = ( f4_s1_group_5 @ B @ C @ D ) )
          & ( p1_s1_group_5 @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_0_group_5) ).

thf(14362,plain,
    ! [A: $i] :
      ( ( ( r2_hidden @ A @ a_0_0_group_5 )
       => ? [B: $i,C: $i,D: $i] :
            ( ( m1_subset_1 @ B @ f1_s1_group_5 )
            & ( m1_subset_1 @ C @ f2_s1_group_5 )
            & ( m1_subset_1 @ D @ f3_s1_group_5 )
            & ( A
              = ( f4_s1_group_5 @ B @ C @ D ) )
            & ( p1_s1_group_5 @ B @ C @ D ) ) )
      & ( ? [B: $i,C: $i,D: $i] :
            ( ( m1_subset_1 @ B @ f1_s1_group_5 )
            & ( m1_subset_1 @ C @ f2_s1_group_5 )
            & ( m1_subset_1 @ D @ f3_s1_group_5 )
            & ( A
              = ( f4_s1_group_5 @ B @ C @ D ) )
            & ( p1_s1_group_5 @ B @ C @ D ) )
       => ( r2_hidden @ A @ a_0_0_group_5 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2469]) ).

thf(1589,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ! [E: $i] :
              ( ( ( v1_funct_1 @ E )
                & ( v1_funct_2 @ E @ A @ B )
                & ( m2_relset_1 @ E @ A @ B ) )
             => ( ( ( r1_partfun1 @ C @ E )
                  & ( r1_partfun1 @ D @ E ) )
               => ( ( ( B = k1_xboole_0 )
                    & ( A != k1_xboole_0 ) )
                  | ( r1_partfun1 @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_funct_2) ).

thf(10090,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ! [E: $i] :
              ( ( ( v1_funct_1 @ E )
                & ( v1_funct_2 @ E @ A @ B )
                & ( m2_relset_1 @ E @ A @ B ) )
             => ( ( ( r1_partfun1 @ C @ E )
                  & ( r1_partfun1 @ D @ E ) )
               => ( ( ( B = k1_xboole_0 )
                    & ( A != k1_xboole_0 ) )
                  | ( r1_partfun1 @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1589]) ).

thf(154,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
             => ( ( k1_relat_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
                = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_lattice2) ).

thf(3422,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
             => ( ( k1_relat_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
                = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(584,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i,E: $i] :
                  ( ( ( v1_relat_1 @ E )
                    & ( v1_funct_1 @ E ) )
                 => ( ( ( k7_relat_1 @ A @ D )
                      = ( k7_relat_1 @ B @ D ) )
                   => ( ( k7_relat_1 @ ( k3_funcop_1 @ E @ A @ C ) @ D )
                      = ( k7_relat_1 @ ( k3_funcop_1 @ E @ B @ C ) @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_funcop_1) ).

thf(5513,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i,E: $i] :
                  ( ( ( v1_relat_1 @ E )
                    & ( v1_funct_1 @ E ) )
                 => ( ( ( k7_relat_1 @ A @ D )
                      = ( k7_relat_1 @ B @ D ) )
                   => ( ( k7_relat_1 @ ( k3_funcop_1 @ E @ A @ C ) @ D )
                      = ( k7_relat_1 @ ( k3_funcop_1 @ E @ B @ C ) @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(901,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_xboole_0 @ ( k1_enumset1 @ A @ B @ C ) @ ( k1_tarski @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_enumset1) ).

thf(6931,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_xboole_0 @ ( k1_enumset1 @ A @ B @ C ) @ ( k1_tarski @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(2103,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
             => ( ( B
                  = ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ C @ D ) )
               => ( ( k8_setfam_1 @ A @ B )
                  = ( k5_subset_1 @ A @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_mssubfam) ).

thf(12823,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
             => ( ( B
                  = ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ C @ D ) )
               => ( ( k8_setfam_1 @ A @ B )
                  = ( k5_subset_1 @ A @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2103]) ).

thf(781,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k2_setwiseo @ A @ B ) @ ( k5_finsub_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_setwiseo) ).

thf(6400,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k2_setwiseo @ A @ B ) @ ( k5_finsub_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(60,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( ( k1_relat_1 @ B )
          = k1_xboole_0 )
       => ( ( v1_funct_1 @ B )
          & ( v1_funct_2 @ B @ k1_xboole_0 @ A )
          & ( m2_relset_1 @ B @ k1_xboole_0 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_2) ).

thf(2995,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( ( k1_relat_1 @ B )
          = k1_xboole_0 )
       => ( ( v1_funct_1 @ B )
          & ( v1_funct_2 @ B @ k1_xboole_0 @ A )
          & ( m2_relset_1 @ B @ k1_xboole_0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(220,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) ) )
     => ( ( ( k1_mcart_1 @ A )
          = B )
        & ( ( k2_mcart_1 @ A )
          = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_mcart_1) ).

thf(3841,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ ( k1_tarski @ C ) ) )
     => ( ( ( k1_mcart_1 @ A )
          = B )
        & ( ( k2_mcart_1 @ A )
          = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(529,axiom,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ C )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ C ) @ D )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ C ) @ D ) )
                         => ! [G: $i] :
                              ( ( m2_finseq_2 @ G @ B @ ( k4_finseq_2 @ A @ B ) )
                             => ( m2_finseq_2 @ ( k4_funcop_1 @ F @ G @ E ) @ D @ ( k4_finseq_2 @ A @ D ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_finseq_2) ).

thf(5295,plain,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ C )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ C ) @ D )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ C ) @ D ) )
                         => ! [G: $i] :
                              ( ( m2_finseq_2 @ G @ B @ ( k4_finseq_2 @ A @ B ) )
                             => ( m2_finseq_2 @ ( k4_funcop_1 @ F @ G @ E ) @ D @ ( k4_finseq_2 @ A @ D ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(1091,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ B )
        & ! [D: $i] :
            ( ( ( r1_tarski @ A @ D )
              & ( r1_tarski @ C @ D ) )
           => ( r1_tarski @ B @ D ) ) )
     => ( B
        = ( k2_xboole_0 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_xboole_1) ).

thf(7802,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ B )
        & ! [D: $i] :
            ( ( ( r1_tarski @ A @ D )
              & ( r1_tarski @ C @ D ) )
           => ( r1_tarski @ B @ D ) ) )
     => ( B
        = ( k2_xboole_0 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).

thf(1615,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ( ( v2_card_fil @ B @ A )
          <=> ? [C: $i] :
                ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                & ( r2_hidden @ C @ B )
                & ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                   => ( ( r2_hidden @ D @ B )
                     => ( r1_tarski @ C @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_card_fil) ).

thf(10190,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ( ( ( v2_card_fil @ B @ A )
             => ? [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                  & ( r2_hidden @ C @ B )
                  & ! [D: $i] :
                      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                     => ( ( r2_hidden @ D @ B )
                       => ( r1_tarski @ C @ D ) ) ) ) )
            & ( ? [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                  & ( r2_hidden @ C @ B )
                  & ! [D: $i] :
                      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                     => ( ( r2_hidden @ D @ B )
                       => ( r1_tarski @ C @ D ) ) ) )
             => ( v2_card_fil @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1615]) ).

thf(1565,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
             => ! [E: $i] :
                  ( ( r2_hidden @ E @ ( k10_setwiseo @ A @ B @ D @ C ) )
                <=> ? [F: $i] :
                      ( ( m1_subset_1 @ F @ A )
                      & ( r2_hidden @ F @ D )
                      & ( r2_hidden @ E @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_setwiseo) ).

thf(9985,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
             => ! [E: $i] :
                  ( ( ( r2_hidden @ E @ ( k10_setwiseo @ A @ B @ D @ C ) )
                   => ? [F: $i] :
                        ( ( m1_subset_1 @ F @ A )
                        & ( r2_hidden @ F @ D )
                        & ( r2_hidden @ E @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ F ) ) ) )
                  & ( ? [F: $i] :
                        ( ( m1_subset_1 @ F @ A )
                        & ( r2_hidden @ F @ D )
                        & ( r2_hidden @ E @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ F ) ) )
                   => ( r2_hidden @ E @ ( k10_setwiseo @ A @ B @ D @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1565]) ).

thf(1490,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A ) )
     => ! [E: $i,F: $i,G: $i,H: $i] :
          ( ( ( g2_vectsp_1 @ A @ B @ C @ D )
            = ( g2_vectsp_1 @ E @ F @ G @ H ) )
         => ( ( A = E )
            & ( B = F )
            & ( C = G )
            & ( D = H ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g2_vectsp_1) ).

thf(9562,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A ) )
     => ! [E: $i,F: $i,G: $i,H: $i] :
          ( ( ( g2_vectsp_1 @ A @ B @ C @ D )
            = ( g2_vectsp_1 @ E @ F @ G @ H ) )
         => ( ( A = E )
            & ( B = F )
            & ( C = G )
            & ( D = H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1490]) ).

thf(2010,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ( ( r2_hidden @ ( k1_tarski @ k1_xboole_0 ) @ A )
        & ( r2_hidden @ ( k4_tarski @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) @ A )
        & ( r2_hidden @ ( k2_zfmisc_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) @ A )
        & ( r2_hidden @ k2_midsp_1 @ A )
        & ( r2_hidden @ k7_vectsp_2 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_grcat_1) ).

thf(12318,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ( ( r2_hidden @ ( k1_tarski @ k1_xboole_0 ) @ A )
        & ( r2_hidden @ ( k4_tarski @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) @ A )
        & ( r2_hidden @ ( k2_zfmisc_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) @ A )
        & ( r2_hidden @ k2_midsp_1 @ A )
        & ( r2_hidden @ k7_vectsp_2 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2010]) ).

thf(2406,axiom,
    ( ( ! [A: $i] :
          ( ( m1_subset_1 @ A @ f1_s23_fraenkel )
         => ( p1_s23_fraenkel @ A @ A ) )
      & ! [A: $i] :
          ( ( m1_subset_1 @ A @ f1_s23_fraenkel )
         => ! [B: $i] :
              ( ( m1_subset_1 @ B @ f1_s23_fraenkel )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ f1_s23_fraenkel )
                 => ( ( ( p1_s23_fraenkel @ A @ B )
                      & ( p1_s23_fraenkel @ B @ C ) )
                   => ( p1_s23_fraenkel @ A @ C ) ) ) ) ) )
   => ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s23_fraenkel )
       => ~ ( ( r2_hidden @ A @ f2_s23_fraenkel )
            & ! [B: $i] :
                ( ( m1_subset_1 @ B @ f1_s23_fraenkel )
               => ~ ( ( r2_hidden @ B @ f2_s23_fraenkel )
                    & ( p1_s23_fraenkel @ B @ A )
                    & ! [C: $i] :
                        ( ( m1_subset_1 @ C @ f1_s23_fraenkel )
                       => ( ( ( r2_hidden @ C @ f2_s23_fraenkel )
                            & ( p1_s23_fraenkel @ C @ B ) )
                         => ( p1_s23_fraenkel @ B @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s23_fraenkel) ).

thf(14085,plain,
    ( ( ! [A: $i] :
          ( ( m1_subset_1 @ A @ f1_s23_fraenkel )
         => ( p1_s23_fraenkel @ A @ A ) )
      & ! [A: $i] :
          ( ( m1_subset_1 @ A @ f1_s23_fraenkel )
         => ! [B: $i] :
              ( ( m1_subset_1 @ B @ f1_s23_fraenkel )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ f1_s23_fraenkel )
                 => ( ( ( p1_s23_fraenkel @ A @ B )
                      & ( p1_s23_fraenkel @ B @ C ) )
                   => ( p1_s23_fraenkel @ A @ C ) ) ) ) ) )
   => ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s23_fraenkel )
       => ~ ( ( r2_hidden @ A @ f2_s23_fraenkel )
            & ! [B: $i] :
                ( ( m1_subset_1 @ B @ f1_s23_fraenkel )
               => ~ ( ( r2_hidden @ B @ f2_s23_fraenkel )
                    & ( p1_s23_fraenkel @ B @ A )
                    & ! [C: $i] :
                        ( ( m1_subset_1 @ C @ f1_s23_fraenkel )
                       => ( ( ( r2_hidden @ C @ f2_s23_fraenkel )
                            & ( p1_s23_fraenkel @ C @ B ) )
                         => ( p1_s23_fraenkel @ B @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2406]) ).

thf(454,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( v1_binop_1 @ B @ A )
           => ( ( r3_binop_1 @ A @ C @ B )
            <=> ( r2_binop_1 @ A @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_binop_1) ).

thf(4995,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( v1_binop_1 @ B @ A )
           => ( ( ( r3_binop_1 @ A @ C @ B )
               => ( r2_binop_1 @ A @ C @ B ) )
              & ( ( r2_binop_1 @ A @ C @ B )
               => ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(1480,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m1_relset_1 @ D @ A @ B )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ C )
        & ( m1_relset_1 @ E @ A @ C ) )
     => ( ( v1_funct_1 @ ( k14_funct_3 @ A @ B @ C @ D @ E ) )
        & ( v1_funct_2 @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( m2_relset_1 @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_funct_3) ).

thf(9517,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m1_relset_1 @ D @ A @ B )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ C )
        & ( m1_relset_1 @ E @ A @ C ) )
     => ( ( v1_funct_1 @ ( k14_funct_3 @ A @ B @ C @ D @ E ) )
        & ( v1_funct_2 @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( m2_relset_1 @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480]) ).

thf(1093,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
      & ( v1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
      & ( v1_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
      & ( v2_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funcop_1) ).

thf(7817,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
      & ( v1_relat_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
      & ( v1_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) )
      & ( v2_funct_1 @ ( k2_funcop_1 @ k1_xboole_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).

thf(2072,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ D @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_enumset1) ).

thf(12677,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ D @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2072]) ).

thf(1990,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( v1_funct_1 @ ( k10_ens_1 @ A ) )
        & ( m2_relset_1 @ ( k10_ens_1 @ A ) @ ( k2_zfmisc_1 @ ( k2_ens_1 @ A ) @ ( k2_ens_1 @ A ) ) @ ( k2_ens_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_ens_1) ).

thf(12173,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( v1_funct_1 @ ( k10_ens_1 @ A ) )
        & ( m2_relset_1 @ ( k10_ens_1 @ A ) @ ( k2_zfmisc_1 @ ( k2_ens_1 @ A ) @ ( k2_ens_1 @ A ) ) @ ( k2_ens_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1990]) ).

thf(1902,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_eqrel_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_eqrel_1 @ D @ B )
                 => ( m1_eqrel_1 @ ( a_4_0_pua2mss1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_pua2mss1) ).

thf(11692,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_eqrel_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_eqrel_1 @ D @ B )
                 => ( m1_eqrel_1 @ ( a_4_0_pua2mss1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1902]) ).

thf(392,axiom,
    ! [A: $i] :
    ? [B: $i] : ( m2_pua2mss1 @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_pua2mss1) ).

thf(4708,plain,
    ! [A: $i] :
    ? [B: $i] : ( m2_pua2mss1 @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(1066,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ B @ A )
     => ( ! [D: $i] :
            ~ ( ( r2_hidden @ D @ B )
              & ! [E: $i] :
                  ~ ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) )
      <=> ( ( k4_relset_1 @ B @ A @ C )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relset_1) ).

thf(7706,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ B @ A )
     => ( ( ! [D: $i] :
              ~ ( ( r2_hidden @ D @ B )
                & ! [E: $i] :
                    ~ ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) )
         => ( ( k4_relset_1 @ B @ A @ C )
            = B ) )
        & ( ( ( k4_relset_1 @ B @ A @ C )
            = B )
         => ! [D: $i] :
              ~ ( ( r2_hidden @ D @ B )
                & ! [E: $i] :
                    ~ ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).

thf(470,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( r1_tarski @ ( k1_setfam_1 @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_setfam_1) ).

thf(5048,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( r1_tarski @ ( k1_setfam_1 @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(737,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_relat_1 @ E )
            & ( v1_funct_1 @ E ) )
         => ( ( r2_hidden @ C @ A )
           => ( ( B = k1_xboole_0 )
              | ( ( k1_funct_1 @ ( k5_relat_1 @ D @ E ) @ C )
                = ( k1_funct_1 @ E @ ( k1_funct_1 @ D @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_2) ).

thf(6192,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_relat_1 @ E )
            & ( v1_funct_1 @ E ) )
         => ( ( r2_hidden @ C @ A )
           => ( ( B = k1_xboole_0 )
              | ( ( k1_funct_1 @ ( k5_relat_1 @ D @ E ) @ C )
                = ( k1_funct_1 @ E @ ( k1_funct_1 @ D @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(2409,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k4_finsub_1 @ A @ B @ C )
        = ( k4_finsub_1 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_finsub_1) ).

thf(14107,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k4_finsub_1 @ A @ B @ C )
        = ( k4_finsub_1 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2409]) ).

thf(1800,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k18_group_2 @ A @ B ) @ ( k5_finsub_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k18_group_2) ).

thf(11165,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k18_group_2 @ A @ B ) @ ( k5_finsub_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1800]) ).

thf(437,axiom,
    r1_tarski @ k5_numbers @ k1_numbers,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_numbers) ).

thf(4921,plain,
    r1_tarski @ k5_numbers @ k1_numbers,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(2226,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
     => ( ( r2_hidden @ A @ C )
       => ( r2_hidden @ ( k1_funct_1 @ ( k6_funct_3 @ B @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funct_3) ).

thf(13444,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
     => ( ( r2_hidden @ A @ C )
       => ( r2_hidden @ ( k1_funct_1 @ ( k6_funct_3 @ B @ C ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2226]) ).

thf(1392,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ( k8_funct_2 @ A @ A @ ( k7_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ C ) @ C )
                = ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funcop_1) ).

thf(9107,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ( k8_funct_2 @ A @ A @ ( k7_funcop_1 @ A @ A @ B @ ( k6_partfun1 @ A ) @ C ) @ C )
                = ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392]) ).

thf(195,axiom,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k1_numbers )
        & ( m1_subset_1 @ B @ k1_numbers ) )
     => ( m1_subset_1 @ ( k9_binop_2 @ A @ B ) @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_binop_2) ).

thf(3660,plain,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k1_numbers )
        & ( m1_subset_1 @ B @ k1_numbers ) )
     => ( m1_subset_1 @ ( k9_binop_2 @ A @ B ) @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(898,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
                    & ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ ( k2_zfmisc_1 @ B @ C ) )
                        & ( m2_relset_1 @ E @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
                     => ( ( ( r4_nattra_1 @ A @ B @ A @ B @ ( k7_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ B @ D @ ( k9_funct_3 @ B @ C ) ) @ ( k7_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ B @ E @ ( k9_funct_3 @ B @ C ) ) )
                          & ( r4_nattra_1 @ A @ C @ A @ C @ ( k7_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ C @ D @ ( k10_funct_3 @ B @ C ) ) @ ( k7_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ C @ E @ ( k10_funct_3 @ B @ C ) ) ) )
                       => ( r4_nattra_1 @ A @ ( k2_zfmisc_1 @ B @ C ) @ A @ ( k2_zfmisc_1 @ B @ C ) @ D @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_isocat_2) ).

thf(6922,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
                    & ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ ( k2_zfmisc_1 @ B @ C ) )
                        & ( m2_relset_1 @ E @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
                     => ( ( ( r4_nattra_1 @ A @ B @ A @ B @ ( k7_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ B @ D @ ( k9_funct_3 @ B @ C ) ) @ ( k7_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ B @ E @ ( k9_funct_3 @ B @ C ) ) )
                          & ( r4_nattra_1 @ A @ C @ A @ C @ ( k7_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ C @ D @ ( k10_funct_3 @ B @ C ) ) @ ( k7_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ C @ E @ ( k10_funct_3 @ B @ C ) ) ) )
                       => ( r4_nattra_1 @ A @ ( k2_zfmisc_1 @ B @ C ) @ A @ ( k2_zfmisc_1 @ B @ C ) @ D @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(1409,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( m1_relset_1 @ E @ A @ B )
        & ( v1_funct_1 @ F )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) )
        & ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_partfun1) ).

thf(9237,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( m1_relset_1 @ E @ A @ B )
        & ( v1_funct_1 @ F )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) )
        & ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ C @ D @ E @ F ) @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409]) ).

thf(204,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ A @ B )
                            & ( m2_relset_1 @ F @ A @ B ) )
                         => ( ( v2_binop_1 @ C @ B )
                           => ( ( k6_funcop_1 @ B @ A @ C @ ( k6_funcop_1 @ B @ A @ C @ D @ E ) @ F )
                              = ( k6_funcop_1 @ B @ A @ C @ D @ ( k6_funcop_1 @ B @ A @ C @ E @ F ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funcop_1) ).

thf(3707,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ A @ B )
                            & ( m2_relset_1 @ F @ A @ B ) )
                         => ( ( v2_binop_1 @ C @ B )
                           => ( ( k6_funcop_1 @ B @ A @ C @ ( k6_funcop_1 @ B @ A @ C @ D @ E ) @ F )
                              = ( k6_funcop_1 @ B @ A @ C @ D @ ( k6_funcop_1 @ B @ A @ C @ E @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(1972,axiom,
    ! [A: $i] :
      ( ( v1_funct_1 @ A )
    <=> ! [B: $i,C: $i,D: $i] :
          ( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
            & ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
         => ( C = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_1) ).

thf(12106,plain,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
       => ! [B: $i,C: $i,D: $i] :
            ( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
              & ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
           => ( C = D ) ) )
      & ( ! [B: $i,C: $i,D: $i] :
            ( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
              & ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
           => ( C = D ) )
       => ( v1_funct_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1972]) ).

thf(765,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_relat_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).

thf(6314,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_relat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(1729,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H )
      = ( k2_xboole_0 @ ( k3_enumset1 @ A @ B @ C @ D @ E ) @ ( k1_enumset1 @ F @ G @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_enumset1) ).

thf(10703,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H )
      = ( k2_xboole_0 @ ( k3_enumset1 @ A @ B @ C @ D @ E ) @ ( k1_enumset1 @ F @ G @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1729]) ).

thf(1696,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ B @ A )
                & ( m2_relset_1 @ C @ B @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
                 => ( ( ( k2_funct_2 @ B @ A @ C @ D )
                      = k1_xboole_0 )
                   => ( D = k1_xboole_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_setwiseo) ).

thf(10556,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ B @ A )
                & ( m2_relset_1 @ C @ B @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
                 => ( ( ( k2_funct_2 @ B @ A @ C @ D )
                      = k1_xboole_0 )
                   => ( D = k1_xboole_0 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1696]) ).

thf(1861,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ A )
                     => ( ( A != k1_xboole_0 )
                       => ( m1_subset_1 @ ( k3_enumset1 @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_subset_1) ).

thf(11506,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ A )
                     => ( ( A != k1_xboole_0 )
                       => ( m1_subset_1 @ ( k3_enumset1 @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1861]) ).

thf(1992,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ~ ( ( ( B = k1_xboole_0 )
           => ( A = k1_xboole_0 ) )
          & ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ~ ( r1_partfun1 @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_funct_2) ).

thf(12238,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ~ ( ( ( B = k1_xboole_0 )
           => ( A = k1_xboole_0 ) )
          & ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ~ ( r1_partfun1 @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1992]) ).

thf(2521,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ A ) )
     => ( m1_subset_1 @ ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_domain_1) ).

thf(14638,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ A ) )
     => ( m1_subset_1 @ ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2521]) ).

thf(1988,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_funcop_1 @ A @ B )
      = ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funcop_1) ).

thf(12168,plain,
    ! [A: $i,B: $i] :
      ( ( k2_funcop_1 @ A @ B )
      = ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1988]) ).

thf(1909,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
          ( ( ( g3_vectsp_1 @ A @ B @ C @ D @ E )
            = ( g3_vectsp_1 @ F @ G @ H @ I @ J ) )
         => ( ( A = F )
            & ( B = G )
            & ( C = H )
            & ( D = I )
            & ( E = J ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_vectsp_1) ).

thf(11710,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
          ( ( ( g3_vectsp_1 @ A @ B @ C @ D @ E )
            = ( g3_vectsp_1 @ F @ G @ H @ I @ J ) )
         => ( ( A = F )
            & ( B = G )
            & ( C = H )
            & ( D = I )
            & ( E = J ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1909]) ).

thf(1592,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ B @ A )
        & ( m1_relset_1 @ C @ B @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ B @ A )
        & ( m1_relset_1 @ D @ B @ A )
        & ( v1_funct_1 @ E )
        & ( m1_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ A @ B )
        & ( m1_relset_1 @ F @ A @ B ) )
     => ! [G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
          ( ( ( g1_cat_1 @ A @ B @ C @ D @ E @ F )
            = ( g1_cat_1 @ G @ H @ I @ J @ K @ L ) )
         => ( ( A = G )
            & ( B = H )
            & ( C = I )
            & ( D = J )
            & ( E = K )
            & ( F = L ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_cat_1) ).

thf(10101,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ B @ A )
        & ( m1_relset_1 @ C @ B @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ B @ A )
        & ( m1_relset_1 @ D @ B @ A )
        & ( v1_funct_1 @ E )
        & ( m1_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ A @ B )
        & ( m1_relset_1 @ F @ A @ B ) )
     => ! [G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
          ( ( ( g1_cat_1 @ A @ B @ C @ D @ E @ F )
            = ( g1_cat_1 @ G @ H @ I @ J @ K @ L ) )
         => ( ( A = G )
            & ( B = H )
            & ( C = I )
            & ( D = J )
            & ( E = K )
            & ( F = L ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1592]) ).

thf(2559,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( m1_subset_1 @ ( k3_cat_5 @ A @ B @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_cat_5) ).

thf(14762,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( m1_subset_1 @ ( k3_cat_5 @ A @ B @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2559]) ).

thf(1907,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

thf(11705,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1907]) ).

thf(426,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r2_hidden @ A @ ( k4_card_3 @ ( k11_finseq_1 @ B @ C @ D ) ) )
    <=> ? [E: $i,F: $i,G: $i] :
          ( ( r2_hidden @ E @ B )
          & ( r2_hidden @ F @ C )
          & ( r2_hidden @ G @ D )
          & ( A
            = ( k11_finseq_1 @ E @ F @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_funct_6) ).

thf(4872,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r2_hidden @ A @ ( k4_card_3 @ ( k11_finseq_1 @ B @ C @ D ) ) )
       => ? [E: $i,F: $i,G: $i] :
            ( ( r2_hidden @ E @ B )
            & ( r2_hidden @ F @ C )
            & ( r2_hidden @ G @ D )
            & ( A
              = ( k11_finseq_1 @ E @ F @ G ) ) ) )
      & ( ? [E: $i,F: $i,G: $i] :
            ( ( r2_hidden @ E @ B )
            & ( r2_hidden @ F @ C )
            & ( r2_hidden @ G @ D )
            & ( A
              = ( k11_finseq_1 @ E @ F @ G ) ) )
       => ( r2_hidden @ A @ ( k4_card_3 @ ( k11_finseq_1 @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(2201,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( r1_tarski @ ( k7_setfam_1 @ A @ B ) @ C )
          <=> ( r1_tarski @ B @ ( k7_setfam_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_setfam_1) ).

thf(13331,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( ( r1_tarski @ ( k7_setfam_1 @ A @ B ) @ C )
             => ( r1_tarski @ B @ ( k7_setfam_1 @ A @ C ) ) )
            & ( ( r1_tarski @ B @ ( k7_setfam_1 @ A @ C ) )
             => ( r1_tarski @ ( k7_setfam_1 @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2201]) ).

thf(2230,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
        & ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
     => ( ( B != k1_xboole_0 )
       => ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_2) ).

thf(13455,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
        & ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
     => ( ( B != k1_xboole_0 )
       => ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2230]) ).

thf(1407,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ B ) )
     => ( ( v1_xboole_0 @ ( k5_relat_1 @ B @ A ) )
        & ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).

thf(9231,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ B ) )
     => ( ( v1_xboole_0 @ ( k5_relat_1 @ B @ A ) )
        & ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1407]) ).

thf(2174,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ A @ A )
            & ( m2_relset_1 @ B @ A @ A ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( r7_binop_1 @ A @ B @ C )
              <=> ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ( ( k8_funct_2 @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
                          = ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ A @ A @ B @ D ) @ ( k8_funct_2 @ A @ A @ B @ E ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d20_binop_1) ).

thf(13201,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ A @ A )
            & ( m2_relset_1 @ B @ A @ A ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( ( r7_binop_1 @ A @ B @ C )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( k8_funct_2 @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
                            = ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ A @ A @ B @ D ) @ ( k8_funct_2 @ A @ A @ B @ E ) ) ) ) ) )
                & ( ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( k8_funct_2 @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) )
                            = ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ A @ A @ B @ D ) @ ( k8_funct_2 @ A @ A @ B @ E ) ) ) ) )
                 => ( r7_binop_1 @ A @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2174]) ).

thf(658,axiom,
    ! [A: $i] : ( v3_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_setwiseo) ).

thf(5808,plain,
    ! [A: $i] : ( v3_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(2259,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( k7_setfam_1 @ A @ ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ B @ C ) )
            = ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ ( k7_setfam_1 @ A @ B ) @ ( k7_setfam_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_setfam_1) ).

thf(13544,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( k7_setfam_1 @ A @ ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ B @ C ) )
            = ( k4_subset_1 @ ( k1_zfmisc_1 @ A ) @ ( k7_setfam_1 @ A @ B ) @ ( k7_setfam_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2259]) ).

thf(289,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
        = A )
      & ( r1_tarski @ ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) ) @ ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funcop_1) ).

thf(4116,plain,
    ! [A: $i,B: $i] :
      ( ( ( k1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
        = A )
      & ( r1_tarski @ ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) ) @ ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(2376,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) )
     => ( ( r2_hidden @ A @ ( a_2_0_card_fil @ B @ C ) )
      <=> ? [D: $i] :
            ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
            & ( A = D )
            & ( r2_hidden @ ( k3_subset_1 @ B @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_card_fil) ).

thf(13989,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) )
     => ( ( ( r2_hidden @ A @ ( a_2_0_card_fil @ B @ C ) )
         => ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
              & ( A = D )
              & ( r2_hidden @ ( k3_subset_1 @ B @ D ) @ C ) ) )
        & ( ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
              & ( A = D )
              & ( r2_hidden @ ( k3_subset_1 @ B @ D ) @ C ) )
         => ( r2_hidden @ A @ ( a_2_0_card_fil @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2376]) ).

thf(373,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ ( k1_relat_1 @ B ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_funct_4) ).

thf(4613,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ ( k1_relat_1 @ B ) )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(944,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_enumset1 @ A @ A @ A @ B )
      = ( k2_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_enumset1) ).

thf(7128,plain,
    ! [A: $i,B: $i] :
      ( ( k2_enumset1 @ A @ A @ A @ B )
      = ( k2_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(832,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( v1_binop_1 @ B @ A )
           => ( ( r3_binop_1 @ A @ C @ B )
            <=> ( r1_binop_1 @ A @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_binop_1) ).

thf(6615,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( v1_binop_1 @ B @ A )
           => ( ( ( r3_binop_1 @ A @ C @ B )
               => ( r1_binop_1 @ A @ C @ B ) )
              & ( ( r1_binop_1 @ A @ C @ B )
               => ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(646,axiom,
    ! [A: $i] :
      ( ( ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_xboole_0 @ ( k2_funct_4 @ A ) )
        & ( v1_relat_1 @ ( k2_funct_4 @ A ) )
        & ( v1_funct_1 @ ( k2_funct_4 @ A ) )
        & ( v2_funct_1 @ ( k2_funct_4 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_functor0) ).

thf(5762,plain,
    ! [A: $i] :
      ( ( ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_xboole_0 @ ( k2_funct_4 @ A ) )
        & ( v1_relat_1 @ ( k2_funct_4 @ A ) )
        & ( v1_funct_1 @ ( k2_funct_4 @ A ) )
        & ( v2_funct_1 @ ( k2_funct_4 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(1622,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k9_classes2 @ A @ B @ C )
        = ( k4_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_classes2) ).

thf(10227,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k9_classes2 @ A @ B @ C )
        = ( k4_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1622]) ).

thf(2129,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_zfmisc_1) ).

thf(12982,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2129]) ).

thf(1017,axiom,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
        & ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) )
     => ( ( A = k35_binop_2 )
      <=> ! [B: $i] :
            ( ( m1_subset_1 @ B @ k1_numbers )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ k1_numbers )
               => ( ( k2_binop_1 @ k1_numbers @ k1_numbers @ k1_numbers @ A @ B @ C )
                  = ( k11_binop_2 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_binop_2) ).

thf(7512,plain,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
        & ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) )
     => ( ( ( A = k35_binop_2 )
         => ! [B: $i] :
              ( ( m1_subset_1 @ B @ k1_numbers )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ k1_numbers )
                 => ( ( k2_binop_1 @ k1_numbers @ k1_numbers @ k1_numbers @ A @ B @ C )
                    = ( k11_binop_2 @ B @ C ) ) ) ) )
        & ( ! [B: $i] :
              ( ( m1_subset_1 @ B @ k1_numbers )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ k1_numbers )
                 => ( ( k2_binop_1 @ k1_numbers @ k1_numbers @ k1_numbers @ A @ B @ C )
                    = ( k11_binop_2 @ B @ C ) ) ) )
         => ( A = k35_binop_2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).

thf(1617,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ B @ C )
     => ( ( r1_tarski @ A @ D )
       => ( m2_relset_1 @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_relset_1) ).

thf(10202,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ B @ C )
     => ( ( r1_tarski @ A @ D )
       => ( m2_relset_1 @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1617]) ).

thf(688,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( v1_xboole_0 @ C )
     => ! [D: $i] :
          ( ~ ( v1_xboole_0 @ D )
         => ! [E: $i] :
              ( ( ( v1_funct_1 @ E )
                & ( v1_funct_2 @ E @ A @ C )
                & ( m2_relset_1 @ E @ A @ C ) )
             => ! [F: $i] :
                  ( ( ( v1_funct_1 @ F )
                    & ( v1_funct_2 @ F @ B @ D )
                    & ( m2_relset_1 @ F @ B @ D ) )
                 => ( ( k16_funct_3 @ A @ B @ C @ D @ E @ F )
                    = ( k13_funct_3 @ ( k5_relat_1 @ ( k9_funct_3 @ A @ B ) @ E ) @ ( k5_relat_1 @ ( k10_funct_3 @ A @ B ) @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_funct_3) ).

thf(5969,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( v1_xboole_0 @ C )
     => ! [D: $i] :
          ( ~ ( v1_xboole_0 @ D )
         => ! [E: $i] :
              ( ( ( v1_funct_1 @ E )
                & ( v1_funct_2 @ E @ A @ C )
                & ( m2_relset_1 @ E @ A @ C ) )
             => ! [F: $i] :
                  ( ( ( v1_funct_1 @ F )
                    & ( v1_funct_2 @ F @ B @ D )
                    & ( m2_relset_1 @ F @ B @ D ) )
                 => ( ( k16_funct_3 @ A @ B @ C @ D @ E @ F )
                    = ( k13_funct_3 @ ( k5_relat_1 @ ( k9_funct_3 @ A @ B ) @ E ) @ ( k5_relat_1 @ ( k10_funct_3 @ A @ B ) @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ~ ( ~ ( v1_finset_1 @ ( k1_relat_1 @ A ) )
          & ( v2_funct_1 @ A )
          & ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_frechet2) ).

thf(2717,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ~ ( ~ ( v1_finset_1 @ ( k1_relat_1 @ A ) )
          & ( v2_funct_1 @ A )
          & ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(2432,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k7_domain_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_domain_1) ).

thf(14195,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k7_domain_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2432]) ).

thf(1403,axiom,
    ! [A: $i] :
      ( ( r2_hidden @ k1_xboole_0 @ A )
     => ( ( k1_setfam_1 @ A )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_setfam_1) ).

thf(9203,plain,
    ! [A: $i] :
      ( ( r2_hidden @ k1_xboole_0 @ A )
     => ( ( k1_setfam_1 @ A )
        = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403]) ).

thf(1289,axiom,
    ! [A: $i,B: $i] :
      ( ( ( r2_hidden @ B @ A )
        & ( v1_membered @ B ) )
     => ( v1_membered @ ( k1_setfam_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_membered) ).

thf(8713,plain,
    ! [A: $i,B: $i] :
      ( ( ( r2_hidden @ B @ A )
        & ( v1_membered @ B ) )
     => ( v1_membered @ ( k1_setfam_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).

thf(2271,axiom,
    ! [A: $i] :
      ( ( v1_funct_1 @ ( k12_funct_3 @ A ) )
      & ( v1_funct_2 @ ( k12_funct_3 @ A ) @ A @ ( k2_zfmisc_1 @ A @ A ) )
      & ( m2_relset_1 @ ( k12_funct_3 @ A ) @ A @ ( k2_zfmisc_1 @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_funct_3) ).

thf(13584,plain,
    ! [A: $i] :
      ( ( v1_funct_1 @ ( k12_funct_3 @ A ) )
      & ( v1_funct_2 @ ( k12_funct_3 @ A ) @ A @ ( k2_zfmisc_1 @ A @ A ) )
      & ( m2_relset_1 @ ( k12_funct_3 @ A ) @ A @ ( k2_zfmisc_1 @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2271]) ).

thf(1577,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ( k3_classes2 @ A @ B )
        = ( k3_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_classes2) ).

thf(10030,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ( k3_classes2 @ A @ B )
        = ( k3_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1577]) ).

thf(1202,axiom,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) )
      = ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_xboole_1) ).

thf(8290,plain,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) )
      = ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).

thf(1073,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ( ( r2_hidden @ C @ B )
                 => ( r1_xboole_0 @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_mcart_1) ).

thf(7742,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ( ( r2_hidden @ C @ B )
                 => ( r1_xboole_0 @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).

thf(1136,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( r1_tarski @ C @ D )
           => ( ( v1_funct_1 @ C )
              & ( m2_relset_1 @ C @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_partfun1) ).

thf(8040,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( r1_tarski @ C @ D )
           => ( ( v1_funct_1 @ C )
              & ( m2_relset_1 @ C @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).

thf(953,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k3_enumset1 @ A @ B @ C @ D @ E )
      = ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k2_enumset1 @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_enumset1) ).

thf(7155,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k3_enumset1 @ A @ B @ C @ D @ E )
      = ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k2_enumset1 @ B @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).

thf(2354,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) ) )
     => ! [C: $i] :
          ( ( m1_triang_1 @ C @ A @ B )
        <=> ( m1_subset_1 @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_triang_1) ).

thf(13896,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) ) )
     => ! [C: $i] :
          ( ( ( m1_triang_1 @ C @ A @ B )
           => ( m1_subset_1 @ C @ B ) )
          & ( ( m1_subset_1 @ C @ B )
           => ( m1_triang_1 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2354]) ).

thf(1974,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
      & ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finset_1) ).

thf(12119,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
      & ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1974]) ).

thf(1586,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ~ ( v1_xboole_0 @ E )
                     => ( ! [F: $i] :
                            ( ( r2_hidden @ F @ A )
                          <=> ? [G: $i] :
                                ( ( m1_subset_1 @ G @ B )
                                & ? [H: $i] :
                                    ( ( m1_subset_1 @ H @ C )
                                    & ? [I: $i] :
                                        ( ( m1_subset_1 @ I @ D )
                                        & ? [J: $i] :
                                            ( ( m1_subset_1 @ J @ E )
                                            & ( F
                                              = ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) ) )
                       => ( A
                          = ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_domain_1) ).

thf(10079,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ~ ( v1_xboole_0 @ E )
                     => ( ! [F: $i] :
                            ( ( ( r2_hidden @ F @ A )
                             => ? [G: $i] :
                                  ( ( m1_subset_1 @ G @ B )
                                  & ? [H: $i] :
                                      ( ( m1_subset_1 @ H @ C )
                                      & ? [I: $i] :
                                          ( ( m1_subset_1 @ I @ D )
                                          & ? [J: $i] :
                                              ( ( m1_subset_1 @ J @ E )
                                              & ( F
                                                = ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) ) )
                            & ( ? [G: $i] :
                                  ( ( m1_subset_1 @ G @ B )
                                  & ? [H: $i] :
                                      ( ( m1_subset_1 @ H @ C )
                                      & ? [I: $i] :
                                          ( ( m1_subset_1 @ I @ D )
                                          & ? [J: $i] :
                                              ( ( m1_subset_1 @ J @ E )
                                              & ( F
                                                = ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) )
                             => ( r2_hidden @ F @ A ) ) )
                       => ( A
                          = ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1586]) ).

thf(825,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).

thf(6578,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(2490,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ! [B: $i] :
            ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
           => ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_lopclset) ).

thf(14469,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ! [B: $i] :
            ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
           => ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2490]) ).

thf(2366,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k8_classes2 @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_classes2) ).

thf(13947,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k8_classes2 @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2366]) ).

thf(1995,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_enumset1 @ A @ A @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_enumset1) ).

thf(12265,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_enumset1 @ A @ A @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1995]) ).

thf(2346,axiom,
    ! [A: $i] :
      ( ( r2_hidden @ A @ a_0_0_domain_1 )
    <=> ? [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s7_domain_1 )
          & ( A = B )
          & ( p1_s7_domain_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_0_domain_1) ).

thf(13864,plain,
    ! [A: $i] :
      ( ( ( r2_hidden @ A @ a_0_0_domain_1 )
       => ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s7_domain_1 )
            & ( A = B )
            & ( p1_s7_domain_1 @ B ) ) )
      & ( ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s7_domain_1 )
            & ( A = B )
            & ( p1_s7_domain_1 @ B ) )
       => ( r2_hidden @ A @ a_0_0_domain_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2346]) ).

thf(359,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ( ( k3_ens_1 @ A @ B )
            = ( k1_mcart_1 @ ( k1_mcart_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ens_1) ).

thf(4562,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ( ( k3_ens_1 @ A @ B )
            = ( k1_mcart_1 @ ( k1_mcart_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(1772,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funct_2) ).

thf(11016,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1772]) ).

thf(1369,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i] :
          ( ! [C: $i] :
              ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
             => ( ( r2_hidden @ C @ ( k4_finseq_1 @ A ) )
               => ( r2_hidden @ ( k1_funct_1 @ A @ C ) @ B ) ) )
         => ( m2_finseq_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finseq_2) ).

thf(9021,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i] :
          ( ! [C: $i] :
              ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
             => ( ( r2_hidden @ C @ ( k4_finseq_1 @ A ) )
               => ( r2_hidden @ ( k1_funct_1 @ A @ C ) @ B ) ) )
         => ( m2_finseq_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).

thf(2470,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ B )
         => ( v1_finset_1 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_triang_1) ).

thf(14373,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ B )
         => ( v1_finset_1 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2470]) ).

thf(749,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k4_subset_1 @ A @ B @ C )
        = ( k2_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).

thf(6243,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k4_subset_1 @ A @ B @ C )
        = ( k2_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(1037,axiom,
    ! [A: $i,B: $i] :
      ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).

thf(7599,plain,
    ! [A: $i,B: $i] :
      ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).

thf(694,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
     => ( ! [F: $i] :
            ( ( m1_subset_1 @ F @ A )
           => ! [G: $i] :
                ( ( m1_subset_1 @ G @ B )
               => ! [H: $i] :
                    ( ( m1_subset_1 @ H @ C )
                   => ( ( E
                        = ( k3_mcart_1 @ F @ G @ H ) )
                     => ( D = F ) ) ) ) )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 )
          | ( C = k1_xboole_0 )
          | ( D
            = ( k5_mcart_1 @ A @ B @ C @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_mcart_1) ).

thf(6001,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
     => ( ! [F: $i] :
            ( ( m1_subset_1 @ F @ A )
           => ! [G: $i] :
                ( ( m1_subset_1 @ G @ B )
               => ! [H: $i] :
                    ( ( m1_subset_1 @ H @ C )
                   => ( ( E
                        = ( k3_mcart_1 @ F @ G @ H ) )
                     => ( D = F ) ) ) ) )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 )
          | ( C = k1_xboole_0 )
          | ( D
            = ( k5_mcart_1 @ A @ B @ C @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(121,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( r1_tarski @ A @ ( k1_funct_4 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_funct_4) ).

thf(3289,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( r1_tarski @ A @ ( k1_funct_4 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(1542,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m2_realset1 @ C @ A @ B ) )
     => ( ( v1_funct_1 @ ( k3_realset1 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k3_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
        & ( m2_relset_1 @ ( k3_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_realset1) ).

thf(9853,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m2_realset1 @ C @ A @ B ) )
     => ( ( v1_funct_1 @ ( k3_realset1 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k3_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
        & ( m2_relset_1 @ ( k3_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1542]) ).

thf(801,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
     => ( ( k5_setwiseo @ A @ B @ C )
        = ( k5_setwiseo @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_setwiseo) ).

thf(6469,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
     => ( ( k5_setwiseo @ A @ B @ C )
        = ( k5_setwiseo @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(1452,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( v1_binop_1 @ C @ A )
               => ( ( r6_binop_1 @ A @ C @ B )
                <=> ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ! [F: $i] :
                              ( ( m1_subset_1 @ F @ A )
                             => ( ( k2_binop_1 @ A @ A @ A @ C @ D @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) )
                                = ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_binop_1) ).

thf(9404,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( v1_binop_1 @ C @ A )
               => ( ( ( r6_binop_1 @ A @ C @ B )
                   => ! [D: $i] :
                        ( ( m1_subset_1 @ D @ A )
                       => ! [E: $i] :
                            ( ( m1_subset_1 @ E @ A )
                           => ! [F: $i] :
                                ( ( m1_subset_1 @ F @ A )
                               => ( ( k2_binop_1 @ A @ A @ A @ C @ D @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) )
                                  = ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) ) ) ) ) ) )
                  & ( ! [D: $i] :
                        ( ( m1_subset_1 @ D @ A )
                       => ! [E: $i] :
                            ( ( m1_subset_1 @ E @ A )
                           => ! [F: $i] :
                                ( ( m1_subset_1 @ F @ A )
                               => ( ( k2_binop_1 @ A @ A @ A @ C @ D @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) )
                                  = ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) ) ) ) ) )
                   => ( r6_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452]) ).

thf(231,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ A )
        & ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_sysrel) ).

thf(3888,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ A )
        & ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(992,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
      = ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_xboole_1) ).

thf(7382,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
      = ( k3_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).

thf(816,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k5_subset_1 @ A @ B @ C )
        = ( k3_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).

thf(6546,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k5_subset_1 @ A @ B @ C )
        = ( k3_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(747,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) )
      = ( k2_xboole_0 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).

thf(6228,plain,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) )
      = ( k2_xboole_0 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(589,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
      = ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ C ) @ B ) @ ( k2_zfmisc_1 @ A @ ( k4_xboole_0 @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t126_zfmisc_1) ).

thf(5525,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
      = ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ C ) @ B ) @ ( k2_zfmisc_1 @ A @ ( k4_xboole_0 @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(2341,axiom,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s1_yellow_3 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s1_yellow_3 )
           => ( r2_hidden @ ( f2_s1_yellow_3 @ A @ B ) @ f1_s1_yellow_3 ) ) )
   => ( m1_subset_1 @ a_0_0_yellow_3 @ ( k1_zfmisc_1 @ f1_s1_yellow_3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_yellow_3) ).

thf(13849,plain,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s1_yellow_3 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s1_yellow_3 )
           => ( r2_hidden @ ( f2_s1_yellow_3 @ A @ B ) @ f1_s1_yellow_3 ) ) )
   => ( m1_subset_1 @ a_0_0_yellow_3 @ ( k1_zfmisc_1 @ f1_s1_yellow_3 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2341]) ).

thf(313,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ( ( ( v3_binop_1 @ C @ A )
                      & ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
                           => ~ ( ( E != k1_xboole_0 )
                                & ( F != k1_xboole_0 )
                                & ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ E @ F ) @ D )
                                 != ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ E @ D ) @ ( k7_setwiseo @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_setwiseo) ).

thf(4269,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ( ( ( v3_binop_1 @ C @ A )
                      & ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k5_finsub_1 @ B ) )
                           => ~ ( ( E != k1_xboole_0 )
                                & ( F != k1_xboole_0 )
                                & ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ E @ F ) @ D )
                                 != ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ E @ D ) @ ( k7_setwiseo @ B @ A @ C @ F @ D ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(1462,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ! [D: $i] :
              ( ( k5_relat_1 @ ( k6_partfun1 @ B ) @ ( k4_funcop_1 @ C @ A @ D ) )
              = ( k4_funcop_1 @ C @ ( k7_relat_1 @ A @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_funcop_1) ).

thf(9451,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ! [D: $i] :
              ( ( k5_relat_1 @ ( k6_partfun1 @ B ) @ ( k4_funcop_1 @ C @ A @ D ) )
              = ( k4_funcop_1 @ C @ ( k7_relat_1 @ A @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462]) ).

thf(201,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( v2_funct_1 @ B ) )
           => ( ( k2_funct_1 @ ( k2_funct_4 @ ( k15_funct_3 @ A @ B ) ) )
              = ( k2_funct_4 @ ( k2_funct_1 @ ( k15_funct_3 @ B @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_functor0) ).

thf(3696,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( v2_funct_1 @ B ) )
           => ( ( k2_funct_1 @ ( k2_funct_4 @ ( k15_funct_3 @ A @ B ) ) )
              = ( k2_funct_4 @ ( k2_funct_1 @ ( k15_funct_3 @ B @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(2563,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( A
        = ( a_1_0_domain_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_domain_1) ).

thf(14776,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( A
        = ( a_1_0_domain_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2563]) ).

thf(1852,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m1_relset_1 @ B @ A @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ A )
        & ( m1_relset_1 @ C @ A @ A ) )
     => ( ( v1_funct_1 @ ( k2_monoid_0 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k2_monoid_0 @ A @ B @ C ) @ A @ A )
        & ( m2_relset_1 @ ( k2_monoid_0 @ A @ B @ C ) @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_monoid_0) ).

thf(11459,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m1_relset_1 @ B @ A @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ A )
        & ( m1_relset_1 @ C @ A @ A ) )
     => ( ( v1_funct_1 @ ( k2_monoid_0 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k2_monoid_0 @ A @ B @ C ) @ A @ A )
        & ( m2_relset_1 @ ( k2_monoid_0 @ A @ B @ C ) @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1852]) ).

thf(2092,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_funct_1 @ k1_xboole_0 )
      & ( m2_relset_1 @ k1_xboole_0 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_partfun1) ).

thf(12778,plain,
    ! [A: $i,B: $i] :
      ( ( v1_funct_1 @ k1_xboole_0 )
      & ( m2_relset_1 @ k1_xboole_0 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2092]) ).

thf(644,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
     => ( m1_subset_1 @ ( k6_mcart_1 @ A @ B @ C @ D ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_mcart_1) ).

thf(5758,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
     => ( m1_subset_1 @ ( k6_mcart_1 @ A @ B @ C @ D ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(789,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ C )
      = ( k2_xboole_0 @ ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) @ ( k4_xboole_0 @ B @ ( k2_xboole_0 @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_xboole_1) ).

thf(6422,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ C )
      = ( k2_xboole_0 @ ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) @ ( k4_xboole_0 @ B @ ( k2_xboole_0 @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(2137,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ ( k3_tarski @ A ) @ B )
        & ( r2_hidden @ C @ A ) )
     => ( r1_tarski @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_setfam_1) ).

thf(13031,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ ( k3_tarski @ A ) @ B )
        & ( r2_hidden @ C @ A ) )
     => ( r1_tarski @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2137]) ).

thf(1751,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( A
         != ( k1_tarski @ B ) )
        & ( A != k1_xboole_0 )
        & ! [C: $i] :
            ~ ( ( r2_hidden @ C @ A )
              & ( C != B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_zfmisc_1) ).

thf(10890,plain,
    ! [A: $i,B: $i] :
      ~ ( ( A
         != ( k1_tarski @ B ) )
        & ( A != k1_xboole_0 )
        & ! [C: $i] :
            ~ ( ( r2_hidden @ C @ A )
              & ( C != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1751]) ).

thf(2196,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ( ( v3_card_fil @ B @ A )
          <=> ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
               => ( ( r2_hidden @ C @ B )
                  | ( r2_hidden @ ( k1_card_fil @ A @ C ) @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_card_fil) ).

thf(13296,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ( ( ( v3_card_fil @ B @ A )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                 => ( ( r2_hidden @ C @ B )
                    | ( r2_hidden @ ( k1_card_fil @ A @ C ) @ B ) ) ) )
            & ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                 => ( ( r2_hidden @ C @ B )
                    | ( r2_hidden @ ( k1_card_fil @ A @ C ) @ B ) ) )
             => ( v3_card_fil @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2196]) ).

thf(612,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ B )
                        & ( m2_relset_1 @ E @ B @ B ) )
                     => ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
                        = ( k6_funcop_1 @ B @ A @ C @ ( k7_funct_2 @ A @ B @ B @ D @ E ) @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funcop_1) ).

thf(5598,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ B )
                        & ( m2_relset_1 @ E @ B @ B ) )
                     => ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ E @ ( k6_partfun1 @ B ) ) )
                        = ( k6_funcop_1 @ B @ A @ C @ ( k7_funct_2 @ A @ B @ B @ D @ E ) @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(2104,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
         => ~ ( ( B != k1_xboole_0 )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ~ ( r2_hidden @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_setwiseo) ).

thf(12827,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
         => ~ ( ( B != k1_xboole_0 )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ~ ( r2_hidden @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2104]) ).

thf(2263,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
             => ! [D: $i,E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ B )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ( ! [F: $i] :
                        ( ( m1_subset_1 @ F @ A )
                       => ( ( r2_hidden @ F @ C )
                         => ( r2_hidden @ ( k8_funct_2 @ A @ B @ E @ F ) @ D ) ) )
                   => ( r1_tarski @ ( k2_funct_2 @ A @ B @ E @ C ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_setwiseo) ).

thf(13559,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
             => ! [D: $i,E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ B )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ( ! [F: $i] :
                        ( ( m1_subset_1 @ F @ A )
                       => ( ( r2_hidden @ F @ C )
                         => ( r2_hidden @ ( k8_funct_2 @ A @ B @ E @ F ) @ D ) ) )
                   => ( r1_tarski @ ( k2_funct_2 @ A @ B @ E @ C ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2263]) ).

thf(1041,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A != C )
     => ( ( k4_funct_4 @ A @ C @ B @ D )
        = ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_funct_4) ).

thf(7611,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A != C )
     => ( ( k4_funct_4 @ A @ C @ B @ D )
        = ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

thf(1103,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( ( k5_relat_1 @ k1_xboole_0 @ A )
          = k1_xboole_0 )
        & ( ( k5_relat_1 @ A @ k1_xboole_0 )
          = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_relat_1) ).

thf(7860,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( ( k5_relat_1 @ k1_xboole_0 @ A )
          = k1_xboole_0 )
        & ( ( k5_relat_1 @ A @ k1_xboole_0 )
          = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).

thf(2003,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                     => ! [F: $i] :
                          ( ( m2_finseq_1 @ F @ A )
                         => ( m2_finseq_1 @ ( k4_funcop_1 @ E @ F @ D ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_finseq_2) ).

thf(12301,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                     => ! [F: $i] :
                          ( ( m2_finseq_1 @ F @ A )
                         => ( m2_finseq_1 @ ( k4_funcop_1 @ E @ F @ D ) @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2003]) ).

thf(2384,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k3_classes2 @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_classes2) ).

thf(14021,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k3_classes2 @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2384]) ).

thf(185,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( ( r1_partfun1 @ A @ B )
            <=> ! [C: $i] :
                  ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
                 => ( ( k1_funct_1 @ A @ C )
                    = ( k1_funct_1 @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_partfun1) ).

thf(3604,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( ( ( r1_partfun1 @ A @ B )
               => ! [C: $i] :
                    ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
                   => ( ( k1_funct_1 @ A @ C )
                      = ( k1_funct_1 @ B @ C ) ) ) )
              & ( ! [C: $i] :
                    ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
                   => ( ( k1_funct_1 @ A @ C )
                      = ( k1_funct_1 @ B @ C ) ) )
               => ( r1_partfun1 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(2296,axiom,
    ? [A: $i] :
      ( ( m1_pboole @ A @ ( k3_zfmisc_1 @ f1_s4_altcat_1 @ f2_s4_altcat_1 @ f3_s4_altcat_1 ) )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s4_altcat_1 )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ f2_s4_altcat_1 )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ f3_s4_altcat_1 )
                 => ( ( k1_multop_1 @ A @ B @ C @ D )
                    = ( f4_s4_altcat_1 @ B @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_altcat_1) ).

thf(13685,plain,
    ? [A: $i] :
      ( ( m1_pboole @ A @ ( k3_zfmisc_1 @ f1_s4_altcat_1 @ f2_s4_altcat_1 @ f3_s4_altcat_1 ) )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s4_altcat_1 )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ f2_s4_altcat_1 )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ f3_s4_altcat_1 )
                 => ( ( k1_multop_1 @ A @ B @ C @ D )
                    = ( f4_s4_altcat_1 @ B @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2296]) ).

thf(1454,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_enumset1 @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_enumset1) ).

thf(9418,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_enumset1 @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454]) ).

thf(2034,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( v1_xboole_0 @ C )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
            & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
         => ( ( k2_funct_4 @ ( k2_funct_4 @ D ) )
            = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funct_4) ).

thf(12441,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( v1_xboole_0 @ C )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
            & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
         => ( ( k2_funct_4 @ ( k2_funct_4 @ D ) )
            = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2034]) ).

thf(98,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( ( ( k1_relat_1 @ D )
                        = ( k1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) ) )
                      & ! [E: $i] :
                          ( ( r2_hidden @ E @ ( k1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) ) )
                         => ( ( k1_funct_1 @ D @ E )
                            = ( k1_binop_1 @ C @ ( k1_funct_1 @ A @ E ) @ ( k1_funct_1 @ B @ E ) ) ) ) )
                   => ( D
                      = ( k3_funcop_1 @ C @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funcop_1) ).

thf(3187,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( ( v1_relat_1 @ D )
                    & ( v1_funct_1 @ D ) )
                 => ( ( ( ( k1_relat_1 @ D )
                        = ( k1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) ) )
                      & ! [E: $i] :
                          ( ( r2_hidden @ E @ ( k1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) ) )
                         => ( ( k1_funct_1 @ D @ E )
                            = ( k1_binop_1 @ C @ ( k1_funct_1 @ A @ E ) @ ( k1_funct_1 @ B @ E ) ) ) ) )
                   => ( D
                      = ( k3_funcop_1 @ C @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(455,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i,D: $i] :
          ( ( k1_funct_4 @ ( k1_funct_4 @ A @ ( k2_funcop_1 @ B @ C ) ) @ ( k2_funcop_1 @ B @ D ) )
          = ( k1_funct_4 @ A @ ( k2_funcop_1 @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_7) ).

thf(4998,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i,D: $i] :
          ( ( k1_funct_4 @ ( k1_funct_4 @ A @ ( k2_funcop_1 @ B @ C ) ) @ ( k2_funcop_1 @ B @ D ) )
          = ( k1_funct_4 @ A @ ( k2_funcop_1 @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(1703,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B )
        & ( v1_finset_1 @ C ) )
     => ( v1_finset_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finset_1) ).

thf(10582,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B )
        & ( v1_finset_1 @ C ) )
     => ( v1_finset_1 @ ( k3_zfmisc_1 @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1703]) ).

thf(2235,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( ( v1_funct_1 @ G )
                                & ( v1_funct_2 @ G @ ( k2_zfmisc_1 @ A @ A ) @ A )
                                & ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                             => ! [H: $i] :
                                  ( ( ( v1_funct_1 @ H )
                                    & ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ B @ B ) @ B )
                                    & ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                                 => ( ( k2_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ G @ H ) @ ( k1_domain_1 @ A @ B @ C @ E ) @ ( k1_domain_1 @ A @ B @ D @ F ) )
                                    = ( k1_domain_1 @ A @ B @ ( k2_binop_1 @ A @ A @ A @ G @ C @ D ) @ ( k2_binop_1 @ B @ B @ B @ H @ E @ F ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_filter_1) ).

thf(13471,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( ( v1_funct_1 @ G )
                                & ( v1_funct_2 @ G @ ( k2_zfmisc_1 @ A @ A ) @ A )
                                & ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                             => ! [H: $i] :
                                  ( ( ( v1_funct_1 @ H )
                                    & ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ B @ B ) @ B )
                                    & ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                                 => ( ( k2_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ G @ H ) @ ( k1_domain_1 @ A @ B @ C @ E ) @ ( k1_domain_1 @ A @ B @ D @ F ) )
                                    = ( k1_domain_1 @ A @ B @ ( k2_binop_1 @ A @ A @ A @ G @ C @ D ) @ ( k2_binop_1 @ B @ B @ B @ H @ E @ F ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2235]) ).

thf(569,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ B )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ( ( ( k2_partfun1 @ A @ B @ D @ C )
                      = ( k2_partfun1 @ A @ B @ E @ C ) )
                  <=> ! [F: $i] :
                        ( ( m1_subset_1 @ F @ A )
                       => ( ( r2_hidden @ F @ C )
                         => ( ( k1_funct_1 @ E @ F )
                            = ( k1_funct_1 @ D @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_lattice2) ).

thf(5456,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ B )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ( ( ( ( k2_partfun1 @ A @ B @ D @ C )
                        = ( k2_partfun1 @ A @ B @ E @ C ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ( ( r2_hidden @ F @ C )
                           => ( ( k1_funct_1 @ E @ F )
                              = ( k1_funct_1 @ D @ F ) ) ) ) )
                    & ( ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ( ( r2_hidden @ F @ C )
                           => ( ( k1_funct_1 @ E @ F )
                              = ( k1_funct_1 @ D @ F ) ) ) )
                     => ( ( k2_partfun1 @ A @ B @ D @ C )
                        = ( k2_partfun1 @ A @ B @ E @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(1121,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ B )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ( ! [F: $i] :
                        ( ( m1_subset_1 @ F @ A )
                       => ( ( r2_hidden @ F @ C )
                         => ( ( k1_funct_1 @ D @ F )
                            = ( k1_funct_1 @ E @ F ) ) ) )
                   => ( ( k1_funct_4 @ E @ ( k2_partfun1 @ A @ B @ D @ C ) )
                      = E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_lattice2) ).

thf(7968,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ B )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ( ! [F: $i] :
                        ( ( m1_subset_1 @ F @ A )
                       => ( ( r2_hidden @ F @ C )
                         => ( ( k1_funct_1 @ D @ F )
                            = ( k1_funct_1 @ E @ F ) ) ) )
                   => ( ( k1_funct_4 @ E @ ( k2_partfun1 @ A @ B @ D @ C ) )
                      = E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).

thf(27,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r2_hidden @ A @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) ) )
           => ( ( k1_funct_1 @ ( k13_funct_3 @ B @ C ) @ A )
              = ( k4_tarski @ ( k1_funct_1 @ B @ A ) @ ( k1_funct_1 @ C @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_3) ).

thf(2727,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r2_hidden @ A @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) ) )
           => ( ( k1_funct_1 @ ( k13_funct_3 @ B @ C ) @ A )
              = ( k4_tarski @ ( k1_funct_1 @ B @ A ) @ ( k1_funct_1 @ C @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(53,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( ( k7_relat_1 @ B @ A )
          = k1_xboole_0 )
      <=> ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_relat_1) ).

thf(2970,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( ( ( k7_relat_1 @ B @ A )
            = k1_xboole_0 )
         => ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A ) )
        & ( ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ A )
         => ( ( k7_relat_1 @ B @ A )
            = k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(2419,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m2_subset_1 @ C @ A @ B )
        <=> ( m1_subset_1 @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_subset_1) ).

thf(14146,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( ( m2_subset_1 @ C @ A @ B )
           => ( m1_subset_1 @ C @ B ) )
          & ( ( m1_subset_1 @ C @ B )
           => ( m2_subset_1 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2419]) ).

thf(1367,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( r1_tarski @ ( k5_relat_1 @ B @ ( k7_relat_1 @ C @ A ) ) @ ( k5_relat_1 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_relat_1) ).

thf(9010,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( r1_tarski @ ( k5_relat_1 @ B @ ( k7_relat_1 @ C @ A ) ) @ ( k5_relat_1 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).

thf(1381,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
            & ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
              = k1_xboole_0 ) )
         => ( ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
            = ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
        & ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
            & ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
              = k1_xboole_0 ) )
         => ( ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
            = ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_sysrel) ).

thf(9062,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
            & ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
              = k1_xboole_0 ) )
         => ( ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
            = ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) )
        & ( ( ( r1_tarski @ A @ ( k5_relat_1 @ A @ A ) )
            & ( ( k5_relat_1 @ ( k4_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) @ A )
              = k1_xboole_0 ) )
         => ( ( k3_xboole_0 @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
            = ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381]) ).

thf(2498,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k10_classes2 @ A @ B @ C )
        = ( k10_classes2 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k10_classes2) ).

thf(14523,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k10_classes2 @ A @ B @ C )
        = ( k10_classes2 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2498]) ).

thf(1197,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( k1_oppcat_1 @ A @ B @ C @ D )
        = ( k2_funct_4 @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_oppcat_1) ).

thf(8259,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( k1_oppcat_1 @ A @ B @ C @ D )
        = ( k2_funct_4 @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).

thf(1789,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).

thf(11105,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1789]) ).

thf(1303,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k4_enumset1 @ A @ B @ C @ D @ E @ F )
      = ( k2_xboole_0 @ ( k3_enumset1 @ A @ B @ C @ D @ E ) @ ( k1_tarski @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_enumset1) ).

thf(8762,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k4_enumset1 @ A @ B @ C @ D @ E @ F )
      = ( k2_xboole_0 @ ( k3_enumset1 @ A @ B @ C @ D @ E ) @ ( k1_tarski @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).

thf(1871,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_relset_1 @ C @ A @ B )
         => ( ( ( v1_funct_1 @ C )
              & ( v1_funct_2 @ C @ A @ B ) )
           => ( ( v1_funct_1 @ C )
              & ( v1_partfun1 @ C @ A @ B )
              & ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_funct_2) ).

thf(11566,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_relset_1 @ C @ A @ B )
         => ( ( ( v1_funct_1 @ C )
              & ( v1_funct_2 @ C @ A @ B ) )
           => ( ( v1_funct_1 @ C )
              & ( v1_partfun1 @ C @ A @ B )
              & ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1871]) ).

thf(166,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( B
            = ( k2_relat_1 @ A ) )
        <=> ! [C: $i] :
              ( ( r2_hidden @ C @ B )
            <=> ? [D: $i] :
                  ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                  & ( C
                    = ( k1_funct_1 @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).

thf(3504,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( B
              = ( k2_relat_1 @ A ) )
           => ! [C: $i] :
                ( ( ( r2_hidden @ C @ B )
                 => ? [D: $i] :
                      ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                      & ( C
                        = ( k1_funct_1 @ A @ D ) ) ) )
                & ( ? [D: $i] :
                      ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                      & ( C
                        = ( k1_funct_1 @ A @ D ) ) )
                 => ( r2_hidden @ C @ B ) ) ) )
          & ( ! [C: $i] :
                ( ( ( r2_hidden @ C @ B )
                 => ? [D: $i] :
                      ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                      & ( C
                        = ( k1_funct_1 @ A @ D ) ) ) )
                & ( ? [D: $i] :
                      ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                      & ( C
                        = ( k1_funct_1 @ A @ D ) ) )
                 => ( r2_hidden @ C @ B ) ) )
           => ( B
              = ( k2_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(2373,axiom,
    ! [A: $i] :
      ( ( r2_hidden @ A @ a_0_0_pre_circ )
    <=> ? [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s1_pre_circ )
          & ( A
            = ( f2_s1_pre_circ @ B ) )
          & ( p1_s1_pre_circ @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_0_pre_circ) ).

thf(13972,plain,
    ! [A: $i] :
      ( ( ( r2_hidden @ A @ a_0_0_pre_circ )
       => ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s1_pre_circ )
            & ( A
              = ( f2_s1_pre_circ @ B ) )
            & ( p1_s1_pre_circ @ B ) ) )
      & ( ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s1_pre_circ )
            & ( A
              = ( f2_s1_pre_circ @ B ) )
            & ( p1_s1_pre_circ @ B ) )
       => ( r2_hidden @ A @ a_0_0_pre_circ ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2373]) ).

thf(1820,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( k3_funct_2 @ A @ B @ C @ B )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_funct_2) ).

thf(11279,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( k3_funct_2 @ A @ B @ C @ B )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1820]) ).

thf(1923,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D ) )
     => ( r1_tarski @ ( k4_partfun1 @ A @ C ) @ ( k4_partfun1 @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_partfun1) ).

thf(11836,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D ) )
     => ( r1_tarski @ ( k4_partfun1 @ A @ C ) @ ( k4_partfun1 @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1923]) ).

thf(578,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ( ( ( k4_relset_1 @ A @ A @ B )
          = A )
        & ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_2) ).

thf(5488,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ( ( ( k4_relset_1 @ A @ A @ B )
          = A )
        & ( r1_tarski @ ( k2_relat_1 @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(1693,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                 => ! [E: $i] :
                      ( ( m2_finseq_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m2_finseq_1 @ F @ B )
                         => ( m2_finseq_1 @ ( k3_funcop_1 @ D @ E @ F ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_finseq_2) ).

thf(10547,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                 => ! [E: $i] :
                      ( ( m2_finseq_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m2_finseq_1 @ F @ B )
                         => ( m2_finseq_1 @ ( k3_funcop_1 @ D @ E @ F ) @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1693]) ).

thf(886,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( k9_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
            = ( k9_relat_1 @ C @ ( k9_relat_1 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t159_relat_1) ).

thf(6881,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( k9_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
            = ( k9_relat_1 @ C @ ( k9_relat_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(812,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ B )
        & ( m1_subset_1 @ F @ C ) )
     => ( ( k4_domain_1 @ A @ B @ C @ D @ E @ F )
        = ( k3_mcart_1 @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_domain_1) ).

thf(6510,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ B )
        & ( m1_subset_1 @ F @ C ) )
     => ( ( k4_domain_1 @ A @ B @ C @ D @ E @ F )
        = ( k3_mcart_1 @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(719,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
          = k1_xboole_0 )
        & ( A != k1_xboole_0 )
        & ( A
         != ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_zfmisc_1) ).

thf(6108,plain,
    ! [A: $i,B: $i] :
      ~ ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
          = k1_xboole_0 )
        & ( A != k1_xboole_0 )
        & ( A
         != ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(110,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r1_tarski @ A @ ( k1_relat_1 @ ( k5_relat_1 @ B @ C ) ) )
           => ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k1_relat_1 @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funct_3) ).

thf(3240,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r1_tarski @ A @ ( k1_relat_1 @ ( k5_relat_1 @ B @ C ) ) )
           => ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k1_relat_1 @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(41,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) )
        = ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).

thf(2789,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) )
        = ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(764,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
         => ( r1_partfun1 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_partfun1) ).

thf(6312,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
         => ( r1_partfun1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(1616,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).

thf(10200,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1616]) ).

thf(1214,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( v1_relat_1 @ ( k4_funct_4 @ A @ B @ C @ D ) )
      & ( v1_funct_1 @ ( k4_funct_4 @ A @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_4) ).

thf(8349,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( v1_relat_1 @ ( k4_funct_4 @ A @ B @ C @ D ) )
      & ( v1_funct_1 @ ( k4_funct_4 @ A @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).

thf(475,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( ( ( k4_relset_1 @ A @ B @ C )
                = ( k4_relset_1 @ A @ B @ D ) )
              & ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
                   => ( ( k1_funct_1 @ C @ E )
                      = ( k1_funct_1 @ D @ E ) ) ) ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_partfun1) ).

thf(5065,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( ( ( k4_relset_1 @ A @ B @ C )
                = ( k4_relset_1 @ A @ B @ D ) )
              & ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
                   => ( ( k1_funct_1 @ C @ E )
                      = ( k1_funct_1 @ D @ E ) ) ) ) )
           => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(1884,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
     => ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
        = ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t175_partfun1) ).

thf(11615,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
     => ( ( k5_partfun1 @ k1_xboole_0 @ A @ B )
        = ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1884]) ).

thf(1906,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( v1_classes2 @ B ) )
         => ! [C: $i] :
              ( ( ~ ( v1_xboole_0 @ C )
                & ( v1_classes2 @ C ) )
             => ( ( ( r2_hidden @ A @ B )
                  & ( r2_hidden @ B @ C ) )
               => ( r2_hidden @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_classes2) ).

thf(11703,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( v1_classes2 @ B ) )
         => ! [C: $i] :
              ( ( ~ ( v1_xboole_0 @ C )
                & ( v1_classes2 @ C ) )
             => ( ( ( r2_hidden @ A @ B )
                  & ( r2_hidden @ B @ C ) )
               => ( r2_hidden @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1906]) ).

thf(1959,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( k3_subset_1 @ A @ ( k6_subset_1 @ A @ B @ C ) )
            = ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_subset_1) ).

thf(12038,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( k3_subset_1 @ A @ ( k6_subset_1 @ A @ B @ C ) )
            = ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1959]) ).

thf(678,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_xboole_0 @ A @ B )
    <=> ( ( k3_xboole_0 @ A @ B )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).

thf(5923,plain,
    ! [A: $i,B: $i] :
      ( ( ( r1_xboole_0 @ A @ B )
       => ( ( k3_xboole_0 @ A @ B )
          = k1_xboole_0 ) )
      & ( ( ( k3_xboole_0 @ A @ B )
          = k1_xboole_0 )
       => ( r1_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(2261,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
         => ( ( ( r1_tarski @ C @ D )
             => ( r1_tarski @ ( k1_cantor_1 @ A @ C ) @ ( k1_cantor_1 @ B @ D ) ) )
            & ( ( C = D )
             => ( ( k1_cantor_1 @ A @ C )
                = ( k1_cantor_1 @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_yellow_9) ).

thf(13550,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
         => ( ( ( r1_tarski @ C @ D )
             => ( r1_tarski @ ( k1_cantor_1 @ A @ C ) @ ( k1_cantor_1 @ B @ D ) ) )
            & ( ( C = D )
             => ( ( k1_cantor_1 @ A @ C )
                = ( k1_cantor_1 @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2261]) ).

thf(960,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v1_finset_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_finseq_1) ).

thf(7223,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v1_finset_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).

thf(1370,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
        & ( r1_xboole_0 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_xboole_1) ).

thf(9025,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
        & ( r1_xboole_0 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).

thf(1075,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
          = ( k1_tarski @ A ) )
        & ( r2_hidden @ B @ C )
        & ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_zfmisc_1) ).

thf(7751,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
          = ( k1_tarski @ A ) )
        & ( r2_hidden @ B @ C )
        & ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).

thf(2162,axiom,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ k1_numbers @ k1_numbers )
        & ( m2_relset_1 @ A @ k1_numbers @ k1_numbers ) )
     => ( ( A = k31_binop_2 )
      <=> ! [B: $i] :
            ( ( m1_subset_1 @ B @ k1_numbers )
           => ( ( k8_funct_2 @ k1_numbers @ k1_numbers @ A @ B )
              = ( k7_binop_2 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_binop_2) ).

thf(13157,plain,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ k1_numbers @ k1_numbers )
        & ( m2_relset_1 @ A @ k1_numbers @ k1_numbers ) )
     => ( ( ( A = k31_binop_2 )
         => ! [B: $i] :
              ( ( m1_subset_1 @ B @ k1_numbers )
             => ( ( k8_funct_2 @ k1_numbers @ k1_numbers @ A @ B )
                = ( k7_binop_2 @ B ) ) ) )
        & ( ! [B: $i] :
              ( ( m1_subset_1 @ B @ k1_numbers )
             => ( ( k8_funct_2 @ k1_numbers @ k1_numbers @ A @ B )
                = ( k7_binop_2 @ B ) ) )
         => ( A = k31_binop_2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2162]) ).

thf(216,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ( ( ( v3_binop_1 @ C @ A )
                      & ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A )
                      & ( r6_binop_1 @ A @ D @ C ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                       => ( ( E != k1_xboole_0 )
                         => ! [F: $i] :
                              ( ( ( v1_funct_1 @ F )
                                & ( v1_funct_2 @ F @ B @ A )
                                & ( m2_relset_1 @ F @ B @ A ) )
                             => ! [G: $i] :
                                  ( ( m1_subset_1 @ G @ A )
                                 => ( ( k2_binop_1 @ A @ A @ A @ D @ G @ ( k7_setwiseo @ B @ A @ C @ E @ F ) )
                                    = ( k7_setwiseo @ B @ A @ C @ E @ ( k8_funcop_1 @ A @ B @ D @ G @ F ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_setwiseo) ).

thf(3758,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ( ( ( v3_binop_1 @ C @ A )
                      & ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A )
                      & ( r6_binop_1 @ A @ D @ C ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                       => ( ( E != k1_xboole_0 )
                         => ! [F: $i] :
                              ( ( ( v1_funct_1 @ F )
                                & ( v1_funct_2 @ F @ B @ A )
                                & ( m2_relset_1 @ F @ B @ A ) )
                             => ! [G: $i] :
                                  ( ( m1_subset_1 @ G @ A )
                                 => ( ( k2_binop_1 @ A @ A @ A @ D @ G @ ( k7_setwiseo @ B @ A @ C @ E @ F ) )
                                    = ( k7_setwiseo @ B @ A @ C @ E @ ( k8_funcop_1 @ A @ B @ D @ G @ F ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(680,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_relat_1 @ ( k13_funct_3 @ A @ B ) )
        & ( v1_funct_1 @ ( k13_funct_3 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_funct_3) ).

thf(5940,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_relat_1 @ ( k13_funct_3 @ A @ B ) )
        & ( v1_funct_1 @ ( k13_funct_3 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(247,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                 => ( ( ( v2_binop_1 @ C @ A )
                      & ( v2_binop_1 @ D @ B ) )
                  <=> ( v2_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_filter_1) ).

thf(3945,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                 => ( ( ( ( v2_binop_1 @ C @ A )
                        & ( v2_binop_1 @ D @ B ) )
                     => ( v2_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) ) )
                    & ( ( v2_binop_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
                     => ( ( v2_binop_1 @ C @ A )
                        & ( v2_binop_1 @ D @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(120,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ~ ( ( ( k1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
              = A )
            & ( ( k2_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
              = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_sysrel) ).

thf(3283,plain,
    ! [A: $i,B: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ~ ( ( ( k1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
              = A )
            & ( ( k2_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
              = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(386,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ! [D: $i] :
              ( ( v1_relat_1 @ D )
             => ( ( ( ( k1_relat_1 @ B )
                    = A )
                  & ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
                  & ( ( k5_relat_1 @ C @ B )
                    = ( k6_relat_1 @ ( k1_relat_1 @ D ) ) )
                  & ( ( k5_relat_1 @ B @ D )
                    = ( k6_relat_1 @ A ) ) )
               => ( D = C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_relat_1) ).

thf(4677,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ! [D: $i] :
              ( ( v1_relat_1 @ D )
             => ( ( ( ( k1_relat_1 @ B )
                    = A )
                  & ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
                  & ( ( k5_relat_1 @ C @ B )
                    = ( k6_relat_1 @ ( k1_relat_1 @ D ) ) )
                  & ( ( k5_relat_1 @ B @ D )
                    = ( k6_relat_1 @ A ) ) )
               => ( D = C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(2122,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
     => ! [C: $i] :
          ( ( r1_tarski @ C @ B )
         => ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_setwiseo) ).

thf(12958,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
     => ! [C: $i] :
          ( ( r1_tarski @ C @ B )
         => ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2122]) ).

thf(1469,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k3_subset_1 @ A @ B )
        = ( k4_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).

thf(9471,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k3_subset_1 @ A @ B )
        = ( k4_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469]) ).

thf(290,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v2_funct_1 @ A ) )
     => ( ( v1_relat_1 @ ( k4_relat_1 @ A ) )
        & ( v1_funct_1 @ ( k4_relat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funct_1) ).

thf(4122,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v2_funct_1 @ A ) )
     => ( ( v1_relat_1 @ ( k4_relat_1 @ A ) )
        & ( v1_funct_1 @ ( k4_relat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(1731,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) )
                 => ( ( A
                      = ( k5_mcart_1 @ B @ C @ D @ E ) )
                  <=> ! [F: $i] :
                        ( ( m1_subset_1 @ F @ B )
                       => ! [G: $i] :
                            ( ( m1_subset_1 @ G @ C )
                           => ! [H: $i] :
                                ( ( m1_subset_1 @ H @ D )
                               => ( ( E
                                    = ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
                                 => ( A = F ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_domain_1) ).

thf(10709,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) )
                 => ( ( ( A
                        = ( k5_mcart_1 @ B @ C @ D @ E ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ C )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ D )
                                 => ( ( E
                                      = ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
                                   => ( A = F ) ) ) ) ) )
                    & ( ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ C )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ D )
                                 => ( ( E
                                      = ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
                                   => ( A = F ) ) ) ) )
                     => ( A
                        = ( k5_mcart_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1731]) ).

thf(2266,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_zfmisc_1) ).

thf(13569,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2266]) ).

thf(1485,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
        & ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
     => ( ( r2_hidden @ C @ A )
       => ( ( k1_funct_1 @ D @ C )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funct_2) ).

thf(9531,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
        & ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
     => ( ( r2_hidden @ C @ A )
       => ( ( k1_funct_1 @ D @ C )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1485]) ).

thf(2138,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ~ ( v1_xboole_0 @ E )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
                            & ( m2_relset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E ) )
                         => ! [G: $i] :
                              ( ( ( v1_funct_1 @ G )
                                & ( v1_funct_2 @ G @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
                                & ( m2_relset_1 @ G @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E ) )
                             => ( ! [H: $i] :
                                    ( ( m1_subset_1 @ H @ A )
                                   => ! [I: $i] :
                                        ( ( m1_subset_1 @ I @ B )
                                       => ! [J: $i] :
                                            ( ( m1_subset_1 @ J @ C )
                                           => ! [K: $i] :
                                                ( ( m1_subset_1 @ K @ D )
                                               => ( ( k8_funct_2 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E @ F @ ( k5_domain_1 @ A @ B @ C @ D @ H @ I @ J @ K ) )
                                                  = ( k8_funct_2 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E @ G @ ( k5_domain_1 @ A @ B @ C @ D @ H @ I @ J @ K ) ) ) ) ) ) )
                               => ( F = G ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_multop_1) ).

thf(13033,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ~ ( v1_xboole_0 @ E )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
                            & ( m2_relset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E ) )
                         => ! [G: $i] :
                              ( ( ( v1_funct_1 @ G )
                                & ( v1_funct_2 @ G @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
                                & ( m2_relset_1 @ G @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E ) )
                             => ( ! [H: $i] :
                                    ( ( m1_subset_1 @ H @ A )
                                   => ! [I: $i] :
                                        ( ( m1_subset_1 @ I @ B )
                                       => ! [J: $i] :
                                            ( ( m1_subset_1 @ J @ C )
                                           => ! [K: $i] :
                                                ( ( m1_subset_1 @ K @ D )
                                               => ( ( k8_funct_2 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E @ F @ ( k5_domain_1 @ A @ B @ C @ D @ H @ I @ J @ K ) )
                                                  = ( k8_funct_2 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E @ G @ ( k5_domain_1 @ A @ B @ C @ D @ H @ I @ J @ K ) ) ) ) ) ) )
                               => ( F = G ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2138]) ).

thf(1428,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).

thf(9295,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428]) ).

thf(1728,axiom,
    ! [A: $i,B: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).

thf(10700,plain,
    ! [A: $i,B: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1728]) ).

thf(2547,axiom,
    ! [A: $i] : ( m1_subset_1 @ ( k1_pcomps_1 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pcomps_1) ).

thf(14714,plain,
    ! [A: $i] : ( m1_subset_1 @ ( k1_pcomps_1 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2547]) ).

thf(1627,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i,D: $i] :
          ( ( ( g1_lattices @ A @ B )
            = ( g1_lattices @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_lattices) ).

thf(10242,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i,D: $i] :
          ( ( ( g1_lattices @ A @ B )
            = ( g1_lattices @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1627]) ).

thf(2329,axiom,
    m1_subset_1 @ k2_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_urysohn1) ).

thf(13798,plain,
    m1_subset_1 @ k2_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2329]) ).

thf(2552,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k5_subset_1 @ A @ B @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).

thf(14731,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k5_subset_1 @ A @ B @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2552]) ).

thf(2106,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
         => ( ( m1_card_fil @ B @ A )
          <=> ( ~ ( r2_hidden @ k1_xboole_0 @ B )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                     => ( ( ( ( r2_hidden @ C @ B )
                            & ( r2_hidden @ D @ B ) )
                         => ( r2_hidden @ ( k5_subset_1 @ A @ C @ D ) @ B ) )
                        & ( ( ( r2_hidden @ C @ B )
                            & ( r1_tarski @ C @ D ) )
                         => ( r2_hidden @ D @ B ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_card_fil) ).

thf(12840,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
         => ( ( ( m1_card_fil @ B @ A )
             => ( ~ ( r2_hidden @ k1_xboole_0 @ B )
                & ! [C: $i] :
                    ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                   => ! [D: $i] :
                        ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                       => ( ( ( ( r2_hidden @ C @ B )
                              & ( r2_hidden @ D @ B ) )
                           => ( r2_hidden @ ( k5_subset_1 @ A @ C @ D ) @ B ) )
                          & ( ( ( r2_hidden @ C @ B )
                              & ( r1_tarski @ C @ D ) )
                           => ( r2_hidden @ D @ B ) ) ) ) ) ) )
            & ( ( ~ ( r2_hidden @ k1_xboole_0 @ B )
                & ! [C: $i] :
                    ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                   => ! [D: $i] :
                        ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                       => ( ( ( ( r2_hidden @ C @ B )
                              & ( r2_hidden @ D @ B ) )
                           => ( r2_hidden @ ( k5_subset_1 @ A @ C @ D ) @ B ) )
                          & ( ( ( r2_hidden @ C @ B )
                              & ( r1_tarski @ C @ D ) )
                           => ( r2_hidden @ D @ B ) ) ) ) ) )
             => ( m1_card_fil @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2106]) ).

thf(234,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
             => ( ( k1_funct_1 @ ( k15_funct_3 @ A @ B ) @ ( k4_tarski @ C @ D ) )
                = ( k4_tarski @ ( k1_funct_1 @ A @ C ) @ ( k1_funct_1 @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_funct_3) ).

thf(3900,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
             => ( ( k1_funct_1 @ ( k15_funct_3 @ A @ B ) @ ( k4_tarski @ C @ D ) )
                = ( k4_tarski @ ( k1_funct_1 @ A @ C ) @ ( k1_funct_1 @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(2264,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( ( r2_hidden @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ ( k11_setwiseo @ A ) @ D ) )
                      & ( r2_hidden @ C @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ ( k11_setwiseo @ A ) @ D ) ) )
                   => ( B = C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_setwiseo) ).

thf(13563,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( ( r2_hidden @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ ( k11_setwiseo @ A ) @ D ) )
                      & ( r2_hidden @ C @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ ( k11_setwiseo @ A ) @ D ) ) )
                   => ( B = C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2264]) ).

thf(471,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( k7_relat_1 @ ( k13_funct_3 @ A @ B ) @ C )
              = ( k13_funct_3 @ ( k7_relat_1 @ A @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_funcop_1) ).

thf(5050,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( k7_relat_1 @ ( k13_funct_3 @ A @ B ) @ C )
              = ( k13_funct_3 @ ( k7_relat_1 @ A @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(484,axiom,
    ! [A: $i] :
      ( ( k6_partfun1 @ A )
      = ( k6_relat_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).

thf(5099,plain,
    ! [A: $i] :
      ( ( k6_partfun1 @ A )
      = ( k6_relat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(1481,axiom,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_qc_lang1 @ k2_qc_lang1 )
     => ! [B: $i] :
          ( ( m2_subset_1 @ B @ k1_qc_lang1 @ k4_qc_lang1 )
         => ( ( v1_funct_1 @ ( k3_cqc_lang @ B @ A ) )
            & ( m2_relset_1 @ ( k3_cqc_lang @ B @ A ) @ k4_qc_lang1 @ k1_qc_lang1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_cqc_lang) ).

thf(9521,plain,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_qc_lang1 @ k2_qc_lang1 )
     => ! [B: $i] :
          ( ( m2_subset_1 @ B @ k1_qc_lang1 @ k4_qc_lang1 )
         => ( ( v1_funct_1 @ ( k3_cqc_lang @ B @ A ) )
            & ( m2_relset_1 @ ( k3_cqc_lang @ B @ A ) @ k4_qc_lang1 @ k1_qc_lang1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481]) ).

thf(1993,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( ( r2_hidden @ B @ D )
          & ( r1_tarski @ B @ C ) )
       => ( r1_tarski @ ( k8_setfam_1 @ A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_mssubfam) ).

thf(12259,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( ( r2_hidden @ B @ D )
          & ( r1_tarski @ B @ C ) )
       => ( r1_tarski @ ( k8_setfam_1 @ A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1993]) ).

thf(1671,axiom,
    ! [A: $i] :
      ( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).

thf(10461,plain,
    ! [A: $i] :
      ( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1671]) ).

thf(1295,axiom,
    ! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_xboole_1) ).

thf(8740,plain,
    ! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295]) ).

thf(2334,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_relset_1 @ C @ A @ B )
             => ! [D: $i] :
                  ( ( m2_relset_1 @ D @ A @ B )
                 => ( ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                           => ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ C )
                            <=> ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) ) ) )
                   => ( C = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_t_0topsp) ).

thf(13809,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_relset_1 @ C @ A @ B )
             => ! [D: $i] :
                  ( ( m2_relset_1 @ D @ A @ B )
                 => ( ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                           => ( ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ C )
                               => ( r2_hidden @ ( k4_tarski @ E @ F ) @ D ) )
                              & ( ( r2_hidden @ ( k4_tarski @ E @ F ) @ D )
                               => ( r2_hidden @ ( k4_tarski @ E @ F ) @ C ) ) ) ) )
                   => ( C = D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2334]) ).

thf(698,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( v1_funct_1 @ ( k1_funct_4 @ C @ D ) )
            & ( m2_relset_1 @ ( k1_funct_4 @ C @ D ) @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_funct_4) ).

thf(6019,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( v1_funct_1 @ ( k1_funct_4 @ C @ D ) )
            & ( m2_relset_1 @ ( k1_funct_4 @ C @ D ) @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(2523,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k11_classes2 @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_classes2) ).

thf(14642,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k11_classes2 @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2523]) ).

thf(1440,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_tarski @ A @ B )
       => ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_relat_1) ).

thf(9339,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_tarski @ A @ B )
       => ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440]) ).

thf(1598,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( k3_subset_1 @ A @ ( k7_subset_1 @ A @ B @ C ) )
            = ( k4_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) @ ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_subset_1) ).

thf(10127,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( k3_subset_1 @ A @ ( k7_subset_1 @ A @ B @ C ) )
            = ( k4_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) @ ( k5_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1598]) ).

thf(2095,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ A )
                     => ! [G: $i] :
                          ( ( m1_subset_1 @ G @ A )
                         => ! [H: $i] :
                              ( ( m1_subset_1 @ H @ A )
                             => ! [I: $i] :
                                  ( ( m1_subset_1 @ I @ A )
                                 => ( ( A != k1_xboole_0 )
                                   => ( m1_subset_1 @ ( k6_enumset1 @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_subset_1) ).

thf(12787,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ A )
                     => ! [G: $i] :
                          ( ( m1_subset_1 @ G @ A )
                         => ! [H: $i] :
                              ( ( m1_subset_1 @ H @ A )
                             => ! [I: $i] :
                                  ( ( m1_subset_1 @ I @ A )
                                 => ( ( A != k1_xboole_0 )
                                   => ( m1_subset_1 @ ( k6_enumset1 @ B @ C @ D @ E @ F @ G @ H @ I ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2095]) ).

thf(2392,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k7_subset_1 @ A @ B @ C )
        = ( k7_subset_1 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k7_subset_1) ).

thf(14044,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k7_subset_1 @ A @ B @ C )
        = ( k7_subset_1 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2392]) ).

thf(855,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r2_hidden @ B @ A )
       => ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
          = ( k1_funct_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).

thf(6705,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r2_hidden @ B @ A )
       => ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
          = ( k1_funct_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(2155,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers ) )
     => ! [C: $i,D: $i] :
          ( ( ( g1_metric_1 @ A @ B )
            = ( g1_metric_1 @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_metric_1) ).

thf(13132,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers ) )
     => ! [C: $i,D: $i] :
          ( ( ( g1_metric_1 @ A @ B )
            = ( g1_metric_1 @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2155]) ).

thf(183,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
              & ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k1_relat_1 @ C ) ) )
           => ( r1_tarski @ A @ ( k1_relat_1 @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_funct_3) ).

thf(3599,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
              & ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k1_relat_1 @ C ) ) )
           => ( r1_tarski @ A @ ( k1_relat_1 @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(560,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).

thf(5427,plain,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(1749,axiom,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k4_qc_lang1 )
        & ( m1_subset_1 @ B @ k2_qc_lang1 ) )
     => ( ( v1_funct_1 @ ( k6_cqc_lang @ A @ B ) )
        & ( m2_relset_1 @ ( k6_cqc_lang @ A @ B ) @ k4_qc_lang1 @ k1_qc_lang1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_cqc_lang) ).

thf(10883,plain,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k4_qc_lang1 )
        & ( m1_subset_1 @ B @ k2_qc_lang1 ) )
     => ( ( v1_funct_1 @ ( k6_cqc_lang @ A @ B ) )
        & ( m2_relset_1 @ ( k6_cqc_lang @ A @ B ) @ k4_qc_lang1 @ k1_qc_lang1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1749]) ).

thf(959,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( k3_setfam_1 @ A @ B ) )
    <=> ! [D: $i] :
          ( ( r2_hidden @ D @ C )
        <=> ? [E: $i,F: $i] :
              ( ( r2_hidden @ E @ A )
              & ( r2_hidden @ F @ B )
              & ( D
                = ( k3_xboole_0 @ E @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_setfam_1) ).

thf(7191,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C
          = ( k3_setfam_1 @ A @ B ) )
       => ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ? [E: $i,F: $i] :
                  ( ( r2_hidden @ E @ A )
                  & ( r2_hidden @ F @ B )
                  & ( D
                    = ( k3_xboole_0 @ E @ F ) ) ) )
            & ( ? [E: $i,F: $i] :
                  ( ( r2_hidden @ E @ A )
                  & ( r2_hidden @ F @ B )
                  & ( D
                    = ( k3_xboole_0 @ E @ F ) ) )
             => ( r2_hidden @ D @ C ) ) ) )
      & ( ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ? [E: $i,F: $i] :
                  ( ( r2_hidden @ E @ A )
                  & ( r2_hidden @ F @ B )
                  & ( D
                    = ( k3_xboole_0 @ E @ F ) ) ) )
            & ( ? [E: $i,F: $i] :
                  ( ( r2_hidden @ E @ A )
                  & ( r2_hidden @ F @ B )
                  & ( D
                    = ( k3_xboole_0 @ E @ F ) ) )
             => ( r2_hidden @ D @ C ) ) )
       => ( C
          = ( k3_setfam_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(1599,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ k1_xboole_0 @ A )
        & ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
     => ( ( k2_funct_2 @ k1_xboole_0 @ A @ C @ B )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_2) ).

thf(10130,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ k1_xboole_0 @ A )
        & ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
     => ( ( k2_funct_2 @ k1_xboole_0 @ A @ C @ B )
        = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1599]) ).

thf(606,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ! [B: $i] :
            ( ( m1_subset_1 @ B @ A )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ( ( r2_hidden @ ( k5_xboole_0 @ B @ C ) @ A )
                  & ( r2_hidden @ ( k3_xboole_0 @ B @ C ) @ A ) ) ) )
       => ( v4_finsub_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_finsub_1) ).

thf(5578,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ! [B: $i] :
            ( ( m1_subset_1 @ B @ A )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ( ( r2_hidden @ ( k5_xboole_0 @ B @ C ) @ A )
                  & ( r2_hidden @ ( k3_xboole_0 @ B @ C ) @ A ) ) ) )
       => ( v4_finsub_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(2533,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) )
     => ( ( r2_hidden @ A @ ( a_2_1_card_fil @ B @ C ) )
      <=> ? [D: $i] :
            ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
            & ( A
              = ( k3_subset_1 @ B @ D ) )
            & ( r2_hidden @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_card_fil) ).

thf(14667,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) )
     => ( ( ( r2_hidden @ A @ ( a_2_1_card_fil @ B @ C ) )
         => ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
              & ( A
                = ( k3_subset_1 @ B @ D ) )
              & ( r2_hidden @ D @ C ) ) )
        & ( ? [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
              & ( A
                = ( k3_subset_1 @ B @ D ) )
              & ( r2_hidden @ D @ C ) )
         => ( r2_hidden @ A @ ( a_2_1_card_fil @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2533]) ).

thf(2358,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ! [B: $i] :
            ( ( m1_subset_1 @ B @ A )
           => ( ( p1_s6_domain_1 @ B )
            <=> ( p2_s6_domain_1 @ B ) ) )
       => ( ( a_1_5_domain_1 @ A )
          = ( a_1_6_domain_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s6_domain_1) ).

thf(13908,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ! [B: $i] :
            ( ( m1_subset_1 @ B @ A )
           => ( ( ( p1_s6_domain_1 @ B )
               => ( p2_s6_domain_1 @ B ) )
              & ( ( p2_s6_domain_1 @ B )
               => ( p1_s6_domain_1 @ B ) ) ) )
       => ( ( a_1_5_domain_1 @ A )
          = ( a_1_6_domain_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2358]) ).

thf(1305,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ! [D: $i] :
            ( ( m1_subset_1 @ D @ A )
           => ! [E: $i] :
                ( ( m1_subset_1 @ E @ A )
               => ( ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
                    & ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
                    & ( ( k1_funct_1 @ C @ D )
                      = ( k1_funct_1 @ C @ E ) ) )
                 => ( D = E ) ) ) )
       => ( v2_funct_1 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_partfun1) ).

thf(8767,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ! [D: $i] :
            ( ( m1_subset_1 @ D @ A )
           => ! [E: $i] :
                ( ( m1_subset_1 @ E @ A )
               => ( ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ B @ C ) )
                    & ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
                    & ( ( k1_funct_1 @ C @ D )
                      = ( k1_funct_1 @ C @ E ) ) )
                 => ( D = E ) ) ) )
       => ( v2_funct_1 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).

thf(2450,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_finset_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).

thf(14268,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_finset_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2450]) ).

thf(349,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( v2_funct_2 @ C @ A @ B )
      <=> ( ( k2_relat_1 @ C )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_funct_2) ).

thf(4485,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( v2_funct_2 @ C @ A @ B )
         => ( ( k2_relat_1 @ C )
            = B ) )
        & ( ( ( k2_relat_1 @ C )
            = B )
         => ( v2_funct_2 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(465,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ C )
              = ( k1_funct_4 @ ( k7_relat_1 @ A @ C ) @ ( k7_relat_1 @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_funct_4) ).

thf(5033,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ C )
              = ( k1_funct_4 @ ( k7_relat_1 @ A @ C ) @ ( k7_relat_1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(213,axiom,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_finseq_2 @ C @ B @ ( k4_finseq_2 @ A @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ A ) )
                    & ( m2_relset_1 @ D @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ A ) ) )
                 => ( ( ( k2_relat_1 @ D )
                      = ( k2_finseq_1 @ A ) )
                   => ( m2_finseq_2 @ ( k1_partfun1 @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ A ) @ k5_numbers @ B @ D @ C ) @ B @ ( k4_finseq_2 @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_finseq_2) ).

thf(3751,plain,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_finseq_2 @ C @ B @ ( k4_finseq_2 @ A @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ A ) )
                    & ( m2_relset_1 @ D @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ A ) ) )
                 => ( ( ( k2_relat_1 @ D )
                      = ( k2_finseq_1 @ A ) )
                   => ( m2_finseq_2 @ ( k1_partfun1 @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ A ) @ k5_numbers @ B @ D @ C ) @ B @ ( k4_finseq_2 @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(292,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ! [B: $i] :
            ( ( ( v1_relat_1 @ B )
              & ( v1_funct_1 @ B ) )
           => ( ( B
                = ( k2_funct_1 @ A ) )
            <=> ( ( ( k1_relat_1 @ B )
                  = ( k2_relat_1 @ A ) )
                & ! [C: $i,D: $i] :
                    ( ( ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
                        & ( D
                          = ( k1_funct_1 @ B @ C ) ) )
                     => ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                        & ( C
                          = ( k1_funct_1 @ A @ D ) ) ) )
                    & ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                        & ( C
                          = ( k1_funct_1 @ A @ D ) ) )
                     => ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
                        & ( D
                          = ( k1_funct_1 @ B @ C ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).

thf(4127,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ! [B: $i] :
            ( ( ( v1_relat_1 @ B )
              & ( v1_funct_1 @ B ) )
           => ( ( ( B
                  = ( k2_funct_1 @ A ) )
               => ( ( ( k1_relat_1 @ B )
                    = ( k2_relat_1 @ A ) )
                  & ! [C: $i,D: $i] :
                      ( ( ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
                          & ( D
                            = ( k1_funct_1 @ B @ C ) ) )
                       => ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                          & ( C
                            = ( k1_funct_1 @ A @ D ) ) ) )
                      & ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                          & ( C
                            = ( k1_funct_1 @ A @ D ) ) )
                       => ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
                          & ( D
                            = ( k1_funct_1 @ B @ C ) ) ) ) ) ) )
              & ( ( ( ( k1_relat_1 @ B )
                    = ( k2_relat_1 @ A ) )
                  & ! [C: $i,D: $i] :
                      ( ( ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
                          & ( D
                            = ( k1_funct_1 @ B @ C ) ) )
                       => ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                          & ( C
                            = ( k1_funct_1 @ A @ D ) ) ) )
                      & ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
                          & ( C
                            = ( k1_funct_1 @ A @ D ) ) )
                       => ( ( r2_hidden @ C @ ( k2_relat_1 @ A ) )
                          & ( D
                            = ( k1_funct_1 @ B @ C ) ) ) ) ) )
               => ( B
                  = ( k2_funct_1 @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(2474,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
             => ( m1_subset_1 @ ( k3_tarski @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_borsuk_1) ).

thf(14384,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
             => ( m1_subset_1 @ ( k3_tarski @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2474]) ).

thf(1497,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_pboole @ D @ B ) )
     => ( m1_pboole @ ( k7_pboole @ A @ B @ C @ D ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_pboole) ).

thf(9587,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_pboole @ D @ B ) )
     => ( m1_pboole @ ( k7_pboole @ A @ B @ C @ D ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1497]) ).

thf(490,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ C )
        = ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
      & ( ( k2_zfmisc_1 @ C @ ( k3_xboole_0 @ A @ B ) )
        = ( k3_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_zfmisc_1) ).

thf(5118,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k2_zfmisc_1 @ ( k3_xboole_0 @ A @ B ) @ C )
        = ( k3_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
      & ( ( k2_zfmisc_1 @ C @ ( k3_xboole_0 @ A @ B ) )
        = ( k3_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(903,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
     => ( ! [F: $i] :
            ( ( m1_subset_1 @ F @ A )
           => ! [G: $i] :
                ( ( m1_subset_1 @ G @ B )
               => ! [H: $i] :
                    ( ( m1_subset_1 @ H @ C )
                   => ( ( E
                        = ( k3_mcart_1 @ F @ G @ H ) )
                     => ( D = G ) ) ) ) )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 )
          | ( C = k1_xboole_0 )
          | ( D
            = ( k6_mcart_1 @ A @ B @ C @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_mcart_1) ).

thf(6937,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
     => ( ! [F: $i] :
            ( ( m1_subset_1 @ F @ A )
           => ! [G: $i] :
                ( ( m1_subset_1 @ G @ B )
               => ! [H: $i] :
                    ( ( m1_subset_1 @ H @ C )
                   => ( ( E
                        = ( k3_mcart_1 @ F @ G @ H ) )
                     => ( D = G ) ) ) ) )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 )
          | ( C = k1_xboole_0 )
          | ( D
            = ( k6_mcart_1 @ A @ B @ C @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

thf(1175,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
     => ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_partfun1) ).

thf(8188,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
     => ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).

thf(411,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
              & ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
           => ( ( k1_funct_1 @ ( k1_funct_4 @ B @ C ) @ A )
              = ( k1_funct_1 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_4) ).

thf(4796,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
              & ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
           => ( ( k1_funct_1 @ ( k1_funct_4 @ B @ C ) @ A )
              = ( k1_funct_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(208,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k4_relat_1 @ ( k5_relat_1 @ A @ B ) )
            = ( k5_relat_1 @ ( k4_relat_1 @ B ) @ ( k4_relat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_relat_1) ).

thf(3726,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k4_relat_1 @ ( k5_relat_1 @ A @ B ) )
            = ( k5_relat_1 @ ( k4_relat_1 @ B ) @ ( k4_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(1234,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( r7_binop_1 @ A @ B @ C )
          <=> ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ! [E: $i] :
                    ( ( m1_subset_1 @ E @ A )
                   => ( ( k1_funct_1 @ B @ ( k1_binop_1 @ C @ D @ E ) )
                      = ( k1_binop_1 @ C @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ B @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_binop_1) ).

thf(8432,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( r7_binop_1 @ A @ B @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ( ( k1_funct_1 @ B @ ( k1_binop_1 @ C @ D @ E ) )
                        = ( k1_binop_1 @ C @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ B @ E ) ) ) ) ) )
            & ( ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ( ( k1_funct_1 @ B @ ( k1_binop_1 @ C @ D @ E ) )
                        = ( k1_binop_1 @ C @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ B @ E ) ) ) ) )
             => ( r7_binop_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).

thf(1165,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( k9_relat_1 @ ( k4_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
            = ( k4_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_2) ).

thf(8152,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( k9_relat_1 @ ( k4_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
            = ( k4_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).

thf(1968,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ( ( A
                      = ( k3_zfmisc_1 @ B @ C @ D ) )
                  <=> ! [E: $i] :
                        ( ( r2_hidden @ E @ A )
                      <=> ? [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                            & ? [G: $i] :
                                ( ( m1_subset_1 @ G @ C )
                                & ? [H: $i] :
                                    ( ( m1_subset_1 @ H @ D )
                                    & ( E
                                      = ( k3_mcart_1 @ F @ G @ H ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_domain_1) ).

thf(12067,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ( ( ( A
                        = ( k3_zfmisc_1 @ B @ C @ D ) )
                     => ! [E: $i] :
                          ( ( ( r2_hidden @ E @ A )
                           => ? [F: $i] :
                                ( ( m1_subset_1 @ F @ B )
                                & ? [G: $i] :
                                    ( ( m1_subset_1 @ G @ C )
                                    & ? [H: $i] :
                                        ( ( m1_subset_1 @ H @ D )
                                        & ( E
                                          = ( k3_mcart_1 @ F @ G @ H ) ) ) ) ) )
                          & ( ? [F: $i] :
                                ( ( m1_subset_1 @ F @ B )
                                & ? [G: $i] :
                                    ( ( m1_subset_1 @ G @ C )
                                    & ? [H: $i] :
                                        ( ( m1_subset_1 @ H @ D )
                                        & ( E
                                          = ( k3_mcart_1 @ F @ G @ H ) ) ) ) )
                           => ( r2_hidden @ E @ A ) ) ) )
                    & ( ! [E: $i] :
                          ( ( ( r2_hidden @ E @ A )
                           => ? [F: $i] :
                                ( ( m1_subset_1 @ F @ B )
                                & ? [G: $i] :
                                    ( ( m1_subset_1 @ G @ C )
                                    & ? [H: $i] :
                                        ( ( m1_subset_1 @ H @ D )
                                        & ( E
                                          = ( k3_mcart_1 @ F @ G @ H ) ) ) ) ) )
                          & ( ? [F: $i] :
                                ( ( m1_subset_1 @ F @ B )
                                & ? [G: $i] :
                                    ( ( m1_subset_1 @ G @ C )
                                    & ? [H: $i] :
                                        ( ( m1_subset_1 @ H @ D )
                                        & ( E
                                          = ( k3_mcart_1 @ F @ G @ H ) ) ) ) )
                           => ( r2_hidden @ E @ A ) ) )
                     => ( A
                        = ( k3_zfmisc_1 @ B @ C @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1968]) ).

thf(1654,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ! [C: $i] :
              ( ( m2_card_fil @ C @ A )
             => ( ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                   => ~ ( ( r2_hidden @ D @ B )
                        & ( r2_hidden @ D @ ( k2_card_fil @ A @ B ) ) ) )
                & ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                   => ~ ( ( r2_hidden @ D @ C )
                        & ( r2_hidden @ D @ ( k7_setfam_1 @ A @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_card_fil) ).

thf(10393,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ! [C: $i] :
              ( ( m2_card_fil @ C @ A )
             => ( ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                   => ~ ( ( r2_hidden @ D @ B )
                        & ( r2_hidden @ D @ ( k2_card_fil @ A @ B ) ) ) )
                & ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                   => ~ ( ( r2_hidden @ D @ C )
                        & ( r2_hidden @ D @ ( k7_setfam_1 @ A @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1654]) ).

thf(847,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( k2_xboole_0 @ A @ B )
          = ( k2_xboole_0 @ C @ D ) )
        & ( r1_xboole_0 @ C @ A )
        & ( r1_xboole_0 @ D @ B ) )
     => ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_xboole_1) ).

thf(6667,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( k2_xboole_0 @ A @ B )
          = ( k2_xboole_0 @ C @ D ) )
        & ( r1_xboole_0 @ C @ A )
        & ( r1_xboole_0 @ D @ B ) )
     => ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(1963,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( r1_tarski @ ( k2_ens_1 @ A ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_ens_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_ens_1) ).

thf(12053,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( r1_tarski @ ( k2_ens_1 @ A ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) @ ( k1_ens_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1963]) ).

thf(1613,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( v1_funct_1 @ ( k1_borsuk_1 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k1_borsuk_1 @ A @ B @ C ) @ B @ A )
        & ( m2_relset_1 @ ( k1_borsuk_1 @ A @ B @ C ) @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_borsuk_1) ).

thf(10183,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( v1_funct_1 @ ( k1_borsuk_1 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k1_borsuk_1 @ A @ B @ C ) @ B @ A )
        & ( m2_relset_1 @ ( k1_borsuk_1 @ A @ B @ C ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1613]) ).

thf(1063,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k6_relat_1 @ ( k2_xboole_0 @ A @ B ) )
        = ( k2_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) )
      & ( ( k6_relat_1 @ ( k3_xboole_0 @ A @ B ) )
        = ( k3_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) )
      & ( ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) )
        = ( k4_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_sysrel) ).

thf(7689,plain,
    ! [A: $i,B: $i] :
      ( ( ( k6_relat_1 @ ( k2_xboole_0 @ A @ B ) )
        = ( k2_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) )
      & ( ( k6_relat_1 @ ( k3_xboole_0 @ A @ B ) )
        = ( k3_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) )
      & ( ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) )
        = ( k4_xboole_0 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).

thf(2232,axiom,
    ! [A: $i] : ( v4_finsub_1 @ ( k5_finsub_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).

thf(13459,plain,
    ! [A: $i] : ( v4_finsub_1 @ ( k5_finsub_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2232]) ).

thf(2245,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( m3_realset1 @ C @ A @ B )
          <=> ! [D: $i] :
                ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
               => ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_realset1) ).

thf(13503,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( m3_realset1 @ C @ A @ B )
             => ! [D: $i] :
                  ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
                 => ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) )
            & ( ! [D: $i] :
                  ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
                 => ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
             => ( m3_realset1 @ C @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2245]) ).

thf(611,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( k2_funct_4 @ ( k2_funct_4 @ D ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_4) ).

thf(5595,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( k2_funct_4 @ ( k2_funct_4 @ D ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(2243,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G )
      = ( k2_xboole_0 @ ( k1_enumset1 @ A @ B @ C ) @ ( k2_enumset1 @ D @ E @ F @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_enumset1) ).

thf(13497,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G )
      = ( k2_xboole_0 @ ( k1_enumset1 @ A @ B @ C ) @ ( k2_enumset1 @ D @ E @ F @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2243]) ).

thf(1274,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ( ( ( ( k4_funct_2 @ A @ B @ C )
                = B )
              & ( ( k2_relat_1 @ B )
                = A ) )
           => ( C
              = ( k6_partfun1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_funct_2) ).

thf(8629,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ( ( ( ( k4_funct_2 @ A @ B @ C )
                = B )
              & ( ( k2_relat_1 @ B )
                = A ) )
           => ( C
              = ( k6_partfun1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).

thf(1193,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( m1_subset_1 @ ( k9_mcart_1 @ A @ B @ C @ D @ E ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_mcart_1) ).

thf(8249,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( m1_subset_1 @ ( k9_mcart_1 @ A @ B @ C @ D @ E ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).

thf(1716,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ B @ C )
                            & ( m2_relset_1 @ F @ B @ C ) )
                         => ( r1_tarski @ ( k3_funct_2 @ A @ B @ E @ ( k6_domain_1 @ B @ D ) ) @ ( k3_funct_2 @ A @ C @ ( k7_funct_2 @ A @ B @ C @ E @ F ) @ ( k6_domain_1 @ C @ ( k8_funct_2 @ B @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_borsuk_1) ).

thf(10640,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ B @ C )
                            & ( m2_relset_1 @ F @ B @ C ) )
                         => ( r1_tarski @ ( k3_funct_2 @ A @ B @ E @ ( k6_domain_1 @ B @ D ) ) @ ( k3_funct_2 @ A @ C @ ( k7_funct_2 @ A @ B @ C @ E @ F ) @ ( k6_domain_1 @ C @ ( k8_funct_2 @ B @ C @ F @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1716]) ).

thf(1944,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
      = ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_zfmisc_1) ).

thf(11951,plain,
    ! [A: $i,B: $i] :
      ( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
      = ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1944]) ).

thf(103,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( v2_funct_1 @ C )
       => ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
          & ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_partfun1) ).

thf(3208,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( v2_funct_1 @ C )
       => ( ( v1_funct_1 @ ( k2_funct_1 @ C ) )
          & ( m2_relset_1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(2147,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k3_tarski @ ( k5_setfam_1 @ A @ B ) )
        = ( k3_tarski @ ( a_2_0_borsuk_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_borsuk_1) ).

thf(13093,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k3_tarski @ ( k5_setfam_1 @ A @ B ) )
        = ( k3_tarski @ ( a_2_0_borsuk_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2147]) ).

thf(1329,axiom,
    ! [A: $i,B: $i] :
      ( ( A != k1_xboole_0 )
     => ( ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) )
        = ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funcop_1) ).

thf(8877,plain,
    ! [A: $i,B: $i] :
      ( ( A != k1_xboole_0 )
     => ( ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) )
        = ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329]) ).

thf(301,axiom,
    ! [A: $i] :
      ( ( k17_mcart_1 @ A )
      = ( k1_mcart_1 @ ( k1_mcart_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_mcart_1) ).

thf(4218,plain,
    ! [A: $i] :
      ( ( k17_mcart_1 @ A )
      = ( k1_mcart_1 @ ( k1_mcart_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(2514,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ? [C: $i] : ( m2_realset1 @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_realset1) ).

thf(14608,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ? [C: $i] : ( m2_realset1 @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2514]) ).

thf(2049,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ B @ C )
       => ( ( v1_funct_1 @ D )
          & ( m2_relset_1 @ D @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_partfun1) ).

thf(12524,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ B @ C )
       => ( ( v1_funct_1 @ D )
          & ( m2_relset_1 @ D @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2049]) ).

thf(1808,axiom,
    ! [A: $i] :
      ( ( k1_toler_1 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_triang_1) ).

thf(11201,plain,
    ! [A: $i] :
      ( ( k1_toler_1 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1808]) ).

thf(1645,axiom,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ( ~ ( v1_xboole_0 @ A )
        & ~ ( v2_setfam_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_yellow21) ).

thf(10348,plain,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ( ~ ( v1_xboole_0 @ A )
        & ~ ( v2_setfam_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1645]) ).

thf(1127,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m2_subset_1 @ F @ A @ B )
                         => ( ( ( D
                                = ( k1_realset1 @ C @ B ) )
                              & ( F = E ) )
                           => ( ( ( r1_binop_1 @ A @ E @ C )
                               => ( r1_binop_1 @ B @ F @ D ) )
                              & ( ( r2_binop_1 @ A @ E @ C )
                               => ( r2_binop_1 @ B @ F @ D ) )
                              & ( ( r3_binop_1 @ A @ E @ C )
                               => ( r3_binop_1 @ B @ F @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_filter_2) ).

thf(8000,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m2_subset_1 @ F @ A @ B )
                         => ( ( ( D
                                = ( k1_realset1 @ C @ B ) )
                              & ( F = E ) )
                           => ( ( ( r1_binop_1 @ A @ E @ C )
                               => ( r1_binop_1 @ B @ F @ D ) )
                              & ( ( r2_binop_1 @ A @ E @ C )
                               => ( r2_binop_1 @ B @ F @ D ) )
                              & ( ( r3_binop_1 @ A @ E @ C )
                               => ( r3_binop_1 @ B @ F @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).

thf(937,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
     => ( ( k10_cat_2 @ A @ B @ C @ D )
        = ( k3_funct_4 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_cat_2) ).

thf(7109,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
     => ( ( k10_cat_2 @ A @ B @ C @ D )
        = ( k3_funct_4 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).

thf(2038,axiom,
    ( ( v1_finset_1 @ f2_s21_fraenkel )
   => ( v1_finset_1 @ a_0_38_fraenkel ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s21_fraenkel) ).

thf(12451,plain,
    ( ( v1_finset_1 @ f2_s21_fraenkel )
   => ( v1_finset_1 @ a_0_38_fraenkel ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2038]) ).

thf(363,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ B ) )
     => ? [C: $i] : ( m2_filter_1 @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_filter_1) ).

thf(4573,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ B ) )
     => ? [C: $i] : ( m2_filter_1 @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(1836,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( r2_hidden @ C @ A )
        <=> ( r2_hidden @ C @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).

thf(11370,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( ( r2_hidden @ C @ A )
           => ( r2_hidden @ C @ B ) )
          & ( ( r2_hidden @ C @ B )
           => ( r2_hidden @ C @ A ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1836]) ).

thf(2398,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k2_finsub_1 @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_finsub_1) ).

thf(14059,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k2_finsub_1 @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2398]) ).

thf(504,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( r1_tarski @ ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k2_relat_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_relat_1) ).

thf(5190,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( r1_tarski @ ( k2_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k2_relat_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(2088,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
                        & ( m2_relset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
                            & ( m2_relset_1 @ F @ ( k3_zfmisc_1 @ A @ B @ C ) @ D ) )
                         => ( ! [G: $i] :
                                ( ( m1_subset_1 @ G @ A )
                               => ! [H: $i] :
                                    ( ( m1_subset_1 @ H @ B )
                                   => ! [I: $i] :
                                        ( ( m1_subset_1 @ I @ C )
                                       => ( ( k8_funct_2 @ ( k3_zfmisc_1 @ A @ B @ C ) @ D @ E @ ( k4_domain_1 @ A @ B @ C @ G @ H @ I ) )
                                          = ( k8_funct_2 @ ( k3_zfmisc_1 @ A @ B @ C ) @ D @ F @ ( k4_domain_1 @ A @ B @ C @ G @ H @ I ) ) ) ) ) )
                           => ( E = F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_multop_1) ).

thf(12759,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
                        & ( m2_relset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
                            & ( m2_relset_1 @ F @ ( k3_zfmisc_1 @ A @ B @ C ) @ D ) )
                         => ( ! [G: $i] :
                                ( ( m1_subset_1 @ G @ A )
                               => ! [H: $i] :
                                    ( ( m1_subset_1 @ H @ B )
                                   => ! [I: $i] :
                                        ( ( m1_subset_1 @ I @ C )
                                       => ( ( k8_funct_2 @ ( k3_zfmisc_1 @ A @ B @ C ) @ D @ E @ ( k4_domain_1 @ A @ B @ C @ G @ H @ I ) )
                                          = ( k8_funct_2 @ ( k3_zfmisc_1 @ A @ B @ C ) @ D @ F @ ( k4_domain_1 @ A @ B @ C @ G @ H @ I ) ) ) ) ) )
                           => ( E = F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2088]) ).

thf(1756,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( r1_zfrefle1 @ A @ ( k1_subset_1 @ k9_zf_lang ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfrefle1) ).

thf(10938,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( r1_zfrefle1 @ A @ ( k1_subset_1 @ k9_zf_lang ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1756]) ).

thf(36,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ~ ( ! [C: $i] :
                  ( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                 => ( ( k1_funct_1 @ A @ C )
                    = ( k1_funct_1 @ B @ C ) ) )
              & ! [C: $i] :
                  ( ( ( v1_relat_1 @ C )
                    & ( v1_funct_1 @ C ) )
                 => ( ( k2_xboole_0 @ A @ B )
                   != C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_partfun1) ).

thf(2753,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ~ ( ! [C: $i] :
                  ( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                 => ( ( k1_funct_1 @ A @ C )
                    = ( k1_funct_1 @ B @ C ) ) )
              & ! [C: $i] :
                  ( ( ( v1_relat_1 @ C )
                    & ( v1_funct_1 @ C ) )
                 => ( ( k2_xboole_0 @ A @ B )
                   != C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(1677,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k6_funct_3 @ A @ B )
        = ( k7_relat_1 @ ( k6_relat_1 @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funct_3) ).

thf(10493,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k6_funct_3 @ A @ B )
        = ( k7_relat_1 @ ( k6_relat_1 @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1677]) ).

thf(536,axiom,
    ! [A: $i,B: $i] :
      ( ( v2_membered @ A )
     => ( ( v1_membered @ ( k4_xboole_0 @ A @ B ) )
        & ( v2_membered @ ( k4_xboole_0 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc38_membered) ).

thf(5314,plain,
    ! [A: $i,B: $i] :
      ( ( v2_membered @ A )
     => ( ( v1_membered @ ( k4_xboole_0 @ A @ B ) )
        & ( v2_membered @ ( k4_xboole_0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(2430,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k5_subset_1 @ A @ B @ C )
        = ( k5_subset_1 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).

thf(14183,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k5_subset_1 @ A @ B @ C )
        = ( k5_subset_1 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2430]) ).

thf(272,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
       => ( ( k1_funct_1 @ C @ B )
          = ( k1_funct_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_1) ).

thf(4060,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
       => ( ( k1_funct_1 @ C @ B )
          = ( k1_funct_1 @ ( k5_relat_1 @ ( k6_relat_1 @ A ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(2375,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ! [C: $i] :
            ( ( m1_subset_1 @ C @ A )
           => ( r2_hidden @ C @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_subset_1) ).

thf(13984,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ! [C: $i] :
            ( ( m1_subset_1 @ C @ A )
           => ( r2_hidden @ C @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2375]) ).

thf(1057,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( r1_tarski @ ( k7_relat_1 @ B @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).

thf(7671,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( r1_tarski @ ( k7_relat_1 @ B @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).

thf(1021,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( k9_relat_1 @ ( k2_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
            = ( k2_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_relset_2) ).

thf(7536,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( k9_relat_1 @ ( k2_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
            = ( k2_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(594,axiom,
    ( ( v1_relat_1 @ a_0_0_altcat_2 )
    & ( v1_funct_1 @ a_0_0_altcat_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_altcat_2) ).

thf(5539,plain,
    ( ( v1_relat_1 @ a_0_0_altcat_2 )
    & ( v1_funct_1 @ a_0_0_altcat_2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(2509,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( r2_hidden @ A @ ( a_3_1_domain_1 @ B @ C @ D ) )
      <=> ? [E: $i] :
            ( ( m1_subset_1 @ E @ B )
            & ( A = E )
            & ( r2_hidden @ E @ C )
            & ( r2_hidden @ E @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_domain_1) ).

thf(14587,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( ( r2_hidden @ A @ ( a_3_1_domain_1 @ B @ C @ D ) )
         => ? [E: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( A = E )
              & ( r2_hidden @ E @ C )
              & ( r2_hidden @ E @ D ) ) )
        & ( ? [E: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( A = E )
              & ( r2_hidden @ E @ C )
              & ( r2_hidden @ E @ D ) )
         => ( r2_hidden @ A @ ( a_3_1_domain_1 @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2509]) ).

thf(1182,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( r3_binop_1 @ A @ B @ C )
          <=> ( ( r1_binop_1 @ A @ B @ C )
              & ( r2_binop_1 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_binop_1) ).

thf(8212,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( r3_binop_1 @ A @ B @ C )
             => ( ( r1_binop_1 @ A @ B @ C )
                & ( r2_binop_1 @ A @ B @ C ) ) )
            & ( ( ( r1_binop_1 @ A @ B @ C )
                & ( r2_binop_1 @ A @ B @ C ) )
             => ( r3_binop_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).

thf(1980,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_enumset1 @ A @ B @ C )
      = ( k1_enumset1 @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_enumset1) ).

thf(12146,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_enumset1 @ A @ B @ C )
      = ( k1_enumset1 @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1980]) ).

thf(640,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
     => ( ! [F: $i] :
            ( ( m1_subset_1 @ F @ A )
           => ! [G: $i] :
                ( ( m1_subset_1 @ G @ B )
               => ! [H: $i] :
                    ( ( m1_subset_1 @ H @ C )
                   => ( ( E
                        = ( k3_mcart_1 @ F @ G @ H ) )
                     => ( D = H ) ) ) ) )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 )
          | ( C = k1_xboole_0 )
          | ( D
            = ( k7_mcart_1 @ A @ B @ C @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_mcart_1) ).

thf(5735,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) )
     => ( ! [F: $i] :
            ( ( m1_subset_1 @ F @ A )
           => ! [G: $i] :
                ( ( m1_subset_1 @ G @ B )
               => ! [H: $i] :
                    ( ( m1_subset_1 @ H @ C )
                   => ( ( E
                        = ( k3_mcart_1 @ F @ G @ H ) )
                     => ( D = H ) ) ) ) )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 )
          | ( C = k1_xboole_0 )
          | ( D
            = ( k7_mcart_1 @ A @ B @ C @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(2501,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v2_cat_5 @ A ) )
     => ! [B: $i] :
          ( ( m1_cat_5 @ B @ A )
        <=> ( m1_subset_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_cat_5) ).

thf(14549,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v2_cat_5 @ A ) )
     => ! [B: $i] :
          ( ( ( m1_cat_5 @ B @ A )
           => ( m1_subset_1 @ B @ A ) )
          & ( ( m1_subset_1 @ B @ A )
           => ( m1_cat_5 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2501]) ).

thf(1513,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F
        = ( k3_enumset1 @ A @ B @ C @ D @ E ) )
    <=> ! [G: $i] :
          ( ( r2_hidden @ G @ F )
        <=> ~ ( ( G != A )
              & ( G != B )
              & ( G != C )
              & ( G != D )
              & ( G != E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_enumset1) ).

thf(9681,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F
          = ( k3_enumset1 @ A @ B @ C @ D @ E ) )
       => ! [G: $i] :
            ( ( ( r2_hidden @ G @ F )
             => ~ ( ( G != A )
                  & ( G != B )
                  & ( G != C )
                  & ( G != D )
                  & ( G != E ) ) )
            & ( ~ ( ( G != A )
                  & ( G != B )
                  & ( G != C )
                  & ( G != D )
                  & ( G != E ) )
             => ( r2_hidden @ G @ F ) ) ) )
      & ( ! [G: $i] :
            ( ( ( r2_hidden @ G @ F )
             => ~ ( ( G != A )
                  & ( G != B )
                  & ( G != C )
                  & ( G != D )
                  & ( G != E ) ) )
            & ( ~ ( ( G != A )
                  & ( G != B )
                  & ( G != C )
                  & ( G != D )
                  & ( G != E ) )
             => ( r2_hidden @ G @ F ) ) )
       => ( F
          = ( k3_enumset1 @ A @ B @ C @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1513]) ).

thf(1925,axiom,
    ! [A: $i] :
      ( ( k4_partfun1 @ A @ k1_xboole_0 )
      = ( k1_tarski @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_partfun1) ).

thf(11841,plain,
    ! [A: $i] :
      ( ( k4_partfun1 @ A @ k1_xboole_0 )
      = ( k1_tarski @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1925]) ).

thf(1249,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ A ) )
     => ~ ( v1_xboole_0 @ ( k2_relat_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).

thf(8524,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ A ) )
     => ~ ( v1_xboole_0 @ ( k2_relat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).

thf(495,axiom,
    ! [A: $i] : ( r3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k9_setwiseo @ A ) ) @ ( k9_setwiseo @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_setwiseo) ).

thf(5158,plain,
    ! [A: $i] : ( r3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k9_setwiseo @ A ) ) @ ( k9_setwiseo @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(2420,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ A )
        & ( m1_subset_1 @ H @ A ) )
     => ( m1_subset_1 @ ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_domain_1) ).

thf(14151,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ A )
        & ( m1_subset_1 @ H @ A ) )
     => ( m1_subset_1 @ ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2420]) ).

thf(927,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H )
      = ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k4_enumset1 @ C @ D @ E @ F @ G @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_enumset1) ).

thf(7062,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H )
      = ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k4_enumset1 @ C @ D @ E @ F @ G @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).

thf(817,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
     => ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_partfun1) ).

thf(6549,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
     => ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

thf(2000,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
        & ( m1_relset_1 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( m1_subset_1 @ ( k14_borsuk_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_borsuk_1) ).

thf(12280,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
        & ( m1_relset_1 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( m1_subset_1 @ ( k14_borsuk_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2000]) ).

thf(651,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k5_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
      = ( k3_xboole_0 @ ( k5_xboole_0 @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_xboole_1) ).

thf(5784,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k5_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
      = ( k3_xboole_0 @ ( k5_xboole_0 @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(1885,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ( ( ( r1_tarski @ B @ A )
              & ( v6_ordinal1 @ B ) )
           => ( ( B = k1_xboole_0 )
              | ( r2_hidden @ ( k3_tarski @ B ) @ A ) ) )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ( C != B )
                    & ( r1_tarski @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t177_orders_1) ).

thf(11618,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ( ( ( r1_tarski @ B @ A )
              & ( v6_ordinal1 @ B ) )
           => ( ( B = k1_xboole_0 )
              | ( r2_hidden @ ( k3_tarski @ B ) @ A ) ) )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ( C != B )
                    & ( r1_tarski @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1885]) ).

thf(773,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k1_funct_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_fraenkel) ).

thf(6372,plain,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k1_funct_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(1128,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( k2_xboole_0 @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).

thf(8010,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( k2_xboole_0 @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).

thf(1999,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ A @ C )
     => ( ( r1_tarski @ A @ B )
       => ( m2_relset_1 @ D @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_relset_1) ).

thf(12278,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ A @ C )
     => ( ( r1_tarski @ A @ B )
       => ( m2_relset_1 @ D @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1999]) ).

thf(977,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
     => ( v2_funct_1 @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_partfun1) ).

thf(7315,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
     => ( v2_funct_1 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).

thf(1778,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_relset_1 @ D @ A @ B )
     => ( m2_relset_1 @ ( k9_relset_1 @ A @ B @ C @ D ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relset_1) ).

thf(11053,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_relset_1 @ D @ A @ B )
     => ( m2_relset_1 @ ( k9_relset_1 @ A @ B @ C @ D ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1778]) ).

thf(1104,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( k17_mcart_1 @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) )
        = A )
      & ( ( k18_mcart_1 @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) )
        = B )
      & ( ( k19_mcart_1 @ ( k4_tarski @ F @ ( k4_tarski @ D @ E ) ) )
        = D )
      & ( ( k20_mcart_1 @ ( k4_tarski @ F @ ( k4_tarski @ D @ E ) ) )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_mcart_1) ).

thf(7865,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( k17_mcart_1 @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) )
        = A )
      & ( ( k18_mcart_1 @ ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) )
        = B )
      & ( ( k19_mcart_1 @ ( k4_tarski @ F @ ( k4_tarski @ D @ E ) ) )
        = D )
      & ( ( k20_mcart_1 @ ( k4_tarski @ F @ ( k4_tarski @ D @ E ) ) )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).

thf(1768,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ( ( v1_tex_2 @ B @ A )
      <=> ( B
         != ( k3_tarski @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tex_2) ).

thf(10989,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ( ( ( v1_tex_2 @ B @ A )
         => ( B
           != ( k3_tarski @ A ) ) )
        & ( ( B
           != ( k3_tarski @ A ) )
         => ( v1_tex_2 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1768]) ).

thf(93,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_binop_1 @ ( k9_funct_2 @ A @ B @ C ) @ A @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_cqc_lang) ).

thf(3170,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_binop_1 @ ( k9_funct_2 @ A @ B @ C ) @ A @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(754,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ C @ ( k3_tarski @ ( k2_xboole_0 @ A @ B ) ) )
        & ! [D: $i] :
            ( ( r2_hidden @ D @ B )
           => ( r1_xboole_0 @ D @ C ) ) )
     => ( r1_tarski @ C @ ( k3_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_setfam_1) ).

thf(6261,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ C @ ( k3_tarski @ ( k2_xboole_0 @ A @ B ) ) )
        & ! [D: $i] :
            ( ( r2_hidden @ D @ B )
           => ( r1_xboole_0 @ D @ C ) ) )
     => ( r1_tarski @ C @ ( k3_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(1191,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m1_relset_1 @ B @ A @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ A )
        & ( m1_relset_1 @ C @ A @ A ) )
     => ( ( k4_funct_2 @ A @ B @ C )
        = ( k5_relat_1 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_funct_2) ).

thf(8244,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m1_relset_1 @ B @ A @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ A )
        & ( m1_relset_1 @ C @ A @ A ) )
     => ( ( k4_funct_2 @ A @ B @ C )
        = ( k5_relat_1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).

thf(2054,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A ) )
     => ( r2_hidden @ k1_xboole_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finsub_1) ).

thf(12547,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A ) )
     => ( r2_hidden @ k1_xboole_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2054]) ).

thf(1582,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_finseq_2 @ B @ A )
    <=> ! [C: $i] :
          ( ( r2_hidden @ C @ B )
         => ( m2_finseq_1 @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_finseq_2) ).

thf(10056,plain,
    ! [A: $i,B: $i] :
      ( ( ( m1_finseq_2 @ B @ A )
       => ! [C: $i] :
            ( ( r2_hidden @ C @ B )
           => ( m2_finseq_1 @ C @ A ) ) )
      & ( ! [C: $i] :
            ( ( r2_hidden @ C @ B )
           => ( m2_finseq_1 @ C @ A ) )
       => ( m1_finseq_2 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1582]) ).

thf(2238,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ D @ A )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ B @ A )
        & ( m1_relset_1 @ E @ B @ A ) )
     => ( ( v1_funct_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) )
        & ( v1_funct_2 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
        & ( m2_relset_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_funcop_1) ).

thf(13482,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ D @ A )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ B @ A )
        & ( m1_relset_1 @ E @ B @ A ) )
     => ( ( v1_funct_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) )
        & ( v1_funct_2 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
        & ( m2_relset_1 @ ( k8_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2238]) ).

thf(1509,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( r2_hidden @ A @ ( k1_orders_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_orders_1) ).

thf(9670,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( r2_hidden @ A @ ( k1_orders_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1509]) ).

thf(2497,axiom,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
         => ( ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ f1_s2_subset_1 )
                 => ( ( r2_hidden @ C @ A )
                  <=> ( p1_s2_subset_1 @ C ) ) )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ f1_s2_subset_1 )
                 => ( ( r2_hidden @ C @ B )
                  <=> ( p1_s2_subset_1 @ C ) ) ) )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_subset_1) ).

thf(14502,plain,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ f1_s2_subset_1 ) )
         => ( ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ f1_s2_subset_1 )
                 => ( ( ( r2_hidden @ C @ A )
                     => ( p1_s2_subset_1 @ C ) )
                    & ( ( p1_s2_subset_1 @ C )
                     => ( r2_hidden @ C @ A ) ) ) )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ f1_s2_subset_1 )
                 => ( ( ( r2_hidden @ C @ B )
                     => ( p1_s2_subset_1 @ C ) )
                    & ( ( p1_s2_subset_1 @ C )
                     => ( r2_hidden @ C @ B ) ) ) ) )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2497]) ).

thf(729,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ? [C: $i] :
          ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ A @ A )
          & ( m2_relset_1 @ C @ A @ A )
          & ( r1_partfun1 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_funct_2) ).

thf(6144,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ? [C: $i] :
          ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ A @ A )
          & ( m2_relset_1 @ C @ A @ A )
          & ( r1_partfun1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(1813,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k1_tarski @ A ) @ B )
    <=> ( r2_hidden @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).

thf(11222,plain,
    ! [A: $i,B: $i] :
      ( ( ( r1_tarski @ ( k1_tarski @ A ) @ B )
       => ( r2_hidden @ A @ B ) )
      & ( ( r2_hidden @ A @ B )
       => ( r1_tarski @ ( k1_tarski @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1813]) ).

thf(1506,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                     => ( ! [F: $i] :
                            ( ( m1_subset_1 @ F @ A )
                           => ! [G: $i] :
                                ( ( m1_subset_1 @ G @ B )
                               => ( ( k2_binop_1 @ A @ B @ C @ D @ F @ G )
                                  = ( k2_binop_1 @ A @ B @ C @ E @ F @ G ) ) ) )
                       => ( D = E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_binop_1) ).

thf(9623,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                     => ( ! [F: $i] :
                            ( ( m1_subset_1 @ F @ A )
                           => ! [G: $i] :
                                ( ( m1_subset_1 @ G @ B )
                               => ( ( k2_binop_1 @ A @ B @ C @ D @ F @ G )
                                  = ( k2_binop_1 @ A @ B @ C @ E @ F @ G ) ) ) )
                       => ( D = E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1506]) ).

thf(1493,axiom,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ ( k1_tarski @ k1_xboole_0 ) )
     => ( A = k8_vectsp_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_vectsp_2) ).

thf(9575,plain,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ ( k1_tarski @ k1_xboole_0 ) )
     => ( A = k8_vectsp_2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1493]) ).

thf(1625,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( v1_realset1 @ B ) )
         => ( ( r1_tarski @ A @ B )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_tex_2) ).

thf(10236,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( v1_realset1 @ B ) )
         => ( ( r1_tarski @ A @ B )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1625]) ).

thf(514,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ! [D: $i] :
          ( ( v1_relat_1 @ D )
         => ( ( ( r1_tarski @ C @ D )
              & ( r1_tarski @ A @ B ) )
           => ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_relat_1) ).

thf(5244,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ! [D: $i] :
          ( ( v1_relat_1 @ D )
         => ( ( ( r1_tarski @ C @ D )
              & ( r1_tarski @ A @ B ) )
           => ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(1354,axiom,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ? [B: $i] :
          ( ( m4_realset1 @ B @ A )
          & ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_realset1) ).

thf(8970,plain,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ? [B: $i] :
          ( ( m4_realset1 @ B @ A )
          & ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354]) ).

thf(616,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ( ( v3_binop_1 @ C @ B )
                   => ( ( k6_funcop_1 @ B @ A @ C @ D @ D )
                      = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_funcop_1) ).

thf(5610,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ( ( v3_binop_1 @ C @ B )
                   => ( ( k6_funcop_1 @ B @ A @ C @ D @ D )
                      = D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(1670,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
         => ( ( ( C = D )
              & ( r2_hidden @ A @ C )
              & ( r1_tarski @ A @ B ) )
           => ( ( k2_cantor_1 @ B @ D )
              = ( k2_xboole_0 @ ( k1_tarski @ B ) @ ( k2_cantor_1 @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_yellow_9) ).

thf(10457,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
         => ( ( ( C = D )
              & ( r2_hidden @ A @ C )
              & ( r1_tarski @ A @ B ) )
           => ( ( k2_cantor_1 @ B @ D )
              = ( k2_xboole_0 @ ( k1_tarski @ B ) @ ( k2_cantor_1 @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1670]) ).

thf(2219,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G )
      = ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_enumset1) ).

thf(13417,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G )
      = ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2219]) ).

thf(954,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( A != k1_xboole_0 )
           => ( m1_subset_1 @ ( k2_tarski @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_subset_1) ).

thf(7158,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( A != k1_xboole_0 )
           => ( m1_subset_1 @ ( k2_tarski @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).

thf(136,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( m2_finseq_1 @ ( k10_finseq_1 @ B @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finseq_2) ).

thf(3352,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( m2_finseq_1 @ ( k10_finseq_1 @ B @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(1588,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) @ k1_numbers )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ B ) )
     => ( m1_subset_1 @ ( k1_metric_1 @ A @ B @ C @ D @ E ) @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_metric_1) ).

thf(10088,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) @ k1_numbers )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ B ) )
     => ( m1_subset_1 @ ( k1_metric_1 @ A @ B @ C @ D @ E ) @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1588]) ).

thf(1035,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r2_hidden @ C @ ( k4_relset_1 @ A @ B @ D ) )
       => ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_partfun1) ).

thf(7594,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r2_hidden @ C @ ( k4_relset_1 @ A @ B @ D ) )
       => ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).

thf(1667,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k4_partfun1 @ k1_xboole_0 @ A ) @ ( k4_partfun1 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t126_partfun1) ).

thf(10448,plain,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k4_partfun1 @ k1_xboole_0 @ A ) @ ( k4_partfun1 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1667]) ).

thf(303,axiom,
    ! [A: $i] :
      ( ( k4_relat_1 @ ( k6_relat_1 @ A ) )
      = ( k6_relat_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_relat_1) ).

thf(4228,plain,
    ! [A: $i] :
      ( ( k4_relat_1 @ ( k6_relat_1 @ A ) )
      = ( k6_relat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(2348,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_finseq_2 @ B @ A )
      & ~ ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finseq_2) ).

thf(13876,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_finseq_2 @ B @ A )
      & ~ ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2348]) ).

thf(626,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( m1_pboole @ D @ A )
             => ! [E: $i] :
                  ( ( m1_pboole @ E @ B )
                 => ! [F: $i] :
                      ( ( m1_pboole @ F @ A )
                     => ( ( m1_functor0 @ F @ A @ B @ C @ D @ E )
                      <=> ( m3_pboole @ F @ A @ D @ ( k7_pboole @ A @ B @ C @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_functor0) ).

thf(5671,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( m1_pboole @ D @ A )
             => ! [E: $i] :
                  ( ( m1_pboole @ E @ B )
                 => ! [F: $i] :
                      ( ( m1_pboole @ F @ A )
                     => ( ( ( m1_functor0 @ F @ A @ B @ C @ D @ E )
                         => ( m3_pboole @ F @ A @ D @ ( k7_pboole @ A @ B @ C @ E ) ) )
                        & ( ( m3_pboole @ F @ A @ D @ ( k7_pboole @ A @ B @ C @ E ) )
                         => ( m1_functor0 @ F @ A @ B @ C @ D @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(113,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ A )
                        & ( m2_relset_1 @ E @ B @ A ) )
                     => ( ( ( v1_binop_1 @ C @ A )
                          & ( v2_binop_1 @ C @ A )
                          & ( v3_binop_1 @ C @ A ) )
                       => ( ( D = k1_xboole_0 )
                          | ! [F: $i] :
                              ( ( m1_subset_1 @ F @ A )
                             => ( ! [G: $i] :
                                    ( ( m1_subset_1 @ G @ B )
                                   => ( ( r2_hidden @ G @ D )
                                     => ( ( k8_funct_2 @ B @ A @ E @ G )
                                        = F ) ) )
                               => ( ( k7_setwiseo @ B @ A @ C @ D @ E )
                                  = F ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_setwiseo) ).

thf(3251,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ A )
                        & ( m2_relset_1 @ E @ B @ A ) )
                     => ( ( ( v1_binop_1 @ C @ A )
                          & ( v2_binop_1 @ C @ A )
                          & ( v3_binop_1 @ C @ A ) )
                       => ( ( D = k1_xboole_0 )
                          | ! [F: $i] :
                              ( ( m1_subset_1 @ F @ A )
                             => ( ! [G: $i] :
                                    ( ( m1_subset_1 @ G @ B )
                                   => ( ( r2_hidden @ G @ D )
                                     => ( ( k8_funct_2 @ B @ A @ E @ G )
                                        = F ) ) )
                               => ( ( k7_setwiseo @ B @ A @ C @ D @ E )
                                  = F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(2249,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_eqrel_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
             => ( ( k3_tarski @ ( k5_subset_1 @ B @ C @ D ) )
                = ( k3_xboole_0 @ ( k3_tarski @ C ) @ ( k3_tarski @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_borsuk_1) ).

thf(13514,plain,
    ! [A: $i,B: $i] :
      ( ( m1_eqrel_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
             => ( ( k3_tarski @ ( k5_subset_1 @ B @ C @ D ) )
                = ( k3_xboole_0 @ ( k3_tarski @ C ) @ ( k3_tarski @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2249]) ).

thf(2132,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k6_relat_1 @ C ) )
    <=> ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k6_relat_1 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_sysrel) ).

thf(12990,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k6_relat_1 @ C ) )
       => ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k6_relat_1 @ C ) ) )
      & ( ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k6_relat_1 @ C ) )
       => ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k6_relat_1 @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2132]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( v1_relat_1 @ E )
     => ( ( E
          = ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
       => ( ( ( k1_relat_1 @ E )
            = ( k2_tarski @ A @ C ) )
          & ( ( k2_relat_1 @ E )
            = ( k2_tarski @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_relat_1) ).

thf(2642,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( v1_relat_1 @ E )
     => ( ( E
          = ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
       => ( ( ( k1_relat_1 @ E )
            = ( k2_tarski @ A @ C ) )
          & ( ( k2_relat_1 @ E )
            = ( k2_tarski @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(1463,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ~ ( ( r1_tarski @ B @ A )
          & ( r1_xboole_0 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_xboole_1) ).

thf(9454,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ~ ( ( r1_tarski @ B @ A )
          & ( r1_xboole_0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ( m1_relset_1 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
     => ( ( ( v1_funct_1 @ A )
          & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 ) )
       => ( ( v1_funct_1 @ A )
          & ( v1_xboole_0 @ A )
          & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
          & ( v1_binop_1 @ A @ k1_xboole_0 )
          & ( v2_binop_1 @ A @ k1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_binop_1) ).

thf(2987,plain,
    ! [A: $i] :
      ( ( m1_relset_1 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
     => ( ( ( v1_funct_1 @ A )
          & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 ) )
       => ( ( v1_funct_1 @ A )
          & ( v1_xboole_0 @ A )
          & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_xboole_0 @ k1_xboole_0 ) @ k1_xboole_0 )
          & ( v1_binop_1 @ A @ k1_xboole_0 )
          & ( v2_binop_1 @ A @ k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(587,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) )
     => ( ( r1_tarski @ A @ B )
        & ( r1_xboole_0 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_xboole_1) ).

thf(5520,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) )
     => ( ( r1_tarski @ A @ B )
        & ( r1_xboole_0 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k2_tarski @ B @ C ) @ ( k1_tarski @ D ) ) )
     => ( ( ( ( k1_mcart_1 @ A )
            = B )
          | ( ( k1_mcart_1 @ A )
            = C ) )
        & ( ( k2_mcart_1 @ A )
          = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_mcart_1) ).

thf(2637,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k2_tarski @ B @ C ) @ ( k1_tarski @ D ) ) )
     => ( ( ( ( k1_mcart_1 @ A )
            = B )
          | ( ( k1_mcart_1 @ A )
            = C ) )
        & ( ( k2_mcart_1 @ A )
          = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(1618,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 ) )
    <=> ( ( k4_zfmisc_1 @ A @ B @ C @ D )
       != k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_mcart_1) ).

thf(10204,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( A != k1_xboole_0 )
          & ( B != k1_xboole_0 )
          & ( C != k1_xboole_0 )
          & ( D != k1_xboole_0 ) )
       => ( ( k4_zfmisc_1 @ A @ B @ C @ D )
         != k1_xboole_0 ) )
      & ( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
         != k1_xboole_0 )
       => ( ( A != k1_xboole_0 )
          & ( B != k1_xboole_0 )
          & ( C != k1_xboole_0 )
          & ( D != k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1618]) ).

thf(1446,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( ( C
                = ( k4_xboole_0 @ B @ ( k1_tarski @ k1_xboole_0 ) ) )
              | ( B
                = ( k2_xboole_0 @ C @ ( k1_tarski @ k1_xboole_0 ) ) ) )
           => ( ( k1_cantor_1 @ A @ B )
              = ( k1_cantor_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_waybel18) ).

thf(9377,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( ( C
                = ( k4_xboole_0 @ B @ ( k1_tarski @ k1_xboole_0 ) ) )
              | ( B
                = ( k2_xboole_0 @ C @ ( k1_tarski @ k1_xboole_0 ) ) ) )
           => ( ( k1_cantor_1 @ A @ B )
              = ( k1_cantor_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446]) ).

thf(170,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( ( r1_tarski @ A @ B )
             => ( r1_tarski @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) )
            & ( ( r1_tarski @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) )
             => ( r1_tarski @ A @ B ) )
            & ( ( r1_tarski @ ( k4_relat_1 @ A ) @ B )
             => ( r1_tarski @ A @ ( k4_relat_1 @ B ) ) )
            & ( ( r1_tarski @ A @ ( k4_relat_1 @ B ) )
             => ( r1_tarski @ ( k4_relat_1 @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_waybel10) ).

thf(3551,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( ( r1_tarski @ A @ B )
             => ( r1_tarski @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) )
            & ( ( r1_tarski @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) )
             => ( r1_tarski @ A @ B ) )
            & ( ( r1_tarski @ ( k4_relat_1 @ A ) @ B )
             => ( r1_tarski @ A @ ( k4_relat_1 @ B ) ) )
            & ( ( r1_tarski @ A @ ( k4_relat_1 @ B ) )
             => ( r1_tarski @ ( k4_relat_1 @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(320,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( v1_binop_1 @ B @ A )
           => ( ( r3_binop_1 @ A @ C @ B )
            <=> ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( k1_binop_1 @ B @ D @ C )
                    = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_binop_1) ).

thf(4305,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( v1_binop_1 @ B @ A )
           => ( ( ( r3_binop_1 @ A @ C @ B )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ( ( k1_binop_1 @ B @ D @ C )
                      = D ) ) )
              & ( ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ( ( k1_binop_1 @ B @ D @ C )
                      = D ) )
               => ( r3_binop_1 @ A @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(794,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) @ ( k2_tarski @ E @ F ) )
      = ( k6_enumset1 @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ A @ D @ E ) @ ( k3_mcart_1 @ A @ C @ F ) @ ( k3_mcart_1 @ A @ D @ F ) @ ( k3_mcart_1 @ B @ C @ E ) @ ( k3_mcart_1 @ B @ D @ E ) @ ( k3_mcart_1 @ B @ C @ F ) @ ( k3_mcart_1 @ B @ D @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_mcart_1) ).

thf(6443,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) @ ( k2_tarski @ E @ F ) )
      = ( k6_enumset1 @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ A @ D @ E ) @ ( k3_mcart_1 @ A @ C @ F ) @ ( k3_mcart_1 @ A @ D @ F ) @ ( k3_mcart_1 @ B @ C @ E ) @ ( k3_mcart_1 @ B @ D @ E ) @ ( k3_mcart_1 @ B @ C @ F ) @ ( k3_mcart_1 @ B @ D @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(1584,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).

thf(10066,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
       => ( ( r1_tarski @ A @ B )
          & ( r1_tarski @ B @ A ) ) )
      & ( ( ( r1_tarski @ A @ B )
          & ( r1_tarski @ B @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1584]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( m1_pboole @ B @ A )
      <=> ( ( k1_relat_1 @ B )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pboole) ).

thf(2774,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( ( m1_pboole @ B @ A )
         => ( ( k1_relat_1 @ B )
            = A ) )
        & ( ( ( k1_relat_1 @ B )
            = A )
         => ( m1_pboole @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(808,axiom,
    ! [A: $i,B: $i] :
      ( ( ( r2_hidden @ B @ A )
        & ( v2_membered @ B ) )
     => ( v2_membered @ ( k1_setfam_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_membered) ).

thf(6500,plain,
    ! [A: $i,B: $i] :
      ( ( ( r2_hidden @ B @ A )
        & ( v2_membered @ B ) )
     => ( v2_membered @ ( k1_setfam_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(1786,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_card_fil @ C @ A )
             => ( ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                   => ~ ( ( r2_hidden @ D @ C )
                        & ( r1_xboole_0 @ D @ B ) ) )
               => ( ( r2_hidden @ B @ ( k3_card_fil @ A @ C @ B ) )
                  & ( m1_card_fil @ ( k3_card_fil @ A @ C @ B ) @ A )
                  & ( r1_tarski @ C @ ( k3_card_fil @ A @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_card_fil) ).

thf(11092,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_card_fil @ C @ A )
             => ( ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                   => ~ ( ( r2_hidden @ D @ C )
                        & ( r1_xboole_0 @ D @ B ) ) )
               => ( ( r2_hidden @ B @ ( k3_card_fil @ A @ C @ B ) )
                  & ( m1_card_fil @ ( k3_card_fil @ A @ C @ B ) @ A )
                  & ( r1_tarski @ C @ ( k3_card_fil @ A @ C @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1786]) ).

thf(1904,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ B @ A @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_enumset1) ).

thf(11697,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ B @ A @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1904]) ).

thf(991,axiom,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ A @ B )
      = ( k5_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_xboole_1) ).

thf(7379,plain,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ A @ B )
      = ( k5_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).

thf(1040,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
        & ( A != C )
        & ( A != D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_zfmisc_1) ).

thf(7607,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
        & ( A != C )
        & ( A != D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).

thf(720,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_xboole_0 @ B @ C ) )
     => ( r1_xboole_0 @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).

thf(6112,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_xboole_0 @ B @ C ) )
     => ( r1_xboole_0 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(2213,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D ) )
     => ( ( r2_hidden @ A @ ( a_3_0_domain_1 @ B @ C @ D ) )
      <=> ? [E: $i,F: $i,G: $i] :
            ( ( m1_subset_1 @ E @ B )
            & ( m1_subset_1 @ F @ C )
            & ( m1_subset_1 @ G @ D )
            & ( A
              = ( k4_domain_1 @ B @ C @ D @ E @ F @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_domain_1) ).

thf(13390,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D ) )
     => ( ( ( r2_hidden @ A @ ( a_3_0_domain_1 @ B @ C @ D ) )
         => ? [E: $i,F: $i,G: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( m1_subset_1 @ F @ C )
              & ( m1_subset_1 @ G @ D )
              & ( A
                = ( k4_domain_1 @ B @ C @ D @ E @ F @ G ) ) ) )
        & ( ? [E: $i,F: $i,G: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( m1_subset_1 @ F @ C )
              & ( m1_subset_1 @ G @ D )
              & ( A
                = ( k4_domain_1 @ B @ C @ D @ E @ F @ G ) ) )
         => ( r2_hidden @ A @ ( a_3_0_domain_1 @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2213]) ).

thf(661,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B )
        & ( v1_finseq_1 @ B ) )
     => ~ ( ( r2_hidden @ A @ B )
          & ! [C: $i] :
              ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
             => ~ ( ( r2_hidden @ C @ ( k4_finseq_1 @ B ) )
                  & ( A
                    = ( k4_tarski @ C @ ( k1_funct_1 @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_finseq_1) ).

thf(5827,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B )
        & ( v1_finseq_1 @ B ) )
     => ~ ( ( r2_hidden @ A @ B )
          & ! [C: $i] :
              ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
             => ~ ( ( r2_hidden @ C @ ( k4_finseq_1 @ B ) )
                  & ( A
                    = ( k4_tarski @ C @ ( k1_funct_1 @ B @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(2536,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k6_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).

thf(14679,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k6_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2536]) ).

thf(668,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( ( v1_funct_1 @ G )
                                & ( v1_funct_2 @ G @ ( k2_zfmisc_1 @ A @ B ) @ C )
                                & ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                             => ! [H: $i] :
                                  ( ( m2_finseq_1 @ H @ B )
                                 => ( ( H
                                      = ( k10_finseq_1 @ E @ F ) )
                                   => ( ( k5_funcop_1 @ G @ D @ H )
                                      = ( k10_finseq_1 @ ( k2_binop_1 @ A @ B @ C @ G @ D @ E ) @ ( k2_binop_1 @ A @ B @ C @ G @ D @ F ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_finseq_2) ).

thf(5853,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( ( v1_funct_1 @ G )
                                & ( v1_funct_2 @ G @ ( k2_zfmisc_1 @ A @ B ) @ C )
                                & ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                             => ! [H: $i] :
                                  ( ( m2_finseq_1 @ H @ B )
                                 => ( ( H
                                      = ( k10_finseq_1 @ E @ F ) )
                                   => ( ( k5_funcop_1 @ G @ D @ H )
                                      = ( k10_finseq_1 @ ( k2_binop_1 @ A @ B @ C @ G @ D @ E ) @ ( k2_binop_1 @ A @ B @ C @ G @ D @ F ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(2027,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_eqrel_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ A ) @ B )
                 => ( ( r2_hidden @ C @ D )
                   => ( D
                      = ( k8_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_borsuk_1) ).

thf(12413,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_eqrel_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ A ) @ B )
                 => ( ( r2_hidden @ C @ D )
                   => ( D
                      = ( k8_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2027]) ).

thf(1699,axiom,
    ! [A: $i] :
      ( ( v1_finset_1 @ A )
     => ( ( k5_finsub_1 @ A )
        = ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finsub_1) ).

thf(10564,plain,
    ! [A: $i] :
      ( ( v1_finset_1 @ A )
     => ( ( k5_finsub_1 @ A )
        = ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1699]) ).

thf(78,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) )
     => ( m1_pboole @ ( k4_closure2 @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_closure2) ).

thf(3106,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) )
     => ( m1_pboole @ ( k4_closure2 @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(1912,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ A @ B )
          & ( m2_relset_1 @ C @ A @ B ) )
       => ( ( ( B = k1_xboole_0 )
            & ( A != k1_xboole_0 ) )
          | ( v1_partfun1 @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_funct_2) ).

thf(11733,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ A @ B )
          & ( m2_relset_1 @ C @ A @ B ) )
       => ( ( ( B = k1_xboole_0 )
            & ( A != k1_xboole_0 ) )
          | ( v1_partfun1 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1912]) ).

thf(1550,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( r3_zfrefle1 @ A @ B )
           => ( r2_zfrefle1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfrefle1) ).

thf(9920,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( r3_zfrefle1 @ A @ B )
           => ( r2_zfrefle1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1550]) ).

thf(967,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_xboole_0 @ A @ B )
     => ( r1_xboole_0 @ ( k3_xboole_0 @ C @ A ) @ ( k3_xboole_0 @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_xboole_1) ).

thf(7255,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_xboole_0 @ A @ B )
     => ( r1_xboole_0 @ ( k3_xboole_0 @ C @ A ) @ ( k3_xboole_0 @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).

thf(1237,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( k3_xboole_0 @ A @ B ) )
    <=> ! [D: $i] :
          ( ( r2_hidden @ D @ C )
        <=> ( ( r2_hidden @ D @ A )
            & ( r2_hidden @ D @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

thf(8445,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C
          = ( k3_xboole_0 @ A @ B ) )
       => ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ( ( r2_hidden @ D @ A )
                & ( r2_hidden @ D @ B ) ) )
            & ( ( ( r2_hidden @ D @ A )
                & ( r2_hidden @ D @ B ) )
             => ( r2_hidden @ D @ C ) ) ) )
      & ( ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ( ( r2_hidden @ D @ A )
                & ( r2_hidden @ D @ B ) ) )
            & ( ( ( r2_hidden @ D @ A )
                & ( r2_hidden @ D @ B ) )
             => ( r2_hidden @ D @ C ) ) )
       => ( C
          = ( k3_xboole_0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).

thf(2327,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k6_classes2 @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_classes2) ).

thf(13794,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k6_classes2 @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2327]) ).

thf(413,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
          & ( r2_hidden @ B @ ( k1_relat_1 @ C ) ) )
       => ( ( k9_relat_1 @ C @ ( k2_tarski @ A @ B ) )
          = ( k2_tarski @ ( k1_funct_1 @ C @ A ) @ ( k1_funct_1 @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_funct_1) ).

thf(4805,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
          & ( r2_hidden @ B @ ( k1_relat_1 @ C ) ) )
       => ( ( k9_relat_1 @ C @ ( k2_tarski @ A @ B ) )
          = ( k2_tarski @ ( k1_funct_1 @ C @ A ) @ ( k1_funct_1 @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(1579,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( m2_relset_1 @ E @ A @ B ) )
     => ( ( ( r1_tarski @ A @ C )
          & ( r1_tarski @ B @ D ) )
       => ( ( v1_funct_1 @ E )
          & ( m2_relset_1 @ E @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_partfun1) ).

thf(10037,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( m2_relset_1 @ E @ A @ B ) )
     => ( ( ( r1_tarski @ A @ C )
          & ( r1_tarski @ B @ D ) )
       => ( ( v1_funct_1 @ E )
          & ( m2_relset_1 @ E @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1579]) ).

thf(1208,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B )
        & ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( v1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
        & ( v1_funct_1 @ ( k3_funcop_1 @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funcop_1) ).

thf(8313,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B )
        & ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( v1_relat_1 @ ( k3_funcop_1 @ A @ B @ C ) )
        & ( v1_funct_1 @ ( k3_funcop_1 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).

thf(2304,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
       => ( ( m1_subset_1 @ B @ A )
        <=> ( r2_hidden @ B @ A ) ) )
      & ( ( v1_xboole_0 @ A )
       => ( ( m1_subset_1 @ B @ A )
        <=> ( v1_xboole_0 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).

thf(13705,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
       => ( ( ( m1_subset_1 @ B @ A )
           => ( r2_hidden @ B @ A ) )
          & ( ( r2_hidden @ B @ A )
           => ( m1_subset_1 @ B @ A ) ) ) )
      & ( ( v1_xboole_0 @ A )
       => ( ( ( m1_subset_1 @ B @ A )
           => ( v1_xboole_0 @ B ) )
          & ( ( v1_xboole_0 @ B )
           => ( m1_subset_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2304]) ).

thf(205,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i,C: $i] :
          ( ( A
            = ( k2_zfmisc_1 @ B @ C ) )
         => ( ( B = k1_xboole_0 )
            | ( C = k1_xboole_0 )
            | ( ( ( k1_relat_1 @ A )
                = B )
              & ( ( k2_relat_1 @ A )
                = C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funcop_1) ).

thf(3710,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i,C: $i] :
          ( ( A
            = ( k2_zfmisc_1 @ B @ C ) )
         => ( ( B = k1_xboole_0 )
            | ( C = k1_xboole_0 )
            | ( ( ( k1_relat_1 @ A )
                = B )
              & ( ( k2_relat_1 @ A )
                = C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(2012,axiom,
    ! [A: $i] :
      ( ( k5_enumset1 @ A @ A @ A @ A @ A @ A @ A )
      = ( k1_tarski @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_enumset1) ).

thf(12337,plain,
    ! [A: $i] :
      ( ( k5_enumset1 @ A @ A @ A @ A @ A @ A @ A )
      = ( k1_tarski @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2012]) ).

thf(2202,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) )
      <=> ( B
          = ( k1_subset_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_subset_1) ).

thf(13334,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) )
         => ( B
            = ( k1_subset_1 @ A ) ) )
        & ( ( B
            = ( k1_subset_1 @ A ) )
         => ( r1_tarski @ B @ ( k3_subset_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2202]) ).

thf(374,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( ( k1_funct_4 @ A @ B )
              = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funct_4) ).

thf(4616,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( ( k1_funct_4 @ A @ B )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(543,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( k7_relat_1 @ B @ A )
        = ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_relat_1) ).

thf(5346,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( k7_relat_1 @ B @ A )
        = ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(482,axiom,
    ! [A: $i,B: $i] :
      ( ( k3_tarski @ ( k3_setfam_1 @ A @ B ) )
      = ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_setfam_1) ).

thf(5093,plain,
    ! [A: $i,B: $i] :
      ( ( k3_tarski @ ( k3_setfam_1 @ A @ B ) )
      = ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(591,axiom,
    ! [A: $i,B: $i] :
      ( ( k7_cat_1 @ A @ B )
      = ( k3_cqc_lang @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_cat_1) ).

thf(5531,plain,
    ! [A: $i,B: $i] :
      ( ( k7_cat_1 @ A @ B )
      = ( k3_cqc_lang @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(1978,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ C )
                         => ( ( k8_funct_2 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) @ ( k16_funct_3 @ A @ C @ B @ C @ D @ ( k6_partfun1 @ C ) ) @ ( k1_domain_1 @ A @ C @ E @ F ) )
                            = ( k1_domain_1 @ B @ C @ ( k8_funct_2 @ A @ B @ D @ E ) @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_borsuk_1) ).

thf(12136,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ C )
                         => ( ( k8_funct_2 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) @ ( k16_funct_3 @ A @ C @ B @ C @ D @ ( k6_partfun1 @ C ) ) @ ( k1_domain_1 @ A @ C @ E @ F ) )
                            = ( k1_domain_1 @ B @ C @ ( k8_funct_2 @ A @ B @ D @ E ) @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1978]) ).

thf(44,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( m1_pboole @ C @ A )
         => ! [D: $i] :
              ( ( m1_pboole @ D @ A )
             => ( ( m3_pboole @ D @ A @ B @ C )
              <=> ! [E: $i] :
                    ( ( r2_hidden @ E @ A )
                   => ( ( v1_funct_1 @ ( k1_funct_1 @ D @ E ) )
                      & ( v1_funct_2 @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) )
                      & ( m2_relset_1 @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_pboole) ).

thf(2802,plain,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( m1_pboole @ C @ A )
         => ! [D: $i] :
              ( ( m1_pboole @ D @ A )
             => ( ( ( m3_pboole @ D @ A @ B @ C )
                 => ! [E: $i] :
                      ( ( r2_hidden @ E @ A )
                     => ( ( v1_funct_1 @ ( k1_funct_1 @ D @ E ) )
                        & ( v1_funct_2 @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) )
                        & ( m2_relset_1 @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) ) ) ) )
                & ( ! [E: $i] :
                      ( ( r2_hidden @ E @ A )
                     => ( ( v1_funct_1 @ ( k1_funct_1 @ D @ E ) )
                        & ( v1_funct_2 @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) )
                        & ( m2_relset_1 @ ( k1_funct_1 @ D @ E ) @ ( k1_funct_1 @ B @ E ) @ ( k1_funct_1 @ C @ E ) ) ) )
                 => ( m3_pboole @ D @ A @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(732,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
     => ( ( r2_hidden @ C @ ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ D ) )
       => ( ( k1_funct_1 @ D @ C )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_partfun1) ).

thf(6154,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
     => ( ( r2_hidden @ C @ ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ D ) )
       => ( ( k1_funct_1 @ D @ C )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(1591,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m2_relset_1 @ E @ A @ B ) )
     => ( ( ( r2_hidden @ C @ A )
          & ( r2_hidden @ ( k1_funct_1 @ E @ C ) @ D ) )
       => ( ( B = k1_xboole_0 )
          | ( ( k1_funct_1 @ ( k9_relset_1 @ A @ B @ D @ E ) @ C )
            = ( k1_funct_1 @ E @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_funct_2) ).

thf(10098,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m2_relset_1 @ E @ A @ B ) )
     => ( ( ( r2_hidden @ C @ A )
          & ( r2_hidden @ ( k1_funct_1 @ E @ C ) @ D ) )
       => ( ( B = k1_xboole_0 )
          | ( ( k1_funct_1 @ ( k9_relset_1 @ A @ B @ D @ E ) @ C )
            = ( k1_funct_1 @ E @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1591]) ).

thf(318,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).

thf(4300,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(736,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( r2_hidden @ ( k4_mcart_1 @ A @ B @ C @ D ) @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
    <=> ( ( r2_hidden @ A @ E )
        & ( r2_hidden @ B @ F )
        & ( r2_hidden @ C @ G )
        & ( r2_hidden @ D @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_mcart_1) ).

thf(6184,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( r2_hidden @ ( k4_mcart_1 @ A @ B @ C @ D ) @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
       => ( ( r2_hidden @ A @ E )
          & ( r2_hidden @ B @ F )
          & ( r2_hidden @ C @ G )
          & ( r2_hidden @ D @ H ) ) )
      & ( ( ( r2_hidden @ A @ E )
          & ( r2_hidden @ B @ F )
          & ( r2_hidden @ C @ G )
          & ( r2_hidden @ D @ H ) )
       => ( r2_hidden @ ( k4_mcart_1 @ A @ B @ C @ D ) @ ( k4_zfmisc_1 @ E @ F @ G @ H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(2394,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k7_subset_1 @ A @ B @ C )
                = ( a_3_5_domain_1 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_domain_1) ).

thf(14048,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k7_subset_1 @ A @ B @ C )
                = ( a_3_5_domain_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2394]) ).

thf(2117,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ~ ( v1_xboole_0 @ E )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
        & ( m1_relset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
        & ( m1_subset_1 @ G @ A )
        & ( m1_subset_1 @ H @ B )
        & ( m1_subset_1 @ I @ C )
        & ( m1_subset_1 @ J @ D ) )
     => ( m1_subset_1 @ ( k4_multop_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_multop_1) ).

thf(12894,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ~ ( v1_xboole_0 @ E )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
        & ( m1_relset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
        & ( m1_subset_1 @ G @ A )
        & ( m1_subset_1 @ H @ B )
        & ( m1_subset_1 @ I @ C )
        & ( m1_subset_1 @ J @ D ) )
     => ( m1_subset_1 @ ( k4_multop_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2117]) ).

thf(179,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ( ( ( v3_binop_1 @ D @ A )
                      & ( v1_binop_1 @ D @ A )
                      & ( v2_binop_1 @ D @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                       => ( ( E != k1_xboole_0 )
                         => ! [F: $i] :
                              ( ( ( v1_funct_1 @ F )
                                & ( v1_funct_2 @ F @ B @ C )
                                & ( m2_relset_1 @ F @ B @ C ) )
                             => ! [G: $i] :
                                  ( ( ( v1_funct_1 @ G )
                                    & ( v1_funct_2 @ G @ C @ A )
                                    & ( m2_relset_1 @ G @ C @ A ) )
                                 => ( ( k7_setwiseo @ C @ A @ D @ ( k8_setwiseo @ B @ C @ F @ E ) @ G )
                                    = ( k7_setwiseo @ B @ A @ D @ E @ ( k7_funct_2 @ B @ C @ A @ F @ G ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_setwiseo) ).

thf(3586,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ( ( ( v3_binop_1 @ D @ A )
                      & ( v1_binop_1 @ D @ A )
                      & ( v2_binop_1 @ D @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                       => ( ( E != k1_xboole_0 )
                         => ! [F: $i] :
                              ( ( ( v1_funct_1 @ F )
                                & ( v1_funct_2 @ F @ B @ C )
                                & ( m2_relset_1 @ F @ B @ C ) )
                             => ! [G: $i] :
                                  ( ( ( v1_funct_1 @ G )
                                    & ( v1_funct_2 @ G @ C @ A )
                                    & ( m2_relset_1 @ G @ C @ A ) )
                                 => ( ( k7_setwiseo @ C @ A @ D @ ( k8_setwiseo @ B @ C @ F @ E ) @ G )
                                    = ( k7_setwiseo @ B @ A @ D @ E @ ( k7_funct_2 @ B @ C @ A @ F @ G ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(689,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_finset_1 @ A ) )
     => ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finseq_1) ).

thf(5972,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_finset_1 @ A ) )
     => ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(1933,axiom,
    m1_subset_1 @ k8_vectsp_2 @ ( k1_tarski @ k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_vectsp_2) ).

thf(11883,plain,
    m1_subset_1 @ k8_vectsp_2 @ ( k1_tarski @ k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1933]) ).

thf(1013,axiom,
    ! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k9_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C ) @ ( k1_tarski @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_borsuk_1) ).

thf(7502,plain,
    ! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k9_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C ) @ ( k1_tarski @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).

thf(2391,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m2_subset_1 @ C @ A @ B )
         => ( m1_subset_1 @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_subset_1) ).

thf(14042,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m2_subset_1 @ C @ A @ B )
         => ( m1_subset_1 @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2391]) ).

thf(618,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( ( k1_tarski @ A )
          = ( k2_xboole_0 @ B @ C ) )
        & ( B != C )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_zfmisc_1) ).

thf(5616,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( ( k1_tarski @ A )
          = ( k2_xboole_0 @ B @ C ) )
        & ( B != C )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(1727,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
         => ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_funct_2) ).

thf(10696,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
         => ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1727]) ).

thf(799,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( k2_funct_2 @ A @ B @ C @ A )
          = ( k2_relat_1 @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_funct_2) ).

thf(6460,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( B = k1_xboole_0 )
         => ( A = k1_xboole_0 ) )
       => ( ( k2_funct_2 @ A @ B @ C @ A )
          = ( k2_relat_1 @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(2396,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k4_subset_1 @ A @ B @ C )
                = ( a_3_2_domain_1 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_domain_1) ).

thf(14053,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k4_subset_1 @ A @ B @ C )
                = ( a_3_2_domain_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2396]) ).

thf(908,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) @ C )
        = ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
      & ( ( k2_zfmisc_1 @ C @ ( k4_xboole_0 @ A @ B ) )
        = ( k4_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_zfmisc_1) ).

thf(6969,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) @ C )
        = ( k4_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
      & ( ( k2_zfmisc_1 @ C @ ( k4_xboole_0 @ A @ B ) )
        = ( k4_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).

thf(1404,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( k3_xboole_0 @ A @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).

thf(9206,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( k3_xboole_0 @ A @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).

thf(1761,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
              & ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ C )
                     => ( A
                       != ( k4_tarski @ D @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_domain_1) ).

thf(10957,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
              & ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ C )
                     => ( A
                       != ( k4_tarski @ D @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1761]) ).

thf(2400,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
      & ~ ( v1_xboole_0 @ B )
      & ( v1_finset_1 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_waybel_7) ).

thf(14063,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
      & ~ ( v1_xboole_0 @ B )
      & ( v1_finset_1 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2400]) ).

thf(875,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k1_tarski @ A )
        = ( k2_tarski @ B @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).

thf(6817,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k1_tarski @ A )
        = ( k2_tarski @ B @ C ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(357,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ ( k2_tarski @ C @ D ) ) )
     => ( ( ( k1_mcart_1 @ A )
          = B )
        & ( ( ( k2_mcart_1 @ A )
            = C )
          | ( ( k2_mcart_1 @ A )
            = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_mcart_1) ).

thf(4554,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ ( k2_tarski @ C @ D ) ) )
     => ( ( ( k1_mcart_1 @ A )
          = B )
        & ( ( ( k2_mcart_1 @ A )
            = C )
          | ( ( k2_mcart_1 @ A )
            = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(2439,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( m1_subset_1 @ ( k15_domain_1 @ A @ B @ C @ D ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_domain_1) ).

thf(14223,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( m1_subset_1 @ ( k15_domain_1 @ A @ B @ C @ D ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2439]) ).

thf(388,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
       => ( ( k2_relat_1 @ ( k2_funct_4 @ C ) )
          = ( k2_relat_1 @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_funct_4) ).

thf(4694,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
       => ( ( k2_relat_1 @ ( k2_funct_4 @ C ) )
          = ( k2_relat_1 @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(2554,axiom,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k6_lattice5 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_lattice5) ).

thf(14736,plain,
    ! [A: $i] :
      ~ ( v1_xboole_0 @ ( k6_lattice5 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2554]) ).

thf(1668,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k4_subset_1 @ A @ B @ ( k2_subset_1 @ A ) )
        = ( k2_subset_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_subset_1) ).

thf(10450,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k4_subset_1 @ A @ B @ ( k2_subset_1 @ A ) )
        = ( k2_subset_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1668]) ).

thf(1014,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ ( k11_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_relset_1) ).

thf(7504,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ ( k11_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(1718,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
              & ! [E: $i] :
                  ( B
                 != ( k1_tarski @ E ) ) )
           => ( r1_tarski @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_funct_2) ).

thf(10645,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) )
              & ! [E: $i] :
                  ( B
                 != ( k1_tarski @ E ) ) )
           => ( r1_tarski @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1718]) ).

thf(1376,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_pboole @ C @ A ) )
     => ( r6_pboole @ A @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r6_pboole) ).

thf(9042,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_pboole @ C @ A ) )
     => ( r6_pboole @ A @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376]) ).

thf(583,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( r1_tarski @ A @ C ) )
     => ( r1_tarski @ ( k1_setfam_1 @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_setfam_1) ).

thf(5511,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( r1_tarski @ A @ C ) )
     => ( r1_tarski @ ( k1_setfam_1 @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(735,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ~ ( ( A != k1_xboole_0 )
          & ( B != k1_xboole_0 )
          & ~ ( ( v2_funct_1 @ C )
            <=> ! [D: $i,E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ D @ A )
                    & ( m2_relset_1 @ E @ D @ A ) )
                 => ! [F: $i] :
                      ( ( ( v1_funct_1 @ F )
                        & ( v1_funct_2 @ F @ D @ A )
                        & ( m2_relset_1 @ F @ D @ A ) )
                     => ( ( ( k1_partfun1 @ D @ A @ A @ B @ E @ C )
                          = ( k1_partfun1 @ D @ A @ A @ B @ F @ C ) )
                       => ( E = F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_2) ).

thf(6165,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ~ ( ( A != k1_xboole_0 )
          & ( B != k1_xboole_0 )
          & ~ ( ( ( v2_funct_1 @ C )
               => ! [D: $i,E: $i] :
                    ( ( ( v1_funct_1 @ E )
                      & ( v1_funct_2 @ E @ D @ A )
                      & ( m2_relset_1 @ E @ D @ A ) )
                   => ! [F: $i] :
                        ( ( ( v1_funct_1 @ F )
                          & ( v1_funct_2 @ F @ D @ A )
                          & ( m2_relset_1 @ F @ D @ A ) )
                       => ( ( ( k1_partfun1 @ D @ A @ A @ B @ E @ C )
                            = ( k1_partfun1 @ D @ A @ A @ B @ F @ C ) )
                         => ( E = F ) ) ) ) )
              & ( ! [D: $i,E: $i] :
                    ( ( ( v1_funct_1 @ E )
                      & ( v1_funct_2 @ E @ D @ A )
                      & ( m2_relset_1 @ E @ D @ A ) )
                   => ! [F: $i] :
                        ( ( ( v1_funct_1 @ F )
                          & ( v1_funct_2 @ F @ D @ A )
                          & ( m2_relset_1 @ F @ D @ A ) )
                       => ( ( ( k1_partfun1 @ D @ A @ A @ B @ E @ C )
                            = ( k1_partfun1 @ D @ A @ A @ B @ F @ C ) )
                         => ( E = F ) ) ) )
               => ( v2_funct_1 @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(1543,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ D @ A )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ B @ A )
        & ( m1_relset_1 @ E @ B @ A ) )
     => ( ( k5_funcsdom @ A @ B @ C @ D @ E )
        = ( k5_funcop_1 @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_funcsdom) ).

thf(9857,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ D @ A )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ B @ A )
        & ( m1_relset_1 @ E @ B @ A ) )
     => ( ( k5_funcsdom @ A @ B @ C @ D @ E )
        = ( k5_funcop_1 @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1543]) ).

thf(2413,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ A )
        & ( m1_subset_1 @ H @ A )
        & ( m1_subset_1 @ I @ A ) )
     => ( ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I )
        = ( k6_enumset1 @ B @ C @ D @ E @ F @ G @ H @ I ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k13_domain_1) ).

thf(14122,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ A )
        & ( m1_subset_1 @ H @ A )
        & ( m1_subset_1 @ I @ A ) )
     => ( ( k13_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I )
        = ( k6_enumset1 @ B @ C @ D @ E @ F @ G @ H @ I ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2413]) ).

thf(46,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ~ ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
             => ( C
                = ( k4_tarski @ ( k1_mcart_1 @ C ) @ ( k2_mcart_1 @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_mcart_1) ).

thf(2812,plain,
    ! [A: $i,B: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ~ ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
             => ( C
                = ( k4_tarski @ ( k1_mcart_1 @ C ) @ ( k2_mcart_1 @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(2222,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ~ ( v1_xboole_0 @ E )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
                            & ( m2_relset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E ) )
                         => ! [G: $i] :
                              ( ( ( v1_funct_1 @ G )
                                & ( v1_funct_2 @ G @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
                                & ( m2_relset_1 @ G @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E ) )
                             => ( ! [H: $i] :
                                    ( ( m1_subset_1 @ H @ A )
                                   => ! [I: $i] :
                                        ( ( m1_subset_1 @ I @ B )
                                       => ! [J: $i] :
                                            ( ( m1_subset_1 @ J @ C )
                                           => ! [K: $i] :
                                                ( ( m1_subset_1 @ K @ D )
                                               => ( ( k4_multop_1 @ A @ B @ C @ D @ E @ F @ H @ I @ J @ K )
                                                  = ( k4_multop_1 @ A @ B @ C @ D @ E @ G @ H @ I @ J @ K ) ) ) ) ) )
                               => ( F = G ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_multop_1) ).

thf(13427,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ~ ( v1_xboole_0 @ E )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
                            & ( m2_relset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E ) )
                         => ! [G: $i] :
                              ( ( ( v1_funct_1 @ G )
                                & ( v1_funct_2 @ G @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
                                & ( m2_relset_1 @ G @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E ) )
                             => ( ! [H: $i] :
                                    ( ( m1_subset_1 @ H @ A )
                                   => ! [I: $i] :
                                        ( ( m1_subset_1 @ I @ B )
                                       => ! [J: $i] :
                                            ( ( m1_subset_1 @ J @ C )
                                           => ! [K: $i] :
                                                ( ( m1_subset_1 @ K @ D )
                                               => ( ( k4_multop_1 @ A @ B @ C @ D @ E @ F @ H @ I @ J @ K )
                                                  = ( k4_multop_1 @ A @ B @ C @ D @ E @ G @ H @ I @ J @ K ) ) ) ) ) )
                               => ( F = G ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2222]) ).

thf(344,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( k4_partfun1 @ A @ B ) )
    <=> ! [D: $i] :
          ( ( r2_hidden @ D @ C )
        <=> ? [E: $i] :
              ( ( v1_relat_1 @ E )
              & ( v1_funct_1 @ E )
              & ( D = E )
              & ( r1_tarski @ ( k1_relat_1 @ E ) @ A )
              & ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_partfun1) ).

thf(4420,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C
          = ( k4_partfun1 @ A @ B ) )
       => ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ? [E: $i] :
                  ( ( v1_relat_1 @ E )
                  & ( v1_funct_1 @ E )
                  & ( D = E )
                  & ( r1_tarski @ ( k1_relat_1 @ E ) @ A )
                  & ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) )
            & ( ? [E: $i] :
                  ( ( v1_relat_1 @ E )
                  & ( v1_funct_1 @ E )
                  & ( D = E )
                  & ( r1_tarski @ ( k1_relat_1 @ E ) @ A )
                  & ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) )
             => ( r2_hidden @ D @ C ) ) ) )
      & ( ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ? [E: $i] :
                  ( ( v1_relat_1 @ E )
                  & ( v1_funct_1 @ E )
                  & ( D = E )
                  & ( r1_tarski @ ( k1_relat_1 @ E ) @ A )
                  & ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) )
            & ( ? [E: $i] :
                  ( ( v1_relat_1 @ E )
                  & ( v1_funct_1 @ E )
                  & ( D = E )
                  & ( r1_tarski @ ( k1_relat_1 @ E ) @ A )
                  & ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) )
             => ( r2_hidden @ D @ C ) ) )
       => ( C
          = ( k4_partfun1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(2363,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ D )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
        & ~ ( v1_xboole_0 @ E )
        & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ C ) ) ) )
     => ( ( r2_hidden @ A @ ( a_4_1_yellow_9 @ B @ C @ D @ E ) )
      <=> ? [F: $i,G: $i] :
            ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
            & ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
            & ( A
              = ( k12_mcart_1 @ B @ C @ F @ G ) )
            & ( r2_hidden @ F @ D )
            & ( r2_hidden @ G @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_1_yellow_9) ).

thf(13930,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ D )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
        & ~ ( v1_xboole_0 @ E )
        & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ C ) ) ) )
     => ( ( ( r2_hidden @ A @ ( a_4_1_yellow_9 @ B @ C @ D @ E ) )
         => ? [F: $i,G: $i] :
              ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
              & ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
              & ( A
                = ( k12_mcart_1 @ B @ C @ F @ G ) )
              & ( r2_hidden @ F @ D )
              & ( r2_hidden @ G @ E ) ) )
        & ( ? [F: $i,G: $i] :
              ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
              & ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
              & ( A
                = ( k12_mcart_1 @ B @ C @ F @ G ) )
              & ( r2_hidden @ F @ D )
              & ( r2_hidden @ G @ E ) )
         => ( r2_hidden @ A @ ( a_4_1_yellow_9 @ B @ C @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2363]) ).

thf(1275,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ~ ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
             => ( ( E
                 != ( k8_mcart_1 @ A @ B @ C @ D @ E ) )
                & ( E
                 != ( k9_mcart_1 @ A @ B @ C @ D @ E ) )
                & ( E
                 != ( k10_mcart_1 @ A @ B @ C @ D @ E ) )
                & ( E
                 != ( k11_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_mcart_1) ).

thf(8633,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ~ ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
             => ( ( E
                 != ( k8_mcart_1 @ A @ B @ C @ D @ E ) )
                & ( E
                 != ( k9_mcart_1 @ A @ B @ C @ D @ E ) )
                & ( E
                 != ( k10_mcart_1 @ A @ B @ C @ D @ E ) )
                & ( E
                 != ( k11_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).

thf(1064,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_pboole @ C @ A )
             => ! [D: $i] :
                  ( ( m1_pboole @ D @ B )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( ( k1_funct_1 @ D @ E )
                         != k1_xboole_0 )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k1_funct_1 @ D @ E ) )
                           => ! [G: $i] :
                                ( ( ( v1_funct_1 @ G )
                                  & ( v1_funct_2 @ G @ A @ B )
                                  & ( m2_relset_1 @ G @ A @ B ) )
                               => ( ( G
                                    = ( k10_pboole @ A @ E ) )
                                 => ( m1_functor0 @ ( a_6_0_functor0 @ A @ B @ C @ D @ E @ F ) @ A @ B @ G @ C @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_functor0) ).

thf(7699,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_pboole @ C @ A )
             => ! [D: $i] :
                  ( ( m1_pboole @ D @ B )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( ( k1_funct_1 @ D @ E )
                         != k1_xboole_0 )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k1_funct_1 @ D @ E ) )
                           => ! [G: $i] :
                                ( ( ( v1_funct_1 @ G )
                                  & ( v1_funct_2 @ G @ A @ B )
                                  & ( m2_relset_1 @ G @ A @ B ) )
                               => ( ( G
                                    = ( k10_pboole @ A @ E ) )
                                 => ( m1_functor0 @ ( a_6_0_functor0 @ A @ B @ C @ D @ E @ F ) @ A @ B @ G @ C @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).

thf(1655,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ A @ B )
                            & ( m2_relset_1 @ F @ A @ B ) )
                         => ( ! [G: $i] :
                                ( ( m1_subset_1 @ G @ A )
                               => ( ( k8_funct_2 @ A @ B @ F @ G )
                                  = ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ A @ B @ D @ G ) @ ( k8_funct_2 @ A @ B @ E @ G ) ) ) )
                           => ( F
                              = ( k6_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funcop_1) ).

thf(10397,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ A @ B )
                            & ( m2_relset_1 @ F @ A @ B ) )
                         => ( ! [G: $i] :
                                ( ( m1_subset_1 @ G @ A )
                               => ( ( k8_funct_2 @ A @ B @ F @ G )
                                  = ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ A @ B @ D @ G ) @ ( k8_funct_2 @ A @ B @ E @ G ) ) ) )
                           => ( F
                              = ( k6_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1655]) ).

thf(427,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( k5_relat_1 @ ( k4_funcop_1 @ C @ B @ D ) @ A )
                  = ( k4_funcop_1 @ ( k5_relat_1 @ C @ A ) @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funcop_1) ).

thf(4882,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( k5_relat_1 @ ( k4_funcop_1 @ C @ B @ D ) @ A )
                  = ( k4_funcop_1 @ ( k5_relat_1 @ C @ A ) @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(260,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_relat_1 @ E )
        & ( v1_funct_1 @ E ) )
     => ( ( ( ( k1_relat_1 @ E )
            = ( k2_tarski @ A @ B ) )
          & ( ( k1_funct_1 @ E @ A )
            = C )
          & ( ( k1_funct_1 @ E @ B )
            = D ) )
       => ( E
          = ( k4_funct_4 @ A @ B @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_funct_4) ).

thf(4009,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_relat_1 @ E )
        & ( v1_funct_1 @ E ) )
     => ( ( ( ( k1_relat_1 @ E )
            = ( k2_tarski @ A @ B ) )
          & ( ( k1_funct_1 @ E @ A )
            = C )
          & ( ( k1_funct_1 @ E @ B )
            = D ) )
       => ( E
          = ( k4_funct_4 @ A @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(940,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ B )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ( ( k1_funct_4 @ ( k2_partfun1 @ A @ B @ D @ C ) @ E )
                    = E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_lattice2) ).

thf(7119,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ B )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ( ( k1_funct_4 @ ( k2_partfun1 @ A @ B @ D @ C ) @ E )
                    = E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).

thf(639,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r1_tarski @ A @ B )
       => ( ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
            = ( k7_relat_1 @ C @ A ) )
          & ( ( k7_relat_1 @ ( k7_relat_1 @ C @ B ) @ A )
            = ( k7_relat_1 @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funct_1) ).

thf(5730,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r1_tarski @ A @ B )
       => ( ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
            = ( k7_relat_1 @ C @ A ) )
          & ( ( k7_relat_1 @ ( k7_relat_1 @ C @ B ) @ A )
            = ( k7_relat_1 @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(2382,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( k13_ens_1 @ A @ B )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_ens_1) ).

thf(14016,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( k13_ens_1 @ A @ B )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2382]) ).

thf(478,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
     => ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_xboole_1) ).

thf(5082,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ C )
     => ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(1386,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_mcart_1 @ A @ B @ C @ D )
      = ( k4_tarski @ ( k3_mcart_1 @ A @ B @ C ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_mcart_1) ).

thf(9079,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_mcart_1 @ A @ B @ C @ D )
      = ( k4_tarski @ ( k3_mcart_1 @ A @ B @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386]) ).

thf(2542,axiom,
    ! [A: $i,B: $i] : ( m1_subset_1 @ ( k1_funct_7 @ A @ B ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_7) ).

thf(14699,plain,
    ! [A: $i,B: $i] : ( m1_subset_1 @ ( k1_funct_7 @ A @ B ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2542]) ).

thf(1769,axiom,
    ! [A: $i] :
      ( ( k2_subset_1 @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).

thf(10995,plain,
    ! [A: $i] :
      ( ( k2_subset_1 @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1769]) ).

thf(2344,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
     => ( ( k16_domain_1 @ A @ B @ C @ D )
        = ( k19_mcart_1 @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k16_domain_1) ).

thf(13857,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
     => ( ( k16_domain_1 @ A @ B @ C @ D )
        = ( k19_mcart_1 @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2344]) ).

thf(1401,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ~ ( ( ( B = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ( r1_partfun1 @ C @ D )
              & ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ~ ( ( v1_partfun1 @ E @ A @ B )
                      & ( r1_partfun1 @ C @ E )
                      & ( r1_partfun1 @ D @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t162_partfun1) ).

thf(9174,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ~ ( ( ( B = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ( r1_partfun1 @ C @ D )
              & ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ~ ( ( v1_partfun1 @ E @ A @ B )
                      & ( r1_partfun1 @ C @ E )
                      & ( r1_partfun1 @ D @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1401]) ).

thf(2311,axiom,
    m1_subset_1 @ k1_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_urysohn1) ).

thf(13734,plain,
    m1_subset_1 @ k1_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2311]) ).

thf(1422,axiom,
    ! [A: $i,B: $i] :
      ( ( k5_finsub_1 @ ( k3_xboole_0 @ A @ B ) )
      = ( k3_xboole_0 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finsub_1) ).

thf(9275,plain,
    ! [A: $i,B: $i] :
      ( ( k5_finsub_1 @ ( k3_xboole_0 @ A @ B ) )
      = ( k3_xboole_0 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422]) ).

thf(1151,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( k7_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
            = ( k5_relat_1 @ ( k7_relat_1 @ B @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_relat_1) ).

thf(8103,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( k7_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
            = ( k5_relat_1 @ ( k7_relat_1 @ B @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).

thf(1030,axiom,
    ! [A: $i] :
      ( ( k2_xboole_0 @ A @ k1_xboole_0 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).

thf(7566,plain,
    ! [A: $i] :
      ( ( k2_xboole_0 @ A @ k1_xboole_0 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(1961,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( r1_partfun1 @ C @ D )
           => ( ( ( B = k1_xboole_0 )
                & ( A != k1_xboole_0 ) )
              | ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_funct_2) ).

thf(12044,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( r1_partfun1 @ C @ D )
           => ( ( ( B = k1_xboole_0 )
                & ( A != k1_xboole_0 ) )
              | ( C = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1961]) ).

thf(1842,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( v1_finset_1 @ A )
       => ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_finsub_1) ).

thf(11392,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( v1_finset_1 @ A )
       => ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1842]) ).

thf(39,axiom,
    ! [A: $i] :
      ( ( k1_setwiseo @ A )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setwiseo) ).

thf(2780,plain,
    ! [A: $i] :
      ( ( k1_setwiseo @ A )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(399,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
       => ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
          & ( r2_hidden @ B @ ( k2_relat_1 @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).

thf(4731,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
       => ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
          & ( r2_hidden @ B @ ( k2_relat_1 @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(2429,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i,D: $i] :
          ( ( ( g2_struct_0 @ A @ B )
            = ( g2_struct_0 @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g2_struct_0) ).

thf(14178,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i,D: $i] :
          ( ( ( g2_struct_0 @ A @ B )
            = ( g2_struct_0 @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2429]) ).

thf(1702,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
             => ( ( k5_setfam_1 @ B @ ( k2_funct_2 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) @ ( k2_funct_3 @ A @ B @ C ) @ D ) )
                = ( k2_funct_2 @ A @ B @ C @ ( k5_setfam_1 @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_borsuk_1) ).

thf(10579,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
             => ( ( k5_setfam_1 @ B @ ( k2_funct_2 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) @ ( k2_funct_3 @ A @ B @ C ) @ D ) )
                = ( k2_funct_2 @ A @ B @ C @ ( k5_setfam_1 @ A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1702]) ).

thf(2187,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ A ) )
     => ( ( k8_funct_2 @ A @ B @ C @ D )
        = ( k1_funct_1 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).

thf(13272,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ A ) )
     => ( ( k8_funct_2 @ A @ B @ C @ D )
        = ( k1_funct_1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2187]) ).

thf(565,axiom,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m3_realset1 @ C @ A @ B )
             => ( ( k4_realset1 @ A @ B @ C )
                = ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_realset1) ).

thf(5439,plain,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m3_realset1 @ C @ A @ B )
             => ( ( k4_realset1 @ A @ B @ C )
                = ( k1_realset1 @ C @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(312,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( ( ( ( k5_relat_1 @ A @ B )
                  = A )
                & ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
                  = k1_xboole_0 ) )
             => ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
                = k1_xboole_0 ) )
            & ( ( ( ( k5_relat_1 @ B @ A )
                  = A )
                & ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
                  = k1_xboole_0 ) )
             => ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ A )
                = k1_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_sysrel) ).

thf(4264,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( ( ( ( k5_relat_1 @ A @ B )
                  = A )
                & ( ( k5_relat_1 @ B @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
                  = k1_xboole_0 ) )
             => ( ( k5_relat_1 @ A @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) )
                = k1_xboole_0 ) )
            & ( ( ( ( k5_relat_1 @ B @ A )
                  = A )
                & ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ B )
                  = k1_xboole_0 ) )
             => ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ ( k1_relat_1 @ B ) ) ) @ A )
                = k1_xboole_0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(432,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ! [E: $i] :
              ( ( ( v1_relat_1 @ E )
                & ( v1_funct_1 @ E ) )
             => ( ( ( r1_partfun1 @ C @ E )
                  & ( r1_tarski @ D @ C ) )
               => ( r1_partfun1 @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_partfun1) ).

thf(4897,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ! [E: $i] :
              ( ( ( v1_relat_1 @ E )
                & ( v1_funct_1 @ E ) )
             => ( ( ( r1_partfun1 @ C @ E )
                  & ( r1_tarski @ D @ C ) )
               => ( r1_partfun1 @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(526,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( ( k3_xboole_0 @ B @ ( k1_tarski @ A ) )
        = ( k1_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_zfmisc_1) ).

thf(5286,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( ( k3_xboole_0 @ B @ ( k1_tarski @ A ) )
        = ( k1_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(92,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( ( ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) )
            = ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
          & ( ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A )
            = ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).

thf(3165,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( ( ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) )
            = ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
          & ( ( k5_relat_1 @ ( k2_funct_1 @ A ) @ A )
            = ( k6_relat_1 @ ( k2_relat_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(2319,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_finset_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).

thf(13777,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_finset_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2319]) ).

thf(2508,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
               => ( ( r2_hidden @ D @ B )
                <=> ( r2_hidden @ D @ C ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_setfam_1) ).

thf(14576,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
               => ( ( ( r2_hidden @ D @ B )
                   => ( r2_hidden @ D @ C ) )
                  & ( ( r2_hidden @ D @ C )
                   => ( r2_hidden @ D @ B ) ) ) )
           => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2508]) ).

thf(2584,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( v1_xboole_0 @ B )
           => ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_tex_2) ).

thf(14892,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( v1_xboole_0 @ B )
           => ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2584]) ).

thf(1115,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C ) @ C )
     => ( r2_hidden @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_zfmisc_1) ).

thf(7928,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ C ) @ C )
     => ( r2_hidden @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).

thf(99,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
            & ( r2_hidden @ C @ ( k1_relat_1 @ A ) ) )
         => ( ( k5_relat_1 @ ( k10_finseq_1 @ B @ C ) @ A )
            = ( k10_finseq_1 @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_finseq_2) ).

thf(3192,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
            & ( r2_hidden @ C @ ( k1_relat_1 @ A ) ) )
         => ( ( k5_relat_1 @ ( k10_finseq_1 @ B @ C ) @ A )
            = ( k10_finseq_1 @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(1251,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_xboole_0 @ A @ B )
     => ( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
        = ( k3_xboole_0 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_xboole_1) ).

thf(8529,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_xboole_0 @ A @ B )
     => ( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
        = ( k3_xboole_0 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).

thf(1865,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ~ ( ( ( B = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ( r1_partfun1 @ C @ D )
              & ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ B )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ~ ( ( r1_partfun1 @ C @ E )
                      & ( r1_partfun1 @ D @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t154_funct_2) ).

thf(11519,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ~ ( ( ( B = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ( r1_partfun1 @ C @ D )
              & ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ B )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ~ ( ( r1_partfun1 @ C @ E )
                      & ( r1_partfun1 @ D @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1865]) ).

thf(187,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( ( ( k1_relat_1 @ A )
              = ( k1_tarski @ B ) )
            & ( ( k2_relat_1 @ A )
              = ( k1_tarski @ C ) ) )
         => ( A
            = ( k1_tarski @ ( k4_tarski @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_pre_circ) ).

thf(3614,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( ( ( k1_relat_1 @ A )
              = ( k1_tarski @ B ) )
            & ( ( k2_relat_1 @ A )
              = ( k1_tarski @ C ) ) )
         => ( A
            = ( k1_tarski @ ( k4_tarski @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( m2_relset_1 @ D @ A @ B )
             => ( m1_subset_1 @ ( a_4_0_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_relset_2) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ~ ( v1_xboole_0 @ A )
       => ! [B: $i,C: $i] :
            ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
           => ! [D: $i] :
                ( ( m2_relset_1 @ D @ A @ B )
               => ( m1_subset_1 @ ( a_4_0_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(2593,plain,
    ~ ! [A: $i] :
        ( ~ ( v1_xboole_0 @ A )
       => ! [B: $i,C: $i] :
            ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
           => ! [D: $i] :
                ( ( m2_relset_1 @ D @ A @ B )
               => ( m1_subset_1 @ ( a_4_0_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(62,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( ( k1_relat_1 @ A )
                = ( k1_relat_1 @ B ) )
              & ( r1_partfun1 @ A @ B ) )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_partfun1) ).

thf(3006,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( ( k1_relat_1 @ A )
                = ( k1_relat_1 @ B ) )
              & ( r1_partfun1 @ A @ B ) )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(2119,axiom,
    ! [A: $i] :
      ( ( v1_funct_1 @ ( k11_setwiseo @ A ) )
      & ( v1_funct_2 @ ( k11_setwiseo @ A ) @ A @ ( k5_finsub_1 @ A ) )
      & ( m2_relset_1 @ ( k11_setwiseo @ A ) @ A @ ( k5_finsub_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_setwiseo) ).

thf(12899,plain,
    ! [A: $i] :
      ( ( v1_funct_1 @ ( k11_setwiseo @ A ) )
      & ( v1_funct_2 @ ( k11_setwiseo @ A ) @ A @ ( k5_finsub_1 @ A ) )
      & ( m2_relset_1 @ ( k11_setwiseo @ A ) @ A @ ( k5_finsub_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2119]) ).

thf(673,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) @ ( k2_tarski @ D @ E ) )
      = ( k2_enumset1 @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ B @ C @ D ) @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ B @ C @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_mcart_1) ).

thf(5885,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k3_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) @ ( k2_tarski @ D @ E ) )
      = ( k2_enumset1 @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ B @ C @ D ) @ ( k3_mcart_1 @ A @ C @ E ) @ ( k3_mcart_1 @ B @ C @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(178,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
              = ( k1_relat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).

thf(3583,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
              = ( k1_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(2044,axiom,
    ! [A: $i,B: $i] :
      ( ( A != k1_xboole_0 )
     => ( ( ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ A )
         != k1_xboole_0 )
        & ( ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) )
         != k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_zfmisc_1) ).

thf(12496,plain,
    ! [A: $i,B: $i] :
      ( ( A != k1_xboole_0 )
     => ( ( ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ A )
         != k1_xboole_0 )
        & ( ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) )
         != k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2044]) ).

thf(1840,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( m1_pboole @ ( k19_pralg_1 @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k19_pralg_1) ).

thf(11387,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( m1_pboole @ ( k19_pralg_1 @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1840]) ).

thf(1611,axiom,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ~ ( ( r2_hidden @ C @ A )
              & ! [D: $i,E: $i] :
                  ( C
                 != ( k4_tarski @ D @ E ) ) )
        & ! [C: $i,D: $i] :
            ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
           => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
     => ( r1_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_zfmisc_1) ).

thf(10172,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ~ ( ( r2_hidden @ C @ A )
              & ! [D: $i,E: $i] :
                  ( C
                 != ( k4_tarski @ D @ E ) ) )
        & ! [C: $i,D: $i] :
            ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
           => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
     => ( r1_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1611]) ).

thf(1239,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_funct_1 @ ( k1_cat_1 @ A @ B @ C ) @ ( k4_tarski @ A @ B ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_cat_1) ).

thf(8473,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_funct_1 @ ( k1_cat_1 @ A @ B @ C ) @ ( k4_tarski @ A @ B ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).

thf(1478,axiom,
    ! [A: $i] :
      ( ( k6_relat_1 @ ( k1_tarski @ A ) )
      = ( k1_tarski @ ( k4_tarski @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_sysrel) ).

thf(9511,plain,
    ! [A: $i] :
      ( ( k6_relat_1 @ ( k1_tarski @ A ) )
      = ( k1_tarski @ ( k4_tarski @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478]) ).

thf(1484,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ C ) )
          <=> ( r1_tarski @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_subset_1) ).

thf(9528,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ C ) )
             => ( r1_tarski @ B @ C ) )
            & ( ( r1_tarski @ B @ C )
             => ( r1_xboole_0 @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1484]) ).

thf(1384,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_relat_1) ).

thf(9074,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( r1_tarski @ ( k2_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).

thf(1511,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
     => ( ( v1_funct_1 @ ( k7_filter_1 @ A @ B @ C @ D ) )
        & ( v1_funct_2 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) )
        & ( m2_relset_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_filter_1) ).

thf(9674,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
     => ( ( v1_funct_1 @ ( k7_filter_1 @ A @ B @ C @ D ) )
        & ( v1_funct_2 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) )
        & ( m2_relset_1 @ ( k7_filter_1 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1511]) ).

thf(795,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( k5_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
        = ( k2_tarski @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_zfmisc_1) ).

thf(6446,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( k5_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
        = ( k2_tarski @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(823,axiom,
    ! [A: $i] :
      ( ( k12_funct_3 @ A )
      = ( k13_funct_3 @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funcop_1) ).

thf(6568,plain,
    ! [A: $i] :
      ( ( k12_funct_3 @ A )
      = ( k13_funct_3 @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(2022,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
             => ( ! [E: $i] :
                    ( ( m1_subset_1 @ E @ A )
                   => ( ( r2_hidden @ E @ B )
                    <=> ( ( r2_hidden @ E @ C )
                        & ( r2_hidden @ E @ D ) ) ) )
               => ( B
                  = ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_subset_1) ).

thf(12381,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
             => ( ! [E: $i] :
                    ( ( m1_subset_1 @ E @ A )
                   => ( ( ( r2_hidden @ E @ B )
                       => ( ( r2_hidden @ E @ C )
                          & ( r2_hidden @ E @ D ) ) )
                      & ( ( ( r2_hidden @ E @ C )
                          & ( r2_hidden @ E @ D ) )
                       => ( r2_hidden @ E @ B ) ) ) )
               => ( B
                  = ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2022]) ).

thf(1570,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_enumset1 @ A @ B @ C )
      = ( k1_enumset1 @ A @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_enumset1) ).

thf(10004,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_enumset1 @ A @ B @ C )
      = ( k1_enumset1 @ A @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1570]) ).

thf(973,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ C )
        = ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
      & ( ( k2_zfmisc_1 @ C @ ( k2_xboole_0 @ A @ B ) )
        = ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).

thf(7297,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ C )
        = ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ C ) ) )
      & ( ( k2_zfmisc_1 @ C @ ( k2_xboole_0 @ A @ B ) )
        = ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ A ) @ ( k2_zfmisc_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).

thf(1211,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( k2_ens_1 @ A )
        = ( a_1_1_ens_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ens_1) ).

thf(8340,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( k2_ens_1 @ A )
        = ( a_1_1_ens_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).

thf(2239,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ( m1_subset_1 @ B @ ( u2_cat_1 @ ( k12_ens_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ens_1) ).

thf(13486,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ( m1_subset_1 @ B @ ( u2_cat_1 @ ( k12_ens_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2239]) ).

thf(664,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k1_tarski @ A )
        = ( k2_tarski @ B @ C ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).

thf(5838,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k1_tarski @ A )
        = ( k2_tarski @ B @ C ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(2254,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m2_relset_1 @ D @ A @ B )
                 => ! [E: $i] :
                      ( ( m2_relset_1 @ E @ B @ C )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ C )
                             => ( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k7_relset_1 @ A @ B @ B @ C @ D @ E ) )
                              <=> ? [H: $i] :
                                    ( ( m1_subset_1 @ H @ B )
                                    & ( r2_hidden @ ( k4_tarski @ F @ H ) @ D )
                                    & ( r2_hidden @ ( k4_tarski @ H @ G ) @ E ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_relset_1) ).

thf(13529,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m2_relset_1 @ D @ A @ B )
                 => ! [E: $i] :
                      ( ( m2_relset_1 @ E @ B @ C )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ C )
                             => ( ( ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k7_relset_1 @ A @ B @ B @ C @ D @ E ) )
                                 => ? [H: $i] :
                                      ( ( m1_subset_1 @ H @ B )
                                      & ( r2_hidden @ ( k4_tarski @ F @ H ) @ D )
                                      & ( r2_hidden @ ( k4_tarski @ H @ G ) @ E ) ) )
                                & ( ? [H: $i] :
                                      ( ( m1_subset_1 @ H @ B )
                                      & ( r2_hidden @ ( k4_tarski @ F @ H ) @ D )
                                      & ( r2_hidden @ ( k4_tarski @ H @ G ) @ E ) )
                                 => ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k7_relset_1 @ A @ B @ B @ C @ D @ E ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2254]) ).

thf(775,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
         => ( ( ( k12_mcart_1 @ A @ B @ C @ D )
             != k1_xboole_0 )
           => ( ( ( k1_funct_1 @ ( k1_funct_3 @ ( k9_funct_3 @ A @ B ) ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
                = C )
              & ( ( k1_funct_1 @ ( k1_funct_3 @ ( k10_funct_3 @ A @ B ) ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
                = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_borsuk_1) ).

thf(6376,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
         => ( ( ( k12_mcart_1 @ A @ B @ C @ D )
             != k1_xboole_0 )
           => ( ( ( k1_funct_1 @ ( k1_funct_3 @ ( k9_funct_3 @ A @ B ) ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
                = C )
              & ( ( k1_funct_1 @ ( k1_funct_3 @ ( k10_funct_3 @ A @ B ) ) @ ( k12_mcart_1 @ A @ B @ C @ D ) )
                = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(1763,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k10_classes2 @ A @ B @ C )
        = ( k5_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_classes2) ).

thf(10970,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k10_classes2 @ A @ B @ C )
        = ( k5_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1763]) ).

thf(691,axiom,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k6_relat_1 @ A ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_sysrel) ).

thf(5987,plain,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ ( k6_relat_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k6_relat_1 @ A ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(1109,axiom,
    ! [A: $i] :
      ( ( k5_xboole_0 @ A @ k1_xboole_0 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_boole) ).

thf(7901,plain,
    ! [A: $i] :
      ( ( k5_xboole_0 @ A @ k1_xboole_0 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).

thf(768,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v6_monoid_0 @ B @ A )
          <=> ! [C: $i] :
                ( ( m1_subset_1 @ C @ A )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
                            = ( k2_binop_1 @ A @ A @ A @ B @ C @ E ) )
                         => ( D = E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_monoid_0) ).

thf(6345,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( v6_monoid_0 @ B @ A )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
                              = ( k2_binop_1 @ A @ A @ A @ B @ C @ E ) )
                           => ( D = E ) ) ) ) ) )
            & ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( ( k2_binop_1 @ A @ A @ A @ B @ C @ D )
                              = ( k2_binop_1 @ A @ A @ A @ B @ C @ E ) )
                           => ( D = E ) ) ) ) )
             => ( v6_monoid_0 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(2099,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k1_funct_5 @ ( k2_zfmisc_1 @ A @ B ) ) @ A )
      & ( r1_tarski @ ( k2_funct_5 @ ( k2_zfmisc_1 @ A @ B ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_5) ).

thf(12802,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k1_funct_5 @ ( k2_zfmisc_1 @ A @ B ) ) @ A )
      & ( r1_tarski @ ( k2_funct_5 @ ( k2_zfmisc_1 @ A @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2099]) ).

thf(2051,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_ens_1 @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_ens_1 @ A ) @ A ) )
         => ( ( B
              = ( k9_ens_1 @ A ) )
          <=> ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
               => ( ( k8_funct_2 @ ( k2_ens_1 @ A ) @ A @ B @ C )
                  = ( k4_ens_1 @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_ens_1) ).

thf(12534,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_ens_1 @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_ens_1 @ A ) @ A ) )
         => ( ( ( B
                = ( k9_ens_1 @ A ) )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
                 => ( ( k8_funct_2 @ ( k2_ens_1 @ A ) @ A @ B @ C )
                    = ( k4_ens_1 @ A @ C ) ) ) )
            & ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
                 => ( ( k8_funct_2 @ ( k2_ens_1 @ A ) @ A @ B @ C )
                    = ( k4_ens_1 @ A @ C ) ) )
             => ( B
                = ( k9_ens_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2051]) ).

thf(1694,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_orders_1 @ B @ A )
         => ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ A @ ( k3_tarski @ A ) )
            & ( m2_relset_1 @ B @ A @ ( k3_tarski @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_orders_1) ).

thf(10549,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_orders_1 @ B @ A )
         => ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ A @ ( k3_tarski @ A ) )
            & ( m2_relset_1 @ B @ A @ ( k3_tarski @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1694]) ).

thf(731,axiom,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
      = ( k3_xboole_0 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).

thf(6151,plain,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
      = ( k3_xboole_0 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(2454,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( r2_hidden @ A @ ( a_3_6_domain_1 @ B @ C @ D ) )
      <=> ? [E: $i] :
            ( ( m1_subset_1 @ E @ B )
            & ( A = E )
            & ( ( r2_hidden @ E @ C )
            <=> ~ ( r2_hidden @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_6_domain_1) ).

thf(14294,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( ( r2_hidden @ A @ ( a_3_6_domain_1 @ B @ C @ D ) )
         => ? [E: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( A = E )
              & ( ( r2_hidden @ E @ C )
               => ~ ( r2_hidden @ E @ D ) )
              & ( ~ ( r2_hidden @ E @ D )
               => ( r2_hidden @ E @ C ) ) ) )
        & ( ? [E: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( A = E )
              & ( ( r2_hidden @ E @ C )
               => ~ ( r2_hidden @ E @ D ) )
              & ( ~ ( r2_hidden @ E @ D )
               => ( r2_hidden @ E @ C ) ) )
         => ( r2_hidden @ A @ ( a_3_6_domain_1 @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2454]) ).

thf(1881,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H )
      = ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_enumset1) ).

thf(11607,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H )
      = ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1881]) ).

thf(2351,axiom,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s6_filter_1 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s6_filter_1 )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ f1_s6_filter_1 )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ f2_s6_filter_1 )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ f2_s6_filter_1 )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ f2_s6_filter_1 )
                           => ( p1_s6_filter_1 @ ( k1_domain_1 @ f1_s6_filter_1 @ f2_s6_filter_1 @ A @ D ) @ ( k1_domain_1 @ f1_s6_filter_1 @ f2_s6_filter_1 @ B @ E ) @ ( k1_domain_1 @ f1_s6_filter_1 @ f2_s6_filter_1 @ C @ F ) ) ) ) ) ) ) )
   => ! [A: $i] :
        ( ( m1_subset_1 @ A @ ( k2_zfmisc_1 @ f1_s6_filter_1 @ f2_s6_filter_1 ) )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ ( k2_zfmisc_1 @ f1_s6_filter_1 @ f2_s6_filter_1 ) )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ f1_s6_filter_1 @ f2_s6_filter_1 ) )
               => ( p1_s6_filter_1 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s6_filter_1) ).

thf(13884,plain,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s6_filter_1 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s6_filter_1 )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ f1_s6_filter_1 )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ f2_s6_filter_1 )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ f2_s6_filter_1 )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ f2_s6_filter_1 )
                           => ( p1_s6_filter_1 @ ( k1_domain_1 @ f1_s6_filter_1 @ f2_s6_filter_1 @ A @ D ) @ ( k1_domain_1 @ f1_s6_filter_1 @ f2_s6_filter_1 @ B @ E ) @ ( k1_domain_1 @ f1_s6_filter_1 @ f2_s6_filter_1 @ C @ F ) ) ) ) ) ) ) )
   => ! [A: $i] :
        ( ( m1_subset_1 @ A @ ( k2_zfmisc_1 @ f1_s6_filter_1 @ f2_s6_filter_1 ) )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ ( k2_zfmisc_1 @ f1_s6_filter_1 @ f2_s6_filter_1 ) )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ f1_s6_filter_1 @ f2_s6_filter_1 ) )
               => ( p1_s6_filter_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2351]) ).

thf(1595,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
        & ~ ( v1_xboole_0 @ D )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
        & ( v1_funct_1 @ E )
        & ( m1_relset_1 @ E @ ( k12_mcart_1 @ A @ A @ C @ C ) @ C )
        & ( v1_funct_1 @ F )
        & ( m1_relset_1 @ F @ ( k12_mcart_1 @ B @ B @ D @ D ) @ D ) )
     => ( ( v1_funct_1 @ ( k2_nattra_1 @ A @ B @ C @ D @ E @ F ) )
        & ( m2_relset_1 @ ( k2_nattra_1 @ A @ B @ C @ D @ E @ F ) @ ( k12_mcart_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k12_mcart_1 @ A @ B @ C @ D ) @ ( k12_mcart_1 @ A @ B @ C @ D ) ) @ ( k12_mcart_1 @ A @ B @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_nattra_1) ).

thf(10119,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
        & ~ ( v1_xboole_0 @ D )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
        & ( v1_funct_1 @ E )
        & ( m1_relset_1 @ E @ ( k12_mcart_1 @ A @ A @ C @ C ) @ C )
        & ( v1_funct_1 @ F )
        & ( m1_relset_1 @ F @ ( k12_mcart_1 @ B @ B @ D @ D ) @ D ) )
     => ( ( v1_funct_1 @ ( k2_nattra_1 @ A @ B @ C @ D @ E @ F ) )
        & ( m2_relset_1 @ ( k2_nattra_1 @ A @ B @ C @ D @ E @ F ) @ ( k12_mcart_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k12_mcart_1 @ A @ B @ C @ D ) @ ( k12_mcart_1 @ A @ B @ C @ D ) ) @ ( k12_mcart_1 @ A @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1595]) ).

thf(2175,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k6_partfun1 @ A ) ) )
     => ( ( k1_funct_5 @ B )
        = ( k2_funct_5 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_waybel20) ).

thf(13208,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k6_partfun1 @ A ) ) )
     => ( ( k1_funct_5 @ B )
        = ( k2_funct_5 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2175]) ).

thf(1679,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m2_relset_1 @ E @ A @ C )
     => ( ( ( r1_tarski @ A @ B )
          & ( r1_tarski @ C @ D ) )
       => ( m2_relset_1 @ E @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_relset_1) ).

thf(10499,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m2_relset_1 @ E @ A @ C )
     => ( ( ( r1_tarski @ A @ B )
          & ( r1_tarski @ C @ D ) )
       => ( m2_relset_1 @ E @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1679]) ).

thf(1656,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m1_relset_1 @ D @ A @ B ) )
     => ( ( k8_waybel_5 @ A @ B @ C @ D )
        = ( k2_funcop_1 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_waybel_5) ).

thf(10402,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m1_relset_1 @ D @ A @ B ) )
     => ( ( k8_waybel_5 @ A @ B @ C @ D )
        = ( k2_funcop_1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1656]) ).

thf(2073,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ? [C: $i] : ( m1_realset1 @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_realset1) ).

thf(12680,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ? [C: $i] : ( m1_realset1 @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2073]) ).

thf(1970,axiom,
    ! [A: $i] :
      ( ( ( ( k1_funct_5 @ A )
          = k1_xboole_0 )
        | ( ( k2_funct_5 @ A )
          = k1_xboole_0 ) )
     => ! [B: $i,C: $i] :
          ~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_5) ).

thf(12092,plain,
    ! [A: $i] :
      ( ( ( ( k1_funct_5 @ A )
          = k1_xboole_0 )
        | ( ( k2_funct_5 @ A )
          = k1_xboole_0 ) )
     => ! [B: $i,C: $i] :
          ~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1970]) ).

thf(1320,axiom,
    ! [A: $i] :
      ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ A ) )
      = ( k6_relat_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_sysrel) ).

thf(8853,plain,
    ! [A: $i] :
      ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ A ) )
      = ( k6_relat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).

thf(421,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
      <=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
          & ( B
            = ( k1_funct_1 @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).

thf(4844,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ C )
         => ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
            & ( B
              = ( k1_funct_1 @ C @ A ) ) ) )
        & ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
            & ( B
              = ( k1_funct_1 @ C @ A ) ) )
         => ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(518,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_pboole @ C @ A ) )
     => ( ( r6_pboole @ A @ B @ C )
      <=> ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r6_pboole) ).

thf(5254,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_pboole @ C @ A ) )
     => ( ( ( r6_pboole @ A @ B @ C )
         => ( B = C ) )
        & ( ( B = C )
         => ( r6_pboole @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(873,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( k1_funct_4 @ A @ ( k7_relat_1 @ A @ B ) )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_funct_4) ).

thf(6811,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( k1_funct_4 @ A @ ( k7_relat_1 @ A @ B ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(2460,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_orders_3 @ A ) )
     => ! [B: $i] :
          ( ( m1_orders_3 @ B @ A )
        <=> ( m1_subset_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_orders_3) ).

thf(14329,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_orders_3 @ A ) )
     => ! [B: $i] :
          ( ( ( m1_orders_3 @ B @ A )
           => ( m1_subset_1 @ B @ A ) )
          & ( ( m1_subset_1 @ B @ A )
           => ( m1_orders_3 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2460]) ).

thf(2269,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
     => ( v1_finset_1 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_finsub_1) ).

thf(13578,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
     => ( v1_finset_1 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2269]) ).

thf(2370,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k7_domain_1 @ A @ B @ C )
        = ( k7_domain_1 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k7_domain_1) ).

thf(13963,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k7_domain_1 @ A @ B @ C )
        = ( k7_domain_1 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2370]) ).

thf(566,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( v1_binop_1 @ C @ A )
               => ( ( r6_binop_1 @ A @ C @ B )
                <=> ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ! [F: $i] :
                              ( ( m1_subset_1 @ F @ A )
                             => ( ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ F )
                                = ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_binop_1) ).

thf(5442,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( v1_binop_1 @ C @ A )
               => ( ( ( r6_binop_1 @ A @ C @ B )
                   => ! [D: $i] :
                        ( ( m1_subset_1 @ D @ A )
                       => ! [E: $i] :
                            ( ( m1_subset_1 @ E @ A )
                           => ! [F: $i] :
                                ( ( m1_subset_1 @ F @ A )
                               => ( ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ F )
                                  = ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) ) ) ) ) ) )
                  & ( ! [D: $i] :
                        ( ( m1_subset_1 @ D @ A )
                       => ! [E: $i] :
                            ( ( m1_subset_1 @ E @ A )
                           => ! [F: $i] :
                                ( ( m1_subset_1 @ F @ A )
                               => ( ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ F )
                                  = ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) ) ) ) ) )
                   => ( r6_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(2031,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ B )
               => ( r2_hidden @ D @ C ) )
           => ( r1_tarski @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_subset_1) ).

thf(12432,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ B )
               => ( r2_hidden @ D @ C ) )
           => ( r1_tarski @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2031]) ).

thf(852,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( k5_relat_1 @ B @ ( k5_funcop_1 @ C @ D @ A ) )
                  = ( k5_funcop_1 @ C @ D @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funcop_1) ).

thf(6687,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( k5_relat_1 @ B @ ( k5_funcop_1 @ C @ D @ A ) )
                  = ( k5_funcop_1 @ C @ D @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(550,axiom,
    ( ( k4_card_3 @ k1_xboole_0 )
    = ( k1_tarski @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_card_3) ).

thf(5372,plain,
    ( ( k4_card_3 @ k1_xboole_0 )
    = ( k1_tarski @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(796,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_zfmisc_1) ).

thf(6449,plain,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k2_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(219,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
       => ( ( v1_funct_1 @ B )
          & ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_partfun1) ).

thf(3838,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
       => ( ( v1_funct_1 @ B )
          & ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(1306,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( ! [G: $i] :
            ( ( m1_subset_1 @ G @ A )
           => ! [H: $i] :
                ( ( m1_subset_1 @ H @ B )
               => ! [I: $i] :
                    ( ( m1_subset_1 @ I @ C )
                   => ! [J: $i] :
                        ( ( m1_subset_1 @ J @ D )
                       => ( ( F
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( E = G ) ) ) ) ) )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 )
          | ( C = k1_xboole_0 )
          | ( D = k1_xboole_0 )
          | ( E
            = ( k8_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_mcart_1) ).

thf(8776,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( ! [G: $i] :
            ( ( m1_subset_1 @ G @ A )
           => ! [H: $i] :
                ( ( m1_subset_1 @ H @ B )
               => ! [I: $i] :
                    ( ( m1_subset_1 @ I @ C )
                   => ! [J: $i] :
                        ( ( m1_subset_1 @ J @ D )
                       => ( ( F
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( E = G ) ) ) ) ) )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 )
          | ( C = k1_xboole_0 )
          | ( D = k1_xboole_0 )
          | ( E
            = ( k8_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).

thf(552,axiom,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k4_qc_lang1 )
        & ( m1_subset_1 @ B @ k2_qc_lang1 ) )
     => ( ( k6_cqc_lang @ A @ B )
        = ( k3_cqc_lang @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_cqc_lang) ).

thf(5377,plain,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k4_qc_lang1 )
        & ( m1_subset_1 @ B @ k2_qc_lang1 ) )
     => ( ( k6_cqc_lang @ A @ B )
        = ( k3_cqc_lang @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(1517,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ( r2_hidden @ ( k8_funct_2 @ A @ B @ D @ C ) @ ( k2_relat_1 @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_isocat_2) ).

thf(9741,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ( r2_hidden @ ( k8_funct_2 @ A @ B @ D @ C ) @ ( k2_relat_1 @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517]) ).

thf(576,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ( B
            = ( k4_tarski @ ( k1_domain_1 @ A @ A @ ( k3_ens_1 @ A @ B ) @ ( k4_ens_1 @ A @ B ) ) @ ( k2_mcart_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_ens_1) ).

thf(5482,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ( B
            = ( k4_tarski @ ( k1_domain_1 @ A @ A @ ( k3_ens_1 @ A @ B ) @ ( k4_ens_1 @ A @ B ) ) @ ( k2_mcart_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(983,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( v1_relat_1 @ ( k5_relset_2 @ A @ B ) )
        & ( v1_funct_1 @ ( k5_relset_2 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_2) ).

thf(7334,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( v1_relat_1 @ ( k5_relset_2 @ A @ B ) )
        & ( v1_funct_1 @ ( k5_relset_2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).

thf(239,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k7_relat_1 @ A @ ( k1_relat_1 @ B ) )
            = ( k7_relat_1 @ A @ ( k1_relat_1 @ ( k7_relat_1 @ B @ ( k1_relat_1 @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t189_relat_1) ).

thf(3917,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( k7_relat_1 @ A @ ( k1_relat_1 @ B ) )
            = ( k7_relat_1 @ A @ ( k1_relat_1 @ ( k7_relat_1 @ B @ ( k1_relat_1 @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(1910,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_funct_1 @ ( k7_cat_1 @ A @ B ) )
      & ( v1_funct_2 @ ( k7_cat_1 @ A @ B ) @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
      & ( m2_relset_1 @ ( k7_cat_1 @ A @ B ) @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_cat_1) ).

thf(11721,plain,
    ! [A: $i,B: $i] :
      ( ( v1_funct_1 @ ( k7_cat_1 @ A @ B ) )
      & ( v1_funct_2 @ ( k7_cat_1 @ A @ B ) @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
      & ( m2_relset_1 @ ( k7_cat_1 @ A @ B ) @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1910]) ).

thf(585,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( r1_tarski @ B @ C )
           => ( r1_tarski @ ( k7_relat_1 @ B @ A ) @ ( k7_relat_1 @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t105_relat_1) ).

thf(5516,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( r1_tarski @ B @ C )
           => ( r1_tarski @ ( k7_relat_1 @ B @ A ) @ ( k7_relat_1 @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(1003,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( r1_tarski @ ( k4_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) @ ( k5_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_relat_1) ).

thf(7469,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( r1_tarski @ ( k4_xboole_0 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) @ ( k5_relat_1 @ A @ ( k4_xboole_0 @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).

thf(280,axiom,
    ! [A: $i] : ( v1_setwiseo @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_setwiseo) ).

thf(4085,plain,
    ! [A: $i] : ( v1_setwiseo @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(1837,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
         => ! [C: $i] :
              ( ( r2_hidden @ C @ B )
             => ( m1_subset_1 @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_setwiseo) ).

thf(11380,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
         => ! [C: $i] :
              ( ( r2_hidden @ C @ B )
             => ( m1_subset_1 @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1837]) ).

thf(1051,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ( k2_setwiseo @ A @ B )
        = ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_setwiseo) ).

thf(7647,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ( k2_setwiseo @ A @ B )
        = ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).

thf(2152,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_funct_1 @ ( k10_pboole @ A @ B ) )
      & ( v1_funct_2 @ ( k10_pboole @ A @ B ) @ A @ ( k1_tarski @ B ) )
      & ( m2_relset_1 @ ( k10_pboole @ A @ B ) @ A @ ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_pboole) ).

thf(13112,plain,
    ! [A: $i,B: $i] :
      ( ( v1_funct_1 @ ( k10_pboole @ A @ B ) )
      & ( v1_funct_2 @ ( k10_pboole @ A @ B ) @ A @ ( k1_tarski @ B ) )
      & ( m2_relset_1 @ ( k10_pboole @ A @ B ) @ A @ ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2152]) ).

thf(1120,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i,E: $i,F: $i] :
                  ~ ( ( ( r2_hidden @ C @ A )
                      | ( r2_hidden @ D @ A ) )
                    & ( B
                      = ( k4_mcart_1 @ C @ D @ E @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_mcart_1) ).

thf(7960,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i,E: $i,F: $i] :
                  ~ ( ( ( r2_hidden @ C @ A )
                      | ( r2_hidden @ D @ A ) )
                    & ( B
                      = ( k4_mcart_1 @ C @ D @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).

thf(2303,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
      & ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tex_2) ).

thf(13702,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
      & ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2303]) ).

thf(1112,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( v2_funct_1 @ B ) )
           => ( v2_funct_1 @ ( k15_funct_3 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_isocat_1) ).

thf(7911,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( v2_funct_1 @ B ) )
           => ( v2_funct_1 @ ( k15_funct_3 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).

thf(418,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( k1_relat_1 @ B )
                  = ( k1_relat_1 @ C ) )
               => ( ( k1_funct_4 @ ( k1_funct_4 @ A @ B ) @ C )
                  = ( k1_funct_4 @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_funct_4) ).

thf(4827,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( k1_relat_1 @ B )
                  = ( k1_relat_1 @ C ) )
               => ( ( k1_funct_4 @ ( k1_funct_4 @ A @ B ) @ C )
                  = ( k1_funct_4 @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(2530,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( ( k9_domain_1 @ A @ B @ C @ D @ E )
        = ( k2_enumset1 @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_domain_1) ).

thf(14660,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( ( k9_domain_1 @ A @ B @ C @ D @ E )
        = ( k2_enumset1 @ B @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2530]) ).

thf(1875,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
      & ( v1_finset_1 @ ( k1_tarski @ A ) )
      & ( v1_realset1 @ ( k1_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_realset1) ).

thf(11590,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
      & ( v1_finset_1 @ ( k1_tarski @ A ) )
      & ( v1_realset1 @ ( k1_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1875]) ).

thf(1548,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ k9_zf_lang ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ k9_zf_lang ) )
             => ( ( ( r1_tarski @ B @ C )
                  & ( r1_zfrefle1 @ A @ C ) )
               => ( r1_zfrefle1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfrefle1) ).

thf(9916,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ k9_zf_lang ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ k9_zf_lang ) )
             => ( ( ( r1_tarski @ B @ C )
                  & ( r1_zfrefle1 @ A @ C ) )
               => ( r1_zfrefle1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1548]) ).

thf(2019,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( B != k1_xboole_0 )
       => ( ( k6_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
          = ( k3_subset_1 @ A @ ( k5_setfam_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_tops_2) ).

thf(12373,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( B != k1_xboole_0 )
       => ( ( k6_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) )
          = ( k3_subset_1 @ A @ ( k5_setfam_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2019]) ).

thf(1766,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ C @ B @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_enumset1) ).

thf(10979,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ C @ B @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1766]) ).

thf(1254,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( k1_realset1 @ A @ B )
          = ( k7_relat_1 @ A @ ( k2_zfmisc_1 @ B @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_realset1) ).

thf(8541,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( k1_realset1 @ A @ B )
          = ( k7_relat_1 @ A @ ( k2_zfmisc_1 @ B @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).

thf(1630,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
     => ( ( ( r1_tarski @ B @ C )
          & ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
       => ( B = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_subset_1) ).

thf(10264,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
     => ( ( ( r1_tarski @ B @ C )
          & ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
       => ( B = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1630]) ).

thf(436,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k1_tarski @ A ) @ B )
        & ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
     => ( ( B != k1_xboole_0 )
       => ( r1_tarski @ ( k2_funct_2 @ ( k1_tarski @ A ) @ B @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_2) ).

thf(4918,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k1_tarski @ A ) @ B )
        & ( m2_relset_1 @ D @ ( k1_tarski @ A ) @ B ) )
     => ( ( B != k1_xboole_0 )
       => ( r1_tarski @ ( k2_funct_2 @ ( k1_tarski @ A ) @ B @ D @ C ) @ ( k1_tarski @ ( k1_funct_1 @ D @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( k1_xboole_0
     != ( k10_finseq_1 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_finseq_3) ).

thf(2633,plain,
    ! [A: $i,B: $i] :
      ( k1_xboole_0
     != ( k10_finseq_1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(140,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i,C: $i] :
          ~ ( ( v2_funct_1 @ A )
            & ( ( k2_relat_1 @ A )
              = ( k2_tarski @ B @ C ) )
            & ( B != C )
            & ( A
             != ( k10_finseq_1 @ B @ C ) )
            & ( A
             != ( k10_finseq_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_finseq_3) ).

thf(3363,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i,C: $i] :
          ~ ( ( v2_funct_1 @ A )
            & ( ( k2_relat_1 @ A )
              = ( k2_tarski @ B @ C ) )
            & ( B != C )
            & ( A
             != ( k10_finseq_1 @ B @ C ) )
            & ( A
             != ( k10_finseq_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(1880,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_2) ).

thf(11605,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( r1_tarski @ ( k9_relat_1 @ D @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1880]) ).

thf(1545,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i,D: $i] :
              ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ B )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ! [F: $i] :
                      ( ( ( v1_funct_1 @ F )
                        & ( v1_funct_2 @ F @ B @ ( k5_finsub_1 @ C ) )
                        & ( m2_relset_1 @ F @ B @ ( k5_finsub_1 @ C ) ) )
                     => ( ( k10_setwiseo @ B @ C @ ( k8_setwiseo @ A @ B @ E @ D ) @ F )
                        = ( k10_setwiseo @ A @ C @ D @ ( k7_funct_2 @ A @ B @ ( k5_finsub_1 @ C ) @ E @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_setwiseo) ).

thf(9871,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i,D: $i] :
              ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ B )
                    & ( m2_relset_1 @ E @ A @ B ) )
                 => ! [F: $i] :
                      ( ( ( v1_funct_1 @ F )
                        & ( v1_funct_2 @ F @ B @ ( k5_finsub_1 @ C ) )
                        & ( m2_relset_1 @ F @ B @ ( k5_finsub_1 @ C ) ) )
                     => ( ( k10_setwiseo @ B @ C @ ( k8_setwiseo @ A @ B @ E @ D ) @ F )
                        = ( k10_setwiseo @ A @ C @ D @ ( k7_funct_2 @ A @ B @ ( k5_finsub_1 @ C ) @ E @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1545]) ).

thf(1583,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k8_classes2 @ A @ B @ C )
        = ( k3_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_classes2) ).

thf(10063,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k8_classes2 @ A @ B @ C )
        = ( k3_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1583]) ).

thf(2273,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] : ( v1_finset_1 @ ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_finset_1) ).

thf(13598,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] : ( v1_finset_1 @ ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2273]) ).

thf(1100,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
     => ( v1_partfun1 @ B @ k1_xboole_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_partfun1) ).

thf(7852,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
     => ( v1_partfun1 @ B @ k1_xboole_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).

thf(637,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
     => ( m1_subset_1 @ ( k5_mcart_1 @ A @ B @ C @ D ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_mcart_1) ).

thf(5725,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
     => ( m1_subset_1 @ ( k5_mcart_1 @ A @ B @ C @ D ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(1659,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_funct_2) ).

thf(10424,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( m1_subset_1 @ ( k3_funct_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1659]) ).

thf(1283,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( r1_tarski @ A @ B )
          <=> ! [C: $i,D: $i] :
                ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
               => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).

thf(8676,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( ( r1_tarski @ A @ B )
             => ! [C: $i,D: $i] :
                  ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
                 => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
            & ( ! [C: $i,D: $i] :
                  ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
                 => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
             => ( r1_tarski @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).

thf(531,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( v2_funct_1 @ C )
       => ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
          = ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_funct_1) ).

thf(5299,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( v2_funct_1 @ C )
       => ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
          = ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(1701,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( v3_binop_1 @ C @ A )
                       => ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ D ) @ E )
                          = ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funcop_1) ).

thf(10576,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( v3_binop_1 @ C @ A )
                       => ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ D ) @ E )
                          = ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1701]) ).

thf(2534,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( m1_subset_1 @ ( a_2_0_relset_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_relset_2) ).

thf(14675,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( m1_subset_1 @ ( a_2_0_relset_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2534]) ).

thf(759,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ C )
        & ( m1_relset_1 @ E @ A @ C )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ B @ D )
        & ( m1_relset_1 @ F @ B @ D ) )
     => ( ( k9_cat_2 @ A @ B @ C @ D @ E @ F )
        = ( k15_funct_3 @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_cat_2) ).

thf(6293,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ C )
        & ( m1_relset_1 @ E @ A @ C )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ B @ D )
        & ( m1_relset_1 @ F @ B @ D ) )
     => ( ( k9_cat_2 @ A @ B @ C @ D @ E @ F )
        = ( k15_funct_3 @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(2006,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).

thf(12308,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2006]) ).

thf(430,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ B ) )
    <=> ( r1_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_4) ).

thf(4890,plain,
    ! [A: $i,B: $i] :
      ( ( ( r1_tarski @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ B ) )
       => ( r1_tarski @ A @ B ) )
      & ( ( r1_tarski @ A @ B )
       => ( r1_tarski @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(1806,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ C @ D @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t105_enumset1) ).

thf(11193,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ C @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1806]) ).

thf(1114,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m2_relset_1 @ E @ A @ B ) )
     => ! [F: $i] :
          ( ( ( v1_funct_1 @ F )
            & ( v1_funct_2 @ F @ C @ D )
            & ( m2_relset_1 @ F @ C @ D ) )
         => ~ ( ( ( B = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ( ( D = k1_xboole_0 )
               => ( C = k1_xboole_0 ) )
              & ( ( k16_funct_3 @ A @ C @ B @ D @ E @ F )
               != ( k13_funct_3 @ ( k5_relat_1 @ ( k9_funct_3 @ A @ C ) @ E ) @ ( k5_relat_1 @ ( k10_funct_3 @ A @ C ) @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_funct_3) ).

thf(7916,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m2_relset_1 @ E @ A @ B ) )
     => ! [F: $i] :
          ( ( ( v1_funct_1 @ F )
            & ( v1_funct_2 @ F @ C @ D )
            & ( m2_relset_1 @ F @ C @ D ) )
         => ~ ( ( ( B = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ( ( D = k1_xboole_0 )
               => ( C = k1_xboole_0 ) )
              & ( ( k16_funct_3 @ A @ C @ B @ D @ E @ F )
               != ( k13_funct_3 @ ( k5_relat_1 @ ( k9_funct_3 @ A @ C ) @ E ) @ ( k5_relat_1 @ ( k10_funct_3 @ A @ C ) @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).

thf(1015,axiom,
    ! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_xboole_1) ).

thf(7507,plain,
    ! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).

thf(2578,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) )
      <=> ( B != A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tex_2) ).

thf(14862,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( B != A ) )
        & ( ( B != A )
         => ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2578]) ).

thf(2555,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
     => ? [C: $i] : ( m2_subset_1 @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_subset_1) ).

thf(14739,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
     => ? [C: $i] : ( m2_subset_1 @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2555]) ).

thf(2309,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) )
          & ~ ( v1_xboole_0 @ B )
          & ~ ( v2_setfam_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_triang_1) ).

thf(13727,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) )
          & ~ ( v1_xboole_0 @ B )
          & ~ ( v2_setfam_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2309]) ).

thf(1360,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( B != k1_xboole_0 )
       => ! [E: $i] :
            ( ? [F: $i] :
                ( ( r2_hidden @ F @ A )
                & ( r2_hidden @ F @ C )
                & ( E
                  = ( k1_funct_1 @ D @ F ) ) )
           => ( r2_hidden @ E @ ( k9_relat_1 @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funct_2) ).

thf(8990,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( B != k1_xboole_0 )
       => ! [E: $i] :
            ( ? [F: $i] :
                ( ( r2_hidden @ F @ A )
                & ( r2_hidden @ F @ C )
                & ( E
                  = ( k1_funct_1 @ D @ F ) ) )
           => ( r2_hidden @ E @ ( k9_relat_1 @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).

thf(2447,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k1_cantor_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_cantor_1) ).

thf(14255,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k1_cantor_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2447]) ).

thf(1726,axiom,
    ( ( v1_funct_1 @ k7_vectsp_2 )
    & ( v1_funct_2 @ k7_vectsp_2 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) )
    & ( m2_relset_1 @ k7_vectsp_2 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_vectsp_2) ).

thf(10692,plain,
    ( ( v1_funct_1 @ k7_vectsp_2 )
    & ( v1_funct_2 @ k7_vectsp_2 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) )
    & ( m2_relset_1 @ k7_vectsp_2 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1726]) ).

thf(299,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B )
            & ( v1_finseq_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ C ) )
               => ( ( v1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) )
                  & ( v1_funct_1 @ ( k3_funcop_1 @ C @ A @ B ) )
                  & ( v1_finseq_1 @ ( k3_funcop_1 @ C @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_finseq_2) ).

thf(4207,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B )
            & ( v1_finseq_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ C ) )
               => ( ( v1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) )
                  & ( v1_funct_1 @ ( k3_funcop_1 @ C @ A @ B ) )
                  & ( v1_finseq_1 @ ( k3_funcop_1 @ C @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(425,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
       => ( ( v1_funct_1 @ B )
          & ( v1_funct_2 @ B @ ( k1_relat_1 @ B ) @ A )
          & ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_2) ).

thf(4868,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
       => ( ( v1_funct_1 @ B )
          & ( v1_funct_2 @ B @ ( k1_relat_1 @ B ) @ A )
          & ( m2_relset_1 @ B @ ( k1_relat_1 @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(1458,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A != B )
     => ( ( ( k1_funct_1 @ ( k4_funct_4 @ A @ B @ C @ D ) @ A )
          = C )
        & ( ( k1_funct_1 @ ( k4_funct_4 @ A @ B @ C @ D ) @ B )
          = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_4) ).

thf(9430,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A != B )
     => ( ( ( k1_funct_1 @ ( k4_funct_4 @ A @ B @ C @ D ) @ A )
          = C )
        & ( ( k1_funct_1 @ ( k4_funct_4 @ A @ B @ C @ D ) @ B )
          = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458]) ).

thf(844,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_realset1 @ A ) )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
         => ( r1_tarski @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tex_2) ).

thf(6659,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_realset1 @ A ) )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
         => ( r1_tarski @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(1124,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
     => ( v2_funct_1 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_partfun1) ).

thf(7992,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
     => ( v2_funct_1 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).

thf(1512,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ A )
         => ( ( k3_relset_2 @ A @ B @ C @ D )
            = ( k11_relset_1 @ A @ B @ C @ ( k1_tarski @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relset_2) ).

thf(9678,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ A )
         => ( ( k3_relset_2 @ A @ B @ C @ D )
            = ( k11_relset_1 @ A @ B @ C @ ( k1_tarski @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512]) ).

thf(1152,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_finseq_1 @ C @ A )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( m2_finseq_1 @ ( k1_partfun1 @ k5_numbers @ A @ A @ B @ C @ D ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_finseq_2) ).

thf(8106,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_finseq_1 @ C @ A )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( m2_finseq_1 @ ( k1_partfun1 @ k5_numbers @ A @ A @ B @ C @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).

thf(711,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_fraenkel @ D @ B @ C )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ D )
        & ( m1_relset_1 @ E @ A @ D )
        & ( m1_subset_1 @ F @ A ) )
     => ( ( k1_cat_2 @ A @ B @ C @ D @ E @ F )
        = ( k1_funct_1 @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_cat_2) ).

thf(6083,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_fraenkel @ D @ B @ C )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ D )
        & ( m1_relset_1 @ E @ A @ D )
        & ( m1_subset_1 @ F @ A ) )
     => ( ( k1_cat_2 @ A @ B @ C @ D @ E @ F )
        = ( k1_funct_1 @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(230,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ( ( ( v1_binop_1 @ C @ B )
                  & ( v2_binop_1 @ C @ B )
                  & ( v3_binop_1 @ C @ B )
                  & ( v1_setwiseo @ C @ B ) )
               => ! [D: $i] :
                    ( ~ ( v1_xboole_0 @ D )
                   => ! [E: $i] :
                        ( ( ( v1_funct_1 @ E )
                          & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D )
                          & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D ) )
                       => ( ( ( v1_binop_1 @ E @ D )
                            & ( v2_binop_1 @ E @ D )
                            & ( v3_binop_1 @ E @ D )
                            & ( v1_setwiseo @ E @ D ) )
                         => ! [F: $i] :
                              ( ( ( v1_funct_1 @ F )
                                & ( v1_funct_2 @ F @ A @ B )
                                & ( m2_relset_1 @ F @ A @ B ) )
                             => ! [G: $i] :
                                  ( ( ( v1_funct_1 @ G )
                                    & ( v1_funct_2 @ G @ B @ D )
                                    & ( m2_relset_1 @ G @ B @ D ) )
                                 => ( ( ( ( k8_funct_2 @ B @ D @ G @ ( k3_binop_1 @ B @ C ) )
                                        = ( k3_binop_1 @ D @ E ) )
                                      & ! [H: $i] :
                                          ( ( m1_subset_1 @ H @ B )
                                         => ! [I: $i] :
                                              ( ( m1_subset_1 @ I @ B )
                                             => ( ( k8_funct_2 @ B @ D @ G @ ( k2_binop_1 @ B @ B @ B @ C @ H @ I ) )
                                                = ( k2_binop_1 @ D @ D @ D @ E @ ( k8_funct_2 @ B @ D @ G @ H ) @ ( k8_funct_2 @ B @ D @ G @ I ) ) ) ) ) )
                                   => ! [H: $i] :
                                        ( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
                                       => ( ( k8_funct_2 @ B @ D @ G @ ( k7_setwiseo @ A @ B @ C @ H @ F ) )
                                          = ( k7_setwiseo @ A @ D @ E @ H @ ( k7_funct_2 @ A @ B @ D @ F @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_setwiseo) ).

thf(3881,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ( ( ( v1_binop_1 @ C @ B )
                  & ( v2_binop_1 @ C @ B )
                  & ( v3_binop_1 @ C @ B )
                  & ( v1_setwiseo @ C @ B ) )
               => ! [D: $i] :
                    ( ~ ( v1_xboole_0 @ D )
                   => ! [E: $i] :
                        ( ( ( v1_funct_1 @ E )
                          & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D )
                          & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D ) )
                       => ( ( ( v1_binop_1 @ E @ D )
                            & ( v2_binop_1 @ E @ D )
                            & ( v3_binop_1 @ E @ D )
                            & ( v1_setwiseo @ E @ D ) )
                         => ! [F: $i] :
                              ( ( ( v1_funct_1 @ F )
                                & ( v1_funct_2 @ F @ A @ B )
                                & ( m2_relset_1 @ F @ A @ B ) )
                             => ! [G: $i] :
                                  ( ( ( v1_funct_1 @ G )
                                    & ( v1_funct_2 @ G @ B @ D )
                                    & ( m2_relset_1 @ G @ B @ D ) )
                                 => ( ( ( ( k8_funct_2 @ B @ D @ G @ ( k3_binop_1 @ B @ C ) )
                                        = ( k3_binop_1 @ D @ E ) )
                                      & ! [H: $i] :
                                          ( ( m1_subset_1 @ H @ B )
                                         => ! [I: $i] :
                                              ( ( m1_subset_1 @ I @ B )
                                             => ( ( k8_funct_2 @ B @ D @ G @ ( k2_binop_1 @ B @ B @ B @ C @ H @ I ) )
                                                = ( k2_binop_1 @ D @ D @ D @ E @ ( k8_funct_2 @ B @ D @ G @ H ) @ ( k8_funct_2 @ B @ D @ G @ I ) ) ) ) ) )
                                   => ! [H: $i] :
                                        ( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
                                       => ( ( k8_funct_2 @ B @ D @ G @ ( k7_setwiseo @ A @ B @ C @ H @ F ) )
                                          = ( k7_setwiseo @ A @ D @ E @ H @ ( k7_funct_2 @ A @ B @ D @ F @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(325,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( r1_tarski @ A @ B )
           => ( r1_tarski @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_sysrel) ).

thf(4331,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( r1_tarski @ A @ B )
           => ( r1_tarski @ ( k4_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(63,axiom,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( k4_finseq_2 @ A @ B )
            = ( k1_funct_2 @ ( k2_finseq_1 @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_finseq_2) ).

thf(3009,plain,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( k4_finseq_2 @ A @ B )
            = ( k1_funct_2 @ ( k2_finseq_1 @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(2186,axiom,
    ( ( v1_funct_1 @ k3_metric_1 )
    & ( v1_funct_2 @ k3_metric_1 @ ( k2_zfmisc_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) @ k1_numbers )
    & ( m2_relset_1 @ k3_metric_1 @ ( k2_zfmisc_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_metric_1) ).

thf(13268,plain,
    ( ( v1_funct_1 @ k3_metric_1 )
    & ( v1_funct_2 @ k3_metric_1 @ ( k2_zfmisc_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) @ k1_numbers )
    & ( m2_relset_1 @ k3_metric_1 @ ( k2_zfmisc_1 @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2186]) ).

thf(1499,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( r1_xboole_0 @ B @ C )
          <=> ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).

thf(9595,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( ( r1_xboole_0 @ B @ C )
             => ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) ) )
            & ( ( r1_tarski @ B @ ( k3_subset_1 @ A @ C ) )
             => ( r1_xboole_0 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499]) ).

thf(341,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ( ( A = k1_xboole_0 )
      <=> ( ( k2_relat_1 @ A )
          = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finseq_1) ).

thf(4405,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ( ( ( A = k1_xboole_0 )
         => ( ( k2_relat_1 @ A )
            = k1_xboole_0 ) )
        & ( ( ( k2_relat_1 @ A )
            = k1_xboole_0 )
         => ( A = k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(1482,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
     => ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_zfmisc_1) ).

thf(9524,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
     => ( r2_hidden @ ( k4_tarski @ B @ A ) @ ( k2_zfmisc_1 @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482]) ).

thf(889,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r1_xboole_0 @ A @ B )
        & ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
        & ~ ( ( r2_hidden @ C @ A )
            & ~ ( r2_hidden @ C @ B ) )
        & ~ ( ( r2_hidden @ C @ B )
            & ~ ( r2_hidden @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_xboole_0) ).

thf(6890,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r1_xboole_0 @ A @ B )
        & ( r2_hidden @ C @ ( k2_xboole_0 @ A @ B ) )
        & ~ ( ( r2_hidden @ C @ A )
            & ~ ( r2_hidden @ C @ B ) )
        & ~ ( ( r2_hidden @ C @ B )
            & ~ ( r2_hidden @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(47,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( C
                  = ( k1_funct_4 @ A @ B ) )
              <=> ( ( ( k1_relat_1 @ C )
                    = ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                  & ! [D: $i] :
                      ( ( r2_hidden @ D @ ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                     => ( ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
                         => ( ( k1_funct_1 @ C @ D )
                            = ( k1_funct_1 @ B @ D ) ) )
                        & ( ~ ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
                         => ( ( k1_funct_1 @ C @ D )
                            = ( k1_funct_1 @ A @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_4) ).

thf(2816,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( C
                    = ( k1_funct_4 @ A @ B ) )
                 => ( ( ( k1_relat_1 @ C )
                      = ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                    & ! [D: $i] :
                        ( ( r2_hidden @ D @ ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                       => ( ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
                           => ( ( k1_funct_1 @ C @ D )
                              = ( k1_funct_1 @ B @ D ) ) )
                          & ( ~ ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
                           => ( ( k1_funct_1 @ C @ D )
                              = ( k1_funct_1 @ A @ D ) ) ) ) ) ) )
                & ( ( ( ( k1_relat_1 @ C )
                      = ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                    & ! [D: $i] :
                        ( ( r2_hidden @ D @ ( k2_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                       => ( ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
                           => ( ( k1_funct_1 @ C @ D )
                              = ( k1_funct_1 @ B @ D ) ) )
                          & ( ~ ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
                           => ( ( k1_funct_1 @ C @ D )
                              = ( k1_funct_1 @ A @ D ) ) ) ) ) )
                 => ( C
                    = ( k1_funct_4 @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(1352,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( m1_fraenkel @ ( k2_setwiseo @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) @ C ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_fraenkel) ).

thf(8965,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( m1_fraenkel @ ( k2_setwiseo @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) @ C ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).

thf(559,axiom,
    ! [A: $i,B: $i] :
      ( ( k1_setfam_1 @ ( k2_tarski @ A @ B ) )
      = ( k3_xboole_0 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_setfam_1) ).

thf(5424,plain,
    ! [A: $i,B: $i] :
      ( ( k1_setfam_1 @ ( k2_tarski @ A @ B ) )
      = ( k3_xboole_0 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(339,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ( v2_binop_1 @ B @ A )
      <=> ! [C: $i] :
            ( ( m1_subset_1 @ C @ A )
           => ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ! [E: $i] :
                    ( ( m1_subset_1 @ E @ A )
                   => ( ( k1_binop_1 @ B @ C @ ( k1_binop_1 @ B @ D @ E ) )
                      = ( k1_binop_1 @ B @ ( k1_binop_1 @ B @ C @ D ) @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_binop_1) ).

thf(4394,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ( ( v2_binop_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ( ( k1_binop_1 @ B @ C @ ( k1_binop_1 @ B @ D @ E ) )
                        = ( k1_binop_1 @ B @ ( k1_binop_1 @ B @ C @ D ) @ E ) ) ) ) ) )
        & ( ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ( ( k1_binop_1 @ B @ C @ ( k1_binop_1 @ B @ D @ E ) )
                        = ( k1_binop_1 @ B @ ( k1_binop_1 @ B @ C @ D ) @ E ) ) ) ) )
         => ( v2_binop_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(1641,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( v3_binop_1 @ C @ A )
                       => ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ ( k8_funct_2 @ B @ A @ D @ E ) ) @ E )
                          = ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_funcop_1) ).

thf(10311,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( v3_binop_1 @ C @ A )
                       => ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ ( k8_funct_2 @ B @ A @ D @ E ) ) @ E )
                          = ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1641]) ).

thf(1741,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( m1_subset_1 @ ( k3_binop_1 @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_binop_1) ).

thf(10824,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( m1_subset_1 @ ( k3_binop_1 @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1741]) ).

thf(675,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_partfun1 @ A @ B )
          <=> ( ( k1_funct_4 @ A @ B )
              = ( k1_funct_4 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_4) ).

thf(5890,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( r1_partfun1 @ A @ B )
             => ( ( k1_funct_4 @ A @ B )
                = ( k1_funct_4 @ B @ A ) ) )
            & ( ( ( k1_funct_4 @ A @ B )
                = ( k1_funct_4 @ B @ A ) )
             => ( r1_partfun1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(1009,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_setfam_1 @ A )
        & ( v1_setfam_1 @ B ) )
     => ( v1_setfam_1 @ ( k2_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_setfam_1) ).

thf(7490,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_setfam_1 @ A )
        & ( v1_setfam_1 @ B ) )
     => ( v1_setfam_1 @ ( k2_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).

thf(261,axiom,
    ( ( v1_funct_1 @ k35_binop_2 )
    & ( v1_funct_2 @ k35_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( v1_binop_1 @ k35_binop_2 @ k1_numbers )
    & ( v2_binop_1 @ k35_binop_2 @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_binop_2) ).

thf(4013,plain,
    ( ( v1_funct_1 @ k35_binop_2 )
    & ( v1_funct_2 @ k35_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( v1_binop_1 @ k35_binop_2 @ k1_numbers )
    & ( v2_binop_1 @ k35_binop_2 @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(244,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
     => ( A
        = ( k4_tarski @ ( k1_mcart_1 @ A ) @ ( k2_mcart_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_mcart_1) ).

thf(3936,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
     => ( A
        = ( k4_tarski @ ( k1_mcart_1 @ A ) @ ( k2_mcart_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(1108,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_finseq_2 @ B @ A ) )
     => ! [C: $i] :
          ( ( m2_finseq_2 @ C @ A @ B )
        <=> ( m1_subset_1 @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_finseq_2) ).

thf(7896,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_finseq_2 @ B @ A ) )
     => ! [C: $i] :
          ( ( ( m2_finseq_2 @ C @ A @ B )
           => ( m1_subset_1 @ C @ B ) )
          & ( ( m1_subset_1 @ C @ B )
           => ( m2_finseq_2 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).

thf(2043,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k4_zfmisc_1 @ A @ A @ A @ A )
        = ( k4_zfmisc_1 @ B @ B @ B @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_mcart_1) ).

thf(12492,plain,
    ! [A: $i,B: $i] :
      ( ( ( k4_zfmisc_1 @ A @ A @ A @ A )
        = ( k4_zfmisc_1 @ B @ B @ B @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2043]) ).

thf(590,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ A )
     => ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).

thf(5528,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ A )
     => ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(1032,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ A @ B )
      = ( k5_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_xboole_1) ).

thf(7571,plain,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ A @ B )
      = ( k5_xboole_0 @ A @ ( k4_xboole_0 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).

thf(311,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ~ ( ( B != k1_xboole_0 )
            & ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
            & ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A ) )
              = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_funcop_1) ).

thf(4260,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ~ ( ( B != k1_xboole_0 )
            & ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
            & ( ( k1_relat_1 @ ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A ) )
              = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(2127,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ C @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_enumset1) ).

thf(12978,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ C @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2127]) ).

thf(746,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
     => ( ( k5_setwiseo @ A @ B @ C )
        = ( k2_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setwiseo) ).

thf(6225,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
     => ( ( k5_setwiseo @ A @ B @ C )
        = ( k2_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(1052,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_relat_1 @ ( k4_funcop_1 @ A @ B @ C ) )
        & ( v1_funct_1 @ ( k4_funcop_1 @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funcop_1) ).

thf(7650,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_relat_1 @ ( k4_funcop_1 @ A @ B @ C ) )
        & ( v1_funct_1 @ ( k4_funcop_1 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).

thf(365,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) )
       => ( ( k9_relat_1 @ B @ ( k3_tarski @ A ) )
          = ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_3) ).

thf(4580,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) )
       => ( ( k9_relat_1 @ B @ ( k3_tarski @ A ) )
          = ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(1122,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( k4_mcart_1 @ A @ B @ C @ D )
        = ( k4_mcart_1 @ E @ F @ G @ H ) )
     => ( ( A = E )
        & ( B = F )
        & ( C = G )
        & ( D = H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_mcart_1) ).

thf(7975,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( k4_mcart_1 @ A @ B @ C @ D )
        = ( k4_mcart_1 @ E @ F @ G @ H ) )
     => ( ( A = E )
        & ( B = F )
        & ( C = G )
        & ( D = H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).

thf(1632,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_finset_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_setwiseo) ).

thf(10269,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_finset_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1632]) ).

thf(1060,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
       => ( ( v1_funct_1 @ D )
          & ( m2_relset_1 @ D @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_partfun1) ).

thf(7681,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ ( k2_relat_1 @ D ) @ C )
       => ( ( v1_funct_1 @ D )
          & ( m2_relset_1 @ D @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).

thf(149,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
            & ( v1_funct_1 @ ( k7_relat_1 @ A @ B ) )
            & ( v1_finseq_1 @ ( k7_relat_1 @ A @ B ) ) )
        <=> ? [C: $i] :
              ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
              & ( ( k3_xboole_0 @ B @ ( k4_finseq_1 @ A ) )
                = ( k2_finseq_1 @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_finseq_3) ).

thf(3395,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i] :
          ( ( ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
              & ( v1_funct_1 @ ( k7_relat_1 @ A @ B ) )
              & ( v1_finseq_1 @ ( k7_relat_1 @ A @ B ) ) )
           => ? [C: $i] :
                ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
                & ( ( k3_xboole_0 @ B @ ( k4_finseq_1 @ A ) )
                  = ( k2_finseq_1 @ C ) ) ) )
          & ( ? [C: $i] :
                ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
                & ( ( k3_xboole_0 @ B @ ( k4_finseq_1 @ A ) )
                  = ( k2_finseq_1 @ C ) ) )
           => ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
              & ( v1_funct_1 @ ( k7_relat_1 @ A @ B ) )
              & ( v1_finseq_1 @ ( k7_relat_1 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(1479,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) )
            = ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_subset_1) ).

thf(9514,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( k3_subset_1 @ A @ ( k5_subset_1 @ A @ B @ C ) )
            = ( k4_subset_1 @ A @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1479]) ).

thf(1416,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k9_funct_2 @ A @ B @ C )
      = ( k3_cqc_lang @ ( k4_tarski @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_cqc_lang) ).

thf(9259,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k9_funct_2 @ A @ B @ C )
      = ( k3_cqc_lang @ ( k4_tarski @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416]) ).

thf(91,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
       => ( ( ( k1_relat_1 @ C )
            = A )
          & ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t169_funct_2) ).

thf(3161,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ B ) )
       => ( ( ( k1_relat_1 @ C )
            = A )
          & ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(1620,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) ) )
     => ( m1_subset_1 @ ( k15_ens_1 @ A @ B ) @ ( u2_cat_1 @ ( k12_ens_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_ens_1) ).

thf(10223,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) ) )
     => ( m1_subset_1 @ ( k15_ens_1 @ A @ B ) @ ( u2_cat_1 @ ( k12_ens_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1620]) ).

thf(1167,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).

thf(8160,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).

thf(2195,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ C )
        & ( v1_classes2 @ C ) )
     => ( ( ( r2_hidden @ A @ C )
          & ( r2_hidden @ B @ C ) )
       => ( ( r2_hidden @ ( k2_tarski @ A @ B ) @ C )
          & ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_classes2) ).

thf(13293,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ C )
        & ( v1_classes2 @ C ) )
     => ( ( ( r2_hidden @ A @ C )
          & ( r2_hidden @ B @ C ) )
       => ( ( r2_hidden @ ( k2_tarski @ A @ B ) @ C )
          & ( r2_hidden @ ( k4_tarski @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2195]) ).

thf(713,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m2_relset_1 @ E @ A @ B ) )
     => ! [F: $i] :
          ( ( ( v1_funct_1 @ F )
            & ( v1_funct_2 @ F @ C @ D )
            & ( m2_relset_1 @ F @ C @ D ) )
         => ( ( r1_partfun1 @ E @ F )
           => ( ( v1_funct_1 @ ( k3_xboole_0 @ E @ F ) )
              & ( v1_funct_2 @ ( k3_xboole_0 @ E @ F ) @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) )
              & ( m2_relset_1 @ ( k3_xboole_0 @ E @ F ) @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_yellow20) ).

thf(6088,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m2_relset_1 @ E @ A @ B ) )
     => ! [F: $i] :
          ( ( ( v1_funct_1 @ F )
            & ( v1_funct_2 @ F @ C @ D )
            & ( m2_relset_1 @ F @ C @ D ) )
         => ( ( r1_partfun1 @ E @ F )
           => ( ( v1_funct_1 @ ( k3_xboole_0 @ E @ F ) )
              & ( v1_funct_2 @ ( k3_xboole_0 @ E @ F ) @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) )
              & ( m2_relset_1 @ ( k3_xboole_0 @ E @ F ) @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(1022,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_relat_1) ).

thf(7539,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).

thf(1156,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( k1_funct_5 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
        = ( k2_tarski @ A @ C ) )
      & ( ( k2_funct_5 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
        = ( k2_tarski @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_5) ).

thf(8116,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( k1_funct_5 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
        = ( k2_tarski @ A @ C ) )
      & ( ( k2_funct_5 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) )
        = ( k2_tarski @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).

thf(905,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
        & ( m1_relset_1 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( ( k14_borsuk_1 @ A @ B @ C @ D )
        = ( k9_relat_1 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k14_borsuk_1) ).

thf(6962,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
        & ( m1_relset_1 @ C @ ( k1_pcomps_1 @ A ) @ ( k1_pcomps_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( ( k14_borsuk_1 @ A @ B @ C @ D )
        = ( k9_relat_1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(952,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_pboole @ C @ B )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ! [E: $i] :
              ( ( ( v1_relat_1 @ E )
                & ( v1_funct_1 @ E ) )
             => ! [F: $i] :
                  ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( k1_closure2 @ B @ C ) ) )
                 => ( ( ( r2_hidden @ A @ B )
                      & ( F
                        = ( k2_tarski @ D @ E ) ) )
                   => ( ( k1_funct_1 @ ( k4_closure2 @ B @ C @ F ) @ A )
                      = ( k2_tarski @ ( k1_funct_1 @ D @ A ) @ ( k1_funct_1 @ E @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_closure2) ).

thf(7151,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_pboole @ C @ B )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ! [E: $i] :
              ( ( ( v1_relat_1 @ E )
                & ( v1_funct_1 @ E ) )
             => ! [F: $i] :
                  ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ ( k1_closure2 @ B @ C ) ) )
                 => ( ( ( r2_hidden @ A @ B )
                      & ( F
                        = ( k2_tarski @ D @ E ) ) )
                   => ( ( k1_funct_1 @ ( k4_closure2 @ B @ C @ F ) @ A )
                      = ( k2_tarski @ ( k1_funct_1 @ D @ A ) @ ( k1_funct_1 @ E @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).

thf(2320,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k12_classes2 @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_classes2) ).

thf(13781,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k12_classes2 @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2320]) ).

thf(89,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( r1_partfun1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_partfun1) ).

thf(3146,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( r1_partfun1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(2427,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( r2_hidden @ A @ ( a_1_4_domain_1 @ B ) )
      <=> ? [C: $i] :
            ( ( m1_subset_1 @ C @ B )
            & ( A = C )
            & ( p2_s5_domain_1 @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_4_domain_1) ).

thf(14169,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( ( r2_hidden @ A @ ( a_1_4_domain_1 @ B ) )
         => ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A = C )
              & ( p2_s5_domain_1 @ C ) ) )
        & ( ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A = C )
              & ( p2_s5_domain_1 @ C ) )
         => ( r2_hidden @ A @ ( a_1_4_domain_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2427]) ).

thf(1307,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( ( k1_funct_2 @ A @ B )
         != k1_xboole_0 )
        & ( ( k1_funct_2 @ B @ C )
         != k1_xboole_0 )
        & ( ( k1_funct_2 @ A @ C )
          = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_altcat_1) ).

thf(8789,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( ( k1_funct_2 @ A @ B )
         != k1_xboole_0 )
        & ( ( k1_funct_2 @ B @ C )
         != k1_xboole_0 )
        & ( ( k1_funct_2 @ A @ C )
          = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).

thf(1652,axiom,
    ! [A: $i] :
      ( ( v1_funct_1 @ ( k5_metric_1 @ A ) )
      & ( v1_funct_2 @ ( k5_metric_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers )
      & ( m2_relset_1 @ ( k5_metric_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_metric_1) ).

thf(10384,plain,
    ! [A: $i] :
      ( ( v1_funct_1 @ ( k5_metric_1 @ A ) )
      & ( v1_funct_2 @ ( k5_metric_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers )
      & ( m2_relset_1 @ ( k5_metric_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1652]) ).

thf(1556,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( ( k1_cantor_1 @ A @ B )
        = ( k1_tarski @ k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_yellow_9) ).

thf(9943,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( ( k1_cantor_1 @ A @ B )
        = ( k1_tarski @ k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1556]) ).

thf(2442,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i,D: $i] :
          ( ( ( g1_pre_topc @ A @ B )
            = ( g1_pre_topc @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_pre_topc) ).

thf(14230,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i,D: $i] :
          ( ( ( g1_pre_topc @ A @ B )
            = ( g1_pre_topc @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2442]) ).

thf(1000,axiom,
    ~ ( v1_finset_1 @ k5_numbers ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_card_4) ).

thf(7420,plain,
    ~ ( v1_finset_1 @ k5_numbers ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).

thf(1081,axiom,
    ! [A: $i,B: $i] :
      ( ( k3_tarski @ ( k2_xboole_0 @ A @ B ) )
      = ( k2_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_zfmisc_1) ).

thf(7773,plain,
    ! [A: $i,B: $i] :
      ( ( k3_tarski @ ( k2_xboole_0 @ A @ B ) )
      = ( k2_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).

thf(941,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D ) )
     => ( r1_tarski @ ( k4_xboole_0 @ A @ D ) @ ( k4_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_xboole_1) ).

thf(7122,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D ) )
     => ( r1_tarski @ ( k4_xboole_0 @ A @ D ) @ ( k4_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).

thf(871,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_pboole @ C @ A ) )
     => ( ( r6_pboole @ A @ B @ C )
       => ( r6_pboole @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r6_pboole) ).

thf(6806,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_pboole @ B @ A )
        & ( m1_pboole @ C @ A ) )
     => ( ( r6_pboole @ A @ B @ C )
       => ( r6_pboole @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(288,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( ( v1_binop_1 @ C @ A )
                  & ( v2_binop_1 @ C @ A )
                  & ( v1_setwiseo @ C @ A ) )
               => ! [D: $i] :
                    ( ( ( v1_funct_1 @ D )
                      & ( v1_funct_2 @ D @ B @ A )
                      & ( m2_relset_1 @ D @ B @ A ) )
                   => ( ( k7_setwiseo @ B @ A @ C @ ( k1_setwiseo @ B ) @ D )
                      = ( k3_binop_1 @ A @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_setwiseo) ).

thf(4113,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( ( v1_binop_1 @ C @ A )
                  & ( v2_binop_1 @ C @ A )
                  & ( v1_setwiseo @ C @ A ) )
               => ! [D: $i] :
                    ( ( ( v1_funct_1 @ D )
                      & ( v1_funct_2 @ D @ B @ A )
                      & ( m2_relset_1 @ D @ B @ A ) )
                   => ( ( k7_setwiseo @ B @ A @ C @ ( k1_setwiseo @ B ) @ D )
                      = ( k3_binop_1 @ A @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(2258,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( v1_funct_1 @ ( k9_relset_1 @ A @ B @ C @ D ) )
        & ( m2_relset_1 @ ( k9_relset_1 @ A @ B @ C @ D ) @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_partfun1) ).

thf(13541,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( v1_funct_1 @ ( k9_relset_1 @ A @ B @ C @ D ) )
        & ( m2_relset_1 @ ( k9_relset_1 @ A @ B @ C @ D ) @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2258]) ).

thf(1736,axiom,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ f1_s1_binop_2 @ f2_s1_binop_2 )
        & ( m2_relset_1 @ A @ f1_s1_binop_2 @ f2_s1_binop_2 ) )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ f1_s1_binop_2 @ f2_s1_binop_2 )
            & ( m2_relset_1 @ B @ f1_s1_binop_2 @ f2_s1_binop_2 ) )
         => ( ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ f1_s1_binop_2 )
                 => ( ( k8_funct_2 @ f1_s1_binop_2 @ f2_s1_binop_2 @ A @ C )
                    = ( f3_s1_binop_2 @ C ) ) )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ f1_s1_binop_2 )
                 => ( ( k8_funct_2 @ f1_s1_binop_2 @ f2_s1_binop_2 @ B @ C )
                    = ( f3_s1_binop_2 @ C ) ) ) )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_binop_2) ).

thf(10788,plain,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ f1_s1_binop_2 @ f2_s1_binop_2 )
        & ( m2_relset_1 @ A @ f1_s1_binop_2 @ f2_s1_binop_2 ) )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ f1_s1_binop_2 @ f2_s1_binop_2 )
            & ( m2_relset_1 @ B @ f1_s1_binop_2 @ f2_s1_binop_2 ) )
         => ( ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ f1_s1_binop_2 )
                 => ( ( k8_funct_2 @ f1_s1_binop_2 @ f2_s1_binop_2 @ A @ C )
                    = ( f3_s1_binop_2 @ C ) ) )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ f1_s1_binop_2 )
                 => ( ( k8_funct_2 @ f1_s1_binop_2 @ f2_s1_binop_2 @ B @ C )
                    = ( f3_s1_binop_2 @ C ) ) ) )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1736]) ).

thf(1477,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m2_realset1 @ C @ A @ B )
         => ( ( v1_funct_1 @ ( k1_realset1 @ C @ B ) )
            & ( v1_funct_2 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
            & ( m2_relset_1 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_realset1) ).

thf(9507,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m2_realset1 @ C @ A @ B )
         => ( ( v1_funct_1 @ ( k1_realset1 @ C @ B ) )
            & ( v1_funct_2 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B )
            & ( m2_relset_1 @ ( k1_realset1 @ C @ B ) @ ( k2_zfmisc_1 @ B @ B ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477]) ).

thf(333,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( k4_funcop_1 @ A @ B @ C )
              = ( k5_relat_1 @ ( k13_funct_3 @ B @ ( k2_funcop_1 @ ( k1_relat_1 @ B ) @ C ) ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funcop_1) ).

thf(4355,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( k4_funcop_1 @ A @ B @ C )
              = ( k5_relat_1 @ ( k13_funct_3 @ B @ ( k2_funcop_1 @ ( k1_relat_1 @ B ) @ C ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(2262,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m2_relset_1 @ E @ A @ B ) )
     => ! [F: $i] :
          ( ( ( v1_funct_1 @ F )
            & ( v1_funct_2 @ F @ C @ D )
            & ( m2_relset_1 @ F @ C @ D ) )
         => ( ( v1_funct_1 @ ( k15_funct_3 @ E @ F ) )
            & ( v1_funct_2 @ ( k15_funct_3 @ E @ F ) @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) )
            & ( m2_relset_1 @ ( k15_funct_3 @ E @ F ) @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_funct_3) ).

thf(13555,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m2_relset_1 @ E @ A @ B ) )
     => ! [F: $i] :
          ( ( ( v1_funct_1 @ F )
            & ( v1_funct_2 @ F @ C @ D )
            & ( m2_relset_1 @ F @ C @ D ) )
         => ( ( v1_funct_1 @ ( k15_funct_3 @ E @ F ) )
            & ( v1_funct_2 @ ( k15_funct_3 @ E @ F ) @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) )
            & ( m2_relset_1 @ ( k15_funct_3 @ E @ F ) @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2262]) ).

thf(1068,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( k7_relat_1 @ ( k13_funct_3 @ A @ B ) @ C )
              = ( k13_funct_3 @ A @ ( k7_relat_1 @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funcop_1) ).

thf(7718,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( k7_relat_1 @ ( k13_funct_3 @ A @ B ) @ C )
              = ( k13_funct_3 @ A @ ( k7_relat_1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).

thf(1920,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( C
              = ( k2_cantor_1 @ A @ B ) )
          <=> ! [D: $i] :
                ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
               => ( ( r2_hidden @ D @ C )
                <=> ? [E: $i] :
                      ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
                      & ( r1_tarski @ E @ B )
                      & ( v1_finset_1 @ E )
                      & ( D
                        = ( k8_setfam_1 @ A @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_cantor_1) ).

thf(11795,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( ( C
                = ( k2_cantor_1 @ A @ B ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                 => ( ( ( r2_hidden @ D @ C )
                     => ? [E: $i] :
                          ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
                          & ( r1_tarski @ E @ B )
                          & ( v1_finset_1 @ E )
                          & ( D
                            = ( k8_setfam_1 @ A @ E ) ) ) )
                    & ( ? [E: $i] :
                          ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
                          & ( r1_tarski @ E @ B )
                          & ( v1_finset_1 @ E )
                          & ( D
                            = ( k8_setfam_1 @ A @ E ) ) )
                     => ( r2_hidden @ D @ C ) ) ) ) )
            & ( ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                 => ( ( ( r2_hidden @ D @ C )
                     => ? [E: $i] :
                          ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
                          & ( r1_tarski @ E @ B )
                          & ( v1_finset_1 @ E )
                          & ( D
                            = ( k8_setfam_1 @ A @ E ) ) ) )
                    & ( ? [E: $i] :
                          ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
                          & ( r1_tarski @ E @ B )
                          & ( v1_finset_1 @ E )
                          & ( D
                            = ( k8_setfam_1 @ A @ E ) ) )
                     => ( r2_hidden @ D @ C ) ) ) )
             => ( C
                = ( k2_cantor_1 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1920]) ).

thf(1132,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k1_funct_2 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t159_funct_2) ).

thf(8020,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k1_funct_2 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).

thf(846,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( ( v1_partfun1 @ C @ A @ B )
              & ( v1_partfun1 @ D @ A @ B )
              & ( r1_partfun1 @ C @ D ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_partfun1) ).

thf(6664,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( ( v1_partfun1 @ C @ A @ B )
              & ( v1_partfun1 @ D @ A @ B )
              & ( r1_partfun1 @ C @ D ) )
           => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(915,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i] :
          ( ( r2_hidden @ E @ A )
        <=> ? [F: $i,G: $i,H: $i] :
              ( ( r2_hidden @ F @ B )
              & ( r2_hidden @ G @ C )
              & ( r2_hidden @ H @ D )
              & ( E
                = ( k3_mcart_1 @ F @ G @ H ) ) ) )
     => ( A
        = ( k3_zfmisc_1 @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_mcart_1) ).

thf(6998,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i] :
          ( ( ( r2_hidden @ E @ A )
           => ? [F: $i,G: $i,H: $i] :
                ( ( r2_hidden @ F @ B )
                & ( r2_hidden @ G @ C )
                & ( r2_hidden @ H @ D )
                & ( E
                  = ( k3_mcart_1 @ F @ G @ H ) ) ) )
          & ( ? [F: $i,G: $i,H: $i] :
                ( ( r2_hidden @ F @ B )
                & ( r2_hidden @ G @ C )
                & ( r2_hidden @ H @ D )
                & ( E
                  = ( k3_mcart_1 @ F @ G @ H ) ) )
           => ( r2_hidden @ E @ A ) ) )
     => ( A
        = ( k3_zfmisc_1 @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(547,axiom,
    ! [A: $i] :
      ( ~ ( ~ ( r1_xboole_0 @ A @ A )
          & ( A = k1_xboole_0 ) )
      & ~ ( ( A != k1_xboole_0 )
          & ( r1_xboole_0 @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_xboole_1) ).

thf(5358,plain,
    ! [A: $i] :
      ( ~ ( ~ ( r1_xboole_0 @ A @ A )
          & ( A = k1_xboole_0 ) )
      & ~ ( ( A != k1_xboole_0 )
          & ( r1_xboole_0 @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(1177,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ( ( k3_zfmisc_1 @ A @ B @ C )
                = ( a_3_0_domain_1 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_domain_1) ).

thf(8194,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ( ( k3_zfmisc_1 @ A @ B @ C )
                = ( a_3_0_domain_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).

thf(327,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ( ( ( v3_binop_1 @ C @ A )
                      & ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ B )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                           => ( ( k7_setwiseo @ B @ A @ C @ ( k3_setwiseo @ B @ E @ F ) @ D )
                              = ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ ( k8_funct_2 @ B @ A @ D @ F ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_setwiseo) ).

thf(4336,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ( ( ( v3_binop_1 @ C @ A )
                      & ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ B )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                           => ( ( k7_setwiseo @ B @ A @ C @ ( k3_setwiseo @ B @ E @ F ) @ D )
                              = ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ ( k8_funct_2 @ B @ A @ D @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(457,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_zfmisc_1) ).

thf(5003,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(452,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k4_enumset1 @ A @ B @ C @ D @ E @ F )
      = ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k3_enumset1 @ B @ C @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_enumset1) ).

thf(4986,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( k4_enumset1 @ A @ B @ C @ D @ E @ F )
      = ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k3_enumset1 @ B @ C @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(820,axiom,
    ! [A: $i] : ( r1_tarski @ ( k1_setfam_1 @ A ) @ ( k3_tarski @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_setfam_1) ).

thf(6557,plain,
    ! [A: $i] : ( r1_tarski @ ( k1_setfam_1 @ A ) @ ( k3_tarski @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(1898,axiom,
    ! [A: $i] :
      ( ( v1_fraenkel @ A )
     => ! [B: $i] :
          ( ( r1_tarski @ B @ A )
         => ( v1_fraenkel @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_fraenkel) ).

thf(11679,plain,
    ! [A: $i] :
      ( ( v1_fraenkel @ A )
     => ! [B: $i] :
          ( ( r1_tarski @ B @ A )
         => ( v1_fraenkel @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1898]) ).

thf(2171,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
    <=> ( ( r2_hidden @ A @ C )
        & ( r2_hidden @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).

thf(13189,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
       => ( ( r2_hidden @ A @ C )
          & ( r2_hidden @ B @ D ) ) )
      & ( ( ( r2_hidden @ A @ C )
          & ( r2_hidden @ B @ D ) )
       => ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2171]) ).

thf(1867,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ( k6_domain_1 @ A @ B )
        = ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).

thf(11547,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ( k6_domain_1 @ A @ B )
        = ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1867]) ).

thf(740,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( v1_partfun1 @ C @ A @ B )
      <=> ( ( k5_partfun1 @ A @ B @ C )
          = ( k1_tarski @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_partfun1) ).

thf(6202,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( v1_partfun1 @ C @ A @ B )
         => ( ( k5_partfun1 @ A @ B @ C )
            = ( k1_tarski @ C ) ) )
        & ( ( ( k5_partfun1 @ A @ B @ C )
            = ( k1_tarski @ C ) )
         => ( v1_partfun1 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(2082,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ? [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
          & ! [D: $i] :
              ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
             => ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_realset1) ).

thf(12740,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ? [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
          & ! [D: $i] :
              ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
             => ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2082]) ).

thf(884,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ( ( k1_funct_4 @ B @ C )
            = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_funct_4) ).

thf(6875,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ( ( k1_funct_4 @ B @ C )
            = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(1434,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
         != k1_xboole_0 )
        & ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
         != ( k1_tarski @ A ) )
        & ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
         != ( k1_tarski @ B ) )
        & ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
         != ( k2_tarski @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_zfmisc_1) ).

thf(9317,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
         != k1_xboole_0 )
        & ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
         != ( k1_tarski @ A ) )
        & ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
         != ( k1_tarski @ B ) )
        & ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
         != ( k2_tarski @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1434]) ).

thf(2481,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k4_partfun1 @ A @ B ) ) ) )
     => ! [D: $i] :
          ( ( m1_pua2mss1 @ D @ A @ B @ C )
        <=> ( m1_subset_1 @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_pua2mss1) ).

thf(14417,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k4_partfun1 @ A @ B ) ) ) )
     => ! [D: $i] :
          ( ( ( m1_pua2mss1 @ D @ A @ B @ C )
           => ( m1_subset_1 @ D @ C ) )
          & ( ( m1_subset_1 @ D @ C )
           => ( m1_pua2mss1 @ D @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2481]) ).

thf(1737,axiom,
    ! [A: $i] :
      ( ( r2_hidden @ A @ k1_qc_lang1 )
    <=> ~ ( ~ ( r2_hidden @ A @ k3_qc_lang1 )
          & ~ ( r2_hidden @ A @ k4_qc_lang1 )
          & ~ ( r2_hidden @ A @ k2_qc_lang1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_cqc_lang) ).

thf(10797,plain,
    ! [A: $i] :
      ( ( ( r2_hidden @ A @ k1_qc_lang1 )
       => ~ ( ~ ( r2_hidden @ A @ k3_qc_lang1 )
            & ~ ( r2_hidden @ A @ k4_qc_lang1 )
            & ~ ( r2_hidden @ A @ k2_qc_lang1 ) ) )
      & ( ~ ( ~ ( r2_hidden @ A @ k3_qc_lang1 )
            & ~ ( r2_hidden @ A @ k4_qc_lang1 )
            & ~ ( r2_hidden @ A @ k2_qc_lang1 ) )
       => ( r2_hidden @ A @ k1_qc_lang1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1737]) ).

thf(1005,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( r1_partfun1 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_partfun1) ).

thf(7475,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( r1_partfun1 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).

thf(1503,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [D: $i,E: $i,F: $i] :
          ( ( ( g3_lattices @ A @ B @ C )
            = ( g3_lattices @ D @ E @ F ) )
         => ( ( A = D )
            & ( B = E )
            & ( C = F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).

thf(9606,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [D: $i,E: $i,F: $i] :
          ( ( ( g3_lattices @ A @ B @ C )
            = ( g3_lattices @ D @ E @ F ) )
         => ( ( A = D )
            & ( B = E )
            & ( C = F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1503]) ).

thf(2487,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( r2_hidden @ A @ ( a_3_2_domain_1 @ B @ C @ D ) )
      <=> ? [E: $i] :
            ( ( m1_subset_1 @ E @ B )
            & ( A = E )
            & ( ( r2_hidden @ E @ C )
              | ( r2_hidden @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_2_domain_1) ).

thf(14444,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( ( r2_hidden @ A @ ( a_3_2_domain_1 @ B @ C @ D ) )
         => ? [E: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( A = E )
              & ( ( r2_hidden @ E @ C )
                | ( r2_hidden @ E @ D ) ) ) )
        & ( ? [E: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( A = E )
              & ( ( r2_hidden @ E @ C )
                | ( r2_hidden @ E @ D ) ) )
         => ( r2_hidden @ A @ ( a_3_2_domain_1 @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2487]) ).

thf(229,axiom,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
     => ! [B: $i] :
        ? [C: $i] :
          ( ( v1_relat_1 @ C )
          & ( v1_funct_1 @ C )
          & ( ( k1_relat_1 @ C )
            = A )
          & ( ( k2_relat_1 @ C )
            = ( k1_tarski @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_1) ).

thf(3872,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
     => ! [B: $i] :
        ? [C: $i] :
          ( ( v1_relat_1 @ C )
          & ( v1_funct_1 @ C )
          & ( ( k1_relat_1 @ C )
            = A )
          & ( ( k2_relat_1 @ C )
            = ( k1_tarski @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(1070,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_tarski @ A @ B )
       => ( ( k7_relat_1 @ ( k7_relat_1 @ C @ B ) @ A )
          = ( k7_relat_1 @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_relat_1) ).

thf(7724,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_tarski @ A @ B )
       => ( ( k7_relat_1 @ ( k7_relat_1 @ C @ B ) @ A )
          = ( k7_relat_1 @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).

thf(369,axiom,
    ! [A: $i] :
      ( ? [B: $i,C: $i] :
          ( A
          = ( k4_tarski @ B @ C ) )
     => ! [B: $i] :
          ( ( B
            = ( k1_mcart_1 @ A ) )
        <=> ! [C: $i,D: $i] :
              ( ( A
                = ( k4_tarski @ C @ D ) )
             => ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_mcart_1) ).

thf(4593,plain,
    ! [A: $i] :
      ( ? [B: $i,C: $i] :
          ( A
          = ( k4_tarski @ B @ C ) )
     => ! [B: $i] :
          ( ( ( B
              = ( k1_mcart_1 @ A ) )
           => ! [C: $i,D: $i] :
                ( ( A
                  = ( k4_tarski @ C @ D ) )
               => ( B = C ) ) )
          & ( ! [C: $i,D: $i] :
                ( ( A
                  = ( k4_tarski @ C @ D ) )
               => ( B = C ) )
           => ( B
              = ( k1_mcart_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(695,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ B @ C )
                    & ( m2_relset_1 @ E @ B @ C ) )
                 => ! [F: $i] :
                      ( ( m1_pboole @ F @ B )
                     => ! [G: $i] :
                          ( ( m1_pboole @ G @ C )
                         => ! [H: $i] :
                              ( ( m1_functor0 @ H @ B @ C @ E @ F @ G )
                             => ( m1_functor0 @ ( k7_pboole @ A @ B @ D @ H ) @ A @ C @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ ( k7_pboole @ A @ B @ D @ F ) @ G ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_functor0) ).

thf(6012,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ B @ C )
                    & ( m2_relset_1 @ E @ B @ C ) )
                 => ! [F: $i] :
                      ( ( m1_pboole @ F @ B )
                     => ! [G: $i] :
                          ( ( m1_pboole @ G @ C )
                         => ! [H: $i] :
                              ( ( m1_functor0 @ H @ B @ C @ E @ F @ G )
                             => ( m1_functor0 @ ( k7_pboole @ A @ B @ D @ H ) @ A @ C @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ ( k7_pboole @ A @ B @ D @ F ) @ G ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(267,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ A ) )
     => ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).

thf(4045,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ A ) )
     => ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(254,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
       => ( r2_hidden @ ( k1_funct_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_1) ).

thf(3988,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
       => ( r2_hidden @ ( k1_funct_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(1042,axiom,
    ! [A: $i,B: $i] :
      ( ( k3_setfam_1 @ A @ B )
      = ( k3_setfam_1 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_setfam_1) ).

thf(7615,plain,
    ! [A: $i,B: $i] :
      ( ( k3_setfam_1 @ A @ B )
      = ( k3_setfam_1 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).

thf(771,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i,D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( ( v1_binop_1 @ D @ A )
                  & ( v2_binop_1 @ D @ A )
                  & ( v3_binop_1 @ D @ A ) )
               => ! [E: $i] :
                    ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                   => ( ( E != k1_xboole_0 )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ B @ ( k5_finsub_1 @ C ) )
                            & ( m2_relset_1 @ F @ B @ ( k5_finsub_1 @ C ) ) )
                         => ! [G: $i] :
                              ( ( ( v1_funct_1 @ G )
                                & ( v1_funct_2 @ G @ ( k5_finsub_1 @ C ) @ A )
                                & ( m2_relset_1 @ G @ ( k5_finsub_1 @ C ) @ A ) )
                             => ( ! [H: $i] :
                                    ( ( m1_subset_1 @ H @ ( k5_finsub_1 @ C ) )
                                   => ! [I: $i] :
                                        ( ( m1_subset_1 @ I @ ( k5_finsub_1 @ C ) )
                                       => ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ ( k5_setwiseo @ C @ H @ I ) )
                                          = ( k2_binop_1 @ A @ A @ A @ D @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ H ) @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ I ) ) ) ) )
                               => ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ ( k10_setwiseo @ B @ C @ E @ F ) )
                                  = ( k7_setwiseo @ B @ A @ D @ E @ ( k7_funct_2 @ B @ ( k5_finsub_1 @ C ) @ A @ F @ G ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_setwiseo) ).

thf(6362,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i,D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ( ( ( v1_binop_1 @ D @ A )
                  & ( v2_binop_1 @ D @ A )
                  & ( v3_binop_1 @ D @ A ) )
               => ! [E: $i] :
                    ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ B ) )
                   => ( ( E != k1_xboole_0 )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ B @ ( k5_finsub_1 @ C ) )
                            & ( m2_relset_1 @ F @ B @ ( k5_finsub_1 @ C ) ) )
                         => ! [G: $i] :
                              ( ( ( v1_funct_1 @ G )
                                & ( v1_funct_2 @ G @ ( k5_finsub_1 @ C ) @ A )
                                & ( m2_relset_1 @ G @ ( k5_finsub_1 @ C ) @ A ) )
                             => ( ! [H: $i] :
                                    ( ( m1_subset_1 @ H @ ( k5_finsub_1 @ C ) )
                                   => ! [I: $i] :
                                        ( ( m1_subset_1 @ I @ ( k5_finsub_1 @ C ) )
                                       => ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ ( k5_setwiseo @ C @ H @ I ) )
                                          = ( k2_binop_1 @ A @ A @ A @ D @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ H ) @ ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ I ) ) ) ) )
                               => ( ( k8_funct_2 @ ( k5_finsub_1 @ C ) @ A @ G @ ( k10_setwiseo @ B @ C @ E @ F ) )
                                  = ( k7_setwiseo @ B @ A @ D @ E @ ( k7_funct_2 @ B @ ( k5_finsub_1 @ C ) @ A @ F @ G ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(1140,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) ) )
     => ( ( B
          = ( k9_setwiseo @ A ) )
      <=> ! [C: $i] :
            ( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
           => ! [D: $i] :
                ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
               => ( ( k2_binop_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) @ B @ C @ D )
                  = ( k5_setwiseo @ A @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_setwiseo) ).

thf(8056,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) ) @ ( k5_finsub_1 @ A ) ) )
     => ( ( ( B
            = ( k9_setwiseo @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
                 => ( ( k2_binop_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) @ B @ C @ D )
                    = ( k5_setwiseo @ A @ C @ D ) ) ) ) )
        & ( ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
                 => ( ( k2_binop_1 @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ A ) @ B @ C @ D )
                    = ( k5_setwiseo @ A @ C @ D ) ) ) )
         => ( B
            = ( k9_setwiseo @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).

thf(1263,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
      = ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_xboole_1) ).

thf(8593,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
      = ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).

thf(603,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
         => ( ! [E: $i] :
                ( ( r2_hidden @ E @ D )
               => ( ( r1_tarski @ E @ C )
                  & ? [F: $i] :
                      ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ A ) )
                      & ? [G: $i] :
                          ( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ B ) )
                          & ( E
                            = ( k12_mcart_1 @ A @ B @ F @ G ) ) ) ) ) )
           => ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_setfam_1 @ ( k9_relat_1 @ ( k1_funct_3 @ ( k9_funct_3 @ A @ B ) ) @ D ) ) @ ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ ( k10_funct_3 @ A @ B ) ) @ D ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_borsuk_1) ).

thf(5570,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
         => ( ! [E: $i] :
                ( ( r2_hidden @ E @ D )
               => ( ( r1_tarski @ E @ C )
                  & ? [F: $i] :
                      ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ A ) )
                      & ? [G: $i] :
                          ( ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ B ) )
                          & ( E
                            = ( k12_mcart_1 @ A @ B @ F @ G ) ) ) ) ) )
           => ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_setfam_1 @ ( k9_relat_1 @ ( k1_funct_3 @ ( k9_funct_3 @ A @ B ) ) @ D ) ) @ ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ ( k10_funct_3 @ A @ B ) ) @ D ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(1335,axiom,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_xboole_1) ).

thf(8905,plain,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).

thf(634,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( v1_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_relat_1) ).

thf(5716,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( v1_relat_1 @ ( k2_tarski @ ( k4_tarski @ A @ B ) @ ( k4_tarski @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(144,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
           => ( ( k1_funct_1 @ ( k5_relat_1 @ B @ C ) @ A )
              = ( k1_funct_1 @ C @ ( k1_funct_1 @ B @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).

thf(3376,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
           => ( ( k1_funct_1 @ ( k5_relat_1 @ B @ C ) @ A )
              = ( k1_funct_1 @ C @ ( k1_funct_1 @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(1637,axiom,
    ! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_1) ).

thf(10290,plain,
    ! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1637]) ).

thf(1527,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( k4_funct_4 @ A @ B @ C @ D )
        = ( k4_funct_4 @ A @ B @ E @ F ) )
     => ( ( A = B )
        | ( ( C = E )
          & ( D = F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_4) ).

thf(9794,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( k4_funct_4 @ A @ B @ C @ D )
        = ( k4_funct_4 @ A @ B @ E @ F ) )
     => ( ( A = B )
        | ( ( C = E )
          & ( D = F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527]) ).

thf(615,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( r2_hidden @ C @ A )
         => ( ( k3_cqc_lang @ C @ ( k1_funct_1 @ B @ C ) )
            = ( k7_relat_1 @ B @ ( k1_tarski @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_funct_7) ).

thf(5607,plain,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( r2_hidden @ C @ A )
         => ( ( k3_cqc_lang @ C @ ( k1_funct_1 @ B @ C ) )
            = ( k7_relat_1 @ B @ ( k1_tarski @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(1831,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ k1_xboole_0 @ A )
        & ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
     => ( ( k3_funct_2 @ k1_xboole_0 @ A @ C @ B )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funct_2) ).

thf(11327,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ k1_xboole_0 @ A )
        & ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
     => ( ( k3_funct_2 @ k1_xboole_0 @ A @ C @ B )
        = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1831]) ).

thf(802,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ C )
                    & ( m2_relset_1 @ E @ A @ C ) )
                 => ( ( ( k7_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ B @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ ( k9_funct_3 @ B @ C ) )
                      = D )
                    & ( ( k7_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ C @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ ( k10_funct_3 @ B @ C ) )
                      = E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funct_3) ).

thf(6472,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ A @ C )
                    & ( m2_relset_1 @ E @ A @ C ) )
                 => ( ( ( k7_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ B @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ ( k9_funct_3 @ B @ C ) )
                      = D )
                    & ( ( k7_funct_2 @ A @ ( k2_zfmisc_1 @ B @ C ) @ C @ ( k14_funct_3 @ A @ B @ C @ D @ E ) @ ( k10_funct_3 @ B @ C ) )
                      = E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(335,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ( v1_binop_1 @ B @ A )
      <=> ! [C: $i] :
            ( ( m1_subset_1 @ C @ A )
           => ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ( k1_binop_1 @ B @ C @ D )
                  = ( k1_binop_1 @ B @ D @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_binop_1) ).

thf(4360,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ( ( v1_binop_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( k1_binop_1 @ B @ C @ D )
                    = ( k1_binop_1 @ B @ D @ C ) ) ) ) )
        & ( ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( k1_binop_1 @ B @ C @ D )
                    = ( k1_binop_1 @ B @ D @ C ) ) ) )
         => ( v1_binop_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(1552,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

thf(9926,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1552]) ).

thf(1540,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_zfmisc_1 @ A @ B @ C )
      = ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_zfmisc_1) ).

thf(9847,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_zfmisc_1 @ A @ B @ C )
      = ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540]) ).

thf(1873,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ A @ C )
            & ( m2_relset_1 @ E @ A @ C ) )
         => ~ ( ( ( B = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ( ( C = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ~ ( ( v1_funct_1 @ ( k13_funct_3 @ D @ E ) )
                  & ( v1_funct_2 @ ( k13_funct_3 @ D @ E ) @ A @ ( k2_zfmisc_1 @ B @ C ) )
                  & ( m2_relset_1 @ ( k13_funct_3 @ D @ E ) @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_funct_3) ).

thf(11573,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ A @ C )
            & ( m2_relset_1 @ E @ A @ C ) )
         => ~ ( ( ( B = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ( ( C = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ~ ( ( v1_funct_1 @ ( k13_funct_3 @ D @ E ) )
                  & ( v1_funct_2 @ ( k13_funct_3 @ D @ E ) @ A @ ( k2_zfmisc_1 @ B @ C ) )
                  & ( m2_relset_1 @ ( k13_funct_3 @ D @ E ) @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1873]) ).

thf(1929,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( r2_hidden @ A @ ( a_1_1_ens_1 @ B ) )
      <=> ? [C: $i,D: $i,E: $i] :
            ( ( m1_subset_1 @ C @ B )
            & ( m1_subset_1 @ D @ B )
            & ( m1_subset_1 @ E @ ( k1_ens_1 @ B ) )
            & ( A
              = ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) )
            & ( ( D = k1_xboole_0 )
             => ( C = k1_xboole_0 ) )
            & ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ C @ D )
            & ( m2_relset_1 @ E @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_1_ens_1) ).

thf(11857,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( ( r2_hidden @ A @ ( a_1_1_ens_1 @ B ) )
         => ? [C: $i,D: $i,E: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( m1_subset_1 @ D @ B )
              & ( m1_subset_1 @ E @ ( k1_ens_1 @ B ) )
              & ( A
                = ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) )
              & ( ( D = k1_xboole_0 )
               => ( C = k1_xboole_0 ) )
              & ( v1_funct_1 @ E )
              & ( v1_funct_2 @ E @ C @ D )
              & ( m2_relset_1 @ E @ C @ D ) ) )
        & ( ? [C: $i,D: $i,E: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( m1_subset_1 @ D @ B )
              & ( m1_subset_1 @ E @ ( k1_ens_1 @ B ) )
              & ( A
                = ( k1_domain_1 @ ( k2_zfmisc_1 @ B @ B ) @ ( k1_ens_1 @ B ) @ ( k1_domain_1 @ B @ B @ C @ D ) @ E ) )
              & ( ( D = k1_xboole_0 )
               => ( C = k1_xboole_0 ) )
              & ( v1_funct_1 @ E )
              & ( v1_funct_2 @ E @ C @ D )
              & ( m2_relset_1 @ E @ C @ D ) )
         => ( r2_hidden @ A @ ( a_1_1_ens_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1929]) ).

thf(2168,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ~ ( v1_realset1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_realset1) ).

thf(13181,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ~ ( v1_realset1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2168]) ).

thf(491,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) @ ( k1_tarski @ D ) )
      = ( k2_tarski @ ( k3_mcart_1 @ A @ B @ D ) @ ( k3_mcart_1 @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_mcart_1) ).

thf(5125,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) @ ( k1_tarski @ D ) )
      = ( k2_tarski @ ( k3_mcart_1 @ A @ B @ D ) @ ( k3_mcart_1 @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(703,axiom,
    ! [A: $i,B: $i] :
      ( ( k3_xboole_0 @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).

thf(6051,plain,
    ! [A: $i] :
      ( ( k3_xboole_0 @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(902,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
                 => ( ( k1_funct_4 @ ( k2_partfun1 @ A @ B @ C @ E ) @ D )
                    = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_lattice2) ).

thf(6934,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
                 => ( ( k1_funct_4 @ ( k2_partfun1 @ A @ B @ C @ E ) @ D )
                    = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(1903,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ B @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_enumset1) ).

thf(11694,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ B @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1903]) ).

thf(1979,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_funct_1 @ ( k9_funct_3 @ A @ B ) )
      & ( v1_funct_2 @ ( k9_funct_3 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ A )
      & ( m2_relset_1 @ ( k9_funct_3 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_funct_3) ).

thf(12139,plain,
    ! [A: $i,B: $i] :
      ( ( v1_funct_1 @ ( k9_funct_3 @ A @ B ) )
      & ( v1_funct_2 @ ( k9_funct_3 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ A )
      & ( m2_relset_1 @ ( k9_funct_3 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1979]) ).

thf(314,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ ( k2_tarski @ C @ D ) ) )
     => ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
        & ( ( ( k2_mcart_1 @ A )
            = C )
          | ( ( k2_mcart_1 @ A )
            = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_mcart_1) ).

thf(4272,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ ( k2_tarski @ C @ D ) ) )
     => ( ( r2_hidden @ ( k1_mcart_1 @ A ) @ B )
        & ( ( ( k2_mcart_1 @ A )
            = C )
          | ( ( k2_mcart_1 @ A )
            = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(2462,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A ) )
     => ( m1_subset_1 @ ( k4_setwiseo @ A @ B @ C @ D ) @ ( k5_finsub_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_setwiseo) ).

thf(14336,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A ) )
     => ( m1_subset_1 @ ( k4_setwiseo @ A @ B @ C @ D ) @ ( k5_finsub_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2462]) ).

thf(2301,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ C @ A )
     => ( m2_relset_1 @ ( k9_relset_1 @ C @ A @ B @ D ) @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_relset_1) ).

thf(13698,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ C @ A )
     => ( m2_relset_1 @ ( k9_relset_1 @ C @ A @ B @ D ) @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2301]) ).

thf(2505,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( r2_hidden @ A @ ( a_3_3_domain_1 @ B @ C @ D ) )
      <=> ? [E: $i] :
            ( ( m1_subset_1 @ E @ B )
            & ( A = E )
            & ( r2_hidden @ E @ C )
            & ~ ( r2_hidden @ E @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_3_domain_1) ).

thf(14562,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( ( r2_hidden @ A @ ( a_3_3_domain_1 @ B @ C @ D ) )
         => ? [E: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( A = E )
              & ( r2_hidden @ E @ C )
              & ~ ( r2_hidden @ E @ D ) ) )
        & ( ? [E: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( A = E )
              & ( r2_hidden @ E @ C )
              & ~ ( r2_hidden @ E @ D ) )
         => ( r2_hidden @ A @ ( a_3_3_domain_1 @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2505]) ).

thf(2140,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ( ( v2_funct_1 @ C )
              <=> ! [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ( ( ( k8_funct_2 @ A @ B @ C @ D )
                            = ( k8_funct_2 @ A @ B @ C @ E ) )
                         => ( D = E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_group_6) ).

thf(13047,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ( ( ( v2_funct_1 @ C )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( ( k8_funct_2 @ A @ B @ C @ D )
                              = ( k8_funct_2 @ A @ B @ C @ E ) )
                           => ( D = E ) ) ) ) )
                & ( ! [D: $i] :
                      ( ( m1_subset_1 @ D @ A )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ A )
                         => ( ( ( k8_funct_2 @ A @ B @ C @ D )
                              = ( k8_funct_2 @ A @ B @ C @ E ) )
                           => ( D = E ) ) ) )
                 => ( v2_funct_1 @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2140]) ).

thf(2008,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
     => ~ ( ( r2_hidden @ B @ ( k3_subset_1 @ A @ C ) )
          & ( r2_hidden @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).

thf(12313,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
     => ~ ( ( r2_hidden @ B @ ( k3_subset_1 @ A @ C ) )
          & ( r2_hidden @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2008]) ).

thf(1746,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) )
                 => ( ( A
                      = ( k6_mcart_1 @ B @ C @ D @ E ) )
                  <=> ! [F: $i] :
                        ( ( m1_subset_1 @ F @ B )
                       => ! [G: $i] :
                            ( ( m1_subset_1 @ G @ C )
                           => ! [H: $i] :
                                ( ( m1_subset_1 @ H @ D )
                               => ( ( E
                                    = ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
                                 => ( A = G ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_domain_1) ).

thf(10856,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) )
                 => ( ( ( A
                        = ( k6_mcart_1 @ B @ C @ D @ E ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ C )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ D )
                                 => ( ( E
                                      = ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
                                   => ( A = G ) ) ) ) ) )
                    & ( ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ C )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ D )
                                 => ( ( E
                                      = ( k4_domain_1 @ B @ C @ D @ F @ G @ H ) )
                                   => ( A = G ) ) ) ) )
                     => ( A
                        = ( k6_mcart_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1746]) ).

thf(105,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
      <=> ( v1_finset_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finset_1) ).

thf(3214,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( ( v1_finset_1 @ ( k1_relat_1 @ A ) )
         => ( v1_finset_1 @ A ) )
        & ( ( v1_finset_1 @ A )
         => ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(2150,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ B @ A )
                & ( m2_relset_1 @ C @ B @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ( r2_hidden @ D @ ( k3_funct_2 @ B @ A @ C @ ( k1_tarski @ ( k8_funct_2 @ B @ A @ C @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_setwiseo) ).

thf(13108,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ B @ A )
                & ( m2_relset_1 @ C @ B @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ( r2_hidden @ D @ ( k3_funct_2 @ B @ A @ C @ ( k1_tarski @ ( k8_funct_2 @ B @ A @ C @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2150]) ).

thf(1997,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
        & ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m1_relset_1 @ E @ A @ B ) )
     => ( m1_subset_1 @ ( k7_setwiseo @ A @ B @ C @ D @ E ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setwiseo) ).

thf(12271,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
        & ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m1_relset_1 @ E @ A @ B ) )
     => ( m1_subset_1 @ ( k7_setwiseo @ A @ B @ C @ D @ E ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1997]) ).

thf(115,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k1_mcart_1 @ ( k4_tarski @ A @ B ) )
        = A )
      & ( ( k2_mcart_1 @ ( k4_tarski @ A @ B ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_mcart_1) ).

thf(3260,plain,
    ! [A: $i,B: $i] :
      ( ( ( k1_mcart_1 @ ( k4_tarski @ A @ B ) )
        = A )
      & ( ( k2_mcart_1 @ ( k4_tarski @ A @ B ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(1265,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ! [B: $i,C: $i] :
            ~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
       => ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).

thf(8598,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ! [B: $i,C: $i] :
            ~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
       => ( A = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).

thf(214,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
          & ( r2_hidden @ B @ A ) )
       => ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ ( k2_relat_1 @ ( k7_relat_1 @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_1) ).

thf(3754,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
          & ( r2_hidden @ B @ A ) )
       => ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ ( k2_relat_1 @ ( k7_relat_1 @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(438,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H )
      = ( k2_xboole_0 @ ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) @ ( k2_tarski @ G @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_enumset1) ).

thf(4922,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H )
      = ( k2_xboole_0 @ ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) @ ( k2_tarski @ G @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(2503,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( ( k2_cqc_lang @ A @ B @ C @ D @ E )
        = ( k1_cqc_lang @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_cqc_lang) ).

thf(14557,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( ( k2_cqc_lang @ A @ B @ C @ D @ E )
        = ( k1_cqc_lang @ B @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2503]) ).

thf(2315,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k6_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).

thf(13759,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k6_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2315]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ( k19_mcart_1 @ A )
      = ( k1_mcart_1 @ ( k2_mcart_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_mcart_1) ).

thf(2732,plain,
    ! [A: $i] :
      ( ( k19_mcart_1 @ A )
      = ( k1_mcart_1 @ ( k2_mcart_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(1724,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
             => ( ( B
                  = ( k2_tarski @ C @ D ) )
               => ( ( k8_setfam_1 @ A @ B )
                  = ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_mssubfam) ).

thf(10684,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
             => ( ( B
                  = ( k2_tarski @ C @ D ) )
               => ( ( k8_setfam_1 @ A @ B )
                  = ( k5_subset_1 @ A @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1724]) ).

thf(2192,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ E @ D ) @ F )
                            = ( k2_binop_1 @ A @ A @ A @ C @ E @ ( k8_funct_2 @ B @ A @ D @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funcop_1) ).

thf(13285,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ( ( k8_funct_2 @ B @ A @ ( k8_funcop_1 @ A @ B @ C @ E @ D ) @ F )
                            = ( k2_binop_1 @ A @ A @ A @ C @ E @ ( k8_funct_2 @ B @ A @ D @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2192]) ).

thf(1168,axiom,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ C ) @ D )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ C ) @ D ) )
                     => ! [F: $i] :
                          ( ( m2_finseq_2 @ F @ B @ ( k4_finseq_2 @ A @ B ) )
                         => ! [G: $i] :
                              ( ( m2_finseq_2 @ G @ C @ ( k4_finseq_2 @ A @ C ) )
                             => ( m2_finseq_2 @ ( k3_funcop_1 @ E @ F @ G ) @ D @ ( k4_finseq_2 @ A @ D ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_finseq_2) ).

thf(8163,plain,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ C ) @ D )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ C ) @ D ) )
                     => ! [F: $i] :
                          ( ( m2_finseq_2 @ F @ B @ ( k4_finseq_2 @ A @ B ) )
                         => ! [G: $i] :
                              ( ( m2_finseq_2 @ G @ C @ ( k4_finseq_2 @ A @ C ) )
                             => ( m2_finseq_2 @ ( k3_funcop_1 @ E @ F @ G ) @ D @ ( k4_finseq_2 @ A @ D ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).

thf(610,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( k7_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
        = ( k2_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_relat_1) ).

thf(5592,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( k7_relat_1 @ C @ ( k2_xboole_0 @ A @ B ) )
        = ( k2_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(1650,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( ( B != k1_xboole_0 )
         => ( ( k8_setfam_1 @ A @ B )
            = ( k6_setfam_1 @ A @ B ) ) )
        & ( ( B = k1_xboole_0 )
         => ( ( k8_setfam_1 @ A @ B )
            = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_setfam_1) ).

thf(10371,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( ( B != k1_xboole_0 )
         => ( ( k8_setfam_1 @ A @ B )
            = ( k6_setfam_1 @ A @ B ) ) )
        & ( ( B = k1_xboole_0 )
         => ( ( k8_setfam_1 @ A @ B )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1650]) ).

thf(86,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( ( k1_relat_1 @ A )
                = k1_xboole_0 )
              & ( ( k1_relat_1 @ B )
                = k1_xboole_0 ) )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funcop_1) ).

thf(3129,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( ( k1_relat_1 @ A )
                = k1_xboole_0 )
              & ( ( k1_relat_1 @ B )
                = k1_xboole_0 ) )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(2100,axiom,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ~ ( v1_xboole_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_realset1) ).

thf(12807,plain,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ~ ( v1_xboole_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2100]) ).

thf(248,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( B
            = ( k1_relat_1 @ A ) )
        <=> ! [C: $i] :
              ( ( r2_hidden @ C @ B )
            <=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).

thf(3949,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( ( B
              = ( k1_relat_1 @ A ) )
           => ! [C: $i] :
                ( ( ( r2_hidden @ C @ B )
                 => ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
                & ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
                 => ( r2_hidden @ C @ B ) ) ) )
          & ( ! [C: $i] :
                ( ( ( r2_hidden @ C @ B )
                 => ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
                & ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
                 => ( r2_hidden @ C @ B ) ) )
           => ( B
              = ( k1_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(588,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( m1_subset_1 @ ( k8_mcart_1 @ A @ B @ C @ D @ E ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_mcart_1) ).

thf(5523,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( m1_subset_1 @ ( k8_mcart_1 @ A @ B @ C @ D @ E ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(13,axiom,
    ! [A: $i] : ( v1_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_setwiseo) ).

thf(2678,plain,
    ! [A: $i] : ( v1_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(922,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ ( k6_relat_1 @ A ) )
      & ( v1_funct_1 @ ( k6_relat_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).

thf(7045,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ ( k6_relat_1 @ A ) )
      & ( v1_funct_1 @ ( k6_relat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).

thf(1695,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( k2_zfmisc_1 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) )
            = ( k3_tarski @ ( a_2_0_lattice5 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_lattice5) ).

thf(10553,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( k2_zfmisc_1 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) )
            = ( k3_tarski @ ( a_2_0_lattice5 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1695]) ).

thf(378,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( ( k2_relat_1 @ A )
          = ( k1_relat_1 @ ( k4_relat_1 @ A ) ) )
        & ( ( k1_relat_1 @ A )
          = ( k2_relat_1 @ ( k4_relat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).

thf(4641,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( ( k2_relat_1 @ A )
          = ( k1_relat_1 @ ( k4_relat_1 @ A ) ) )
        & ( ( k1_relat_1 @ A )
          = ( k2_relat_1 @ ( k4_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(636,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ B )
                                 => ! [I: $i] :
                                      ( ( m1_subset_1 @ I @ B )
                                     => ! [J: $i] :
                                          ( ( ( v1_funct_1 @ J )
                                            & ( v1_funct_2 @ J @ ( k2_zfmisc_1 @ A @ B ) @ C )
                                            & ( m2_relset_1 @ J @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                                         => ! [K: $i] :
                                              ( ( m2_finseq_1 @ K @ A )
                                             => ! [L: $i] :
                                                  ( ( m2_finseq_1 @ L @ B )
                                                 => ( ( ( K
                                                        = ( k11_finseq_1 @ D @ E @ F ) )
                                                      & ( L
                                                        = ( k11_finseq_1 @ G @ H @ I ) ) )
                                                   => ( ( k3_funcop_1 @ J @ K @ L )
                                                      = ( k11_finseq_1 @ ( k2_binop_1 @ A @ B @ C @ J @ D @ G ) @ ( k2_binop_1 @ A @ B @ C @ J @ E @ H ) @ ( k2_binop_1 @ A @ B @ C @ J @ F @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_finseq_2) ).

thf(5721,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ B )
                                 => ! [I: $i] :
                                      ( ( m1_subset_1 @ I @ B )
                                     => ! [J: $i] :
                                          ( ( ( v1_funct_1 @ J )
                                            & ( v1_funct_2 @ J @ ( k2_zfmisc_1 @ A @ B ) @ C )
                                            & ( m2_relset_1 @ J @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                                         => ! [K: $i] :
                                              ( ( m2_finseq_1 @ K @ A )
                                             => ! [L: $i] :
                                                  ( ( m2_finseq_1 @ L @ B )
                                                 => ( ( ( K
                                                        = ( k11_finseq_1 @ D @ E @ F ) )
                                                      & ( L
                                                        = ( k11_finseq_1 @ G @ H @ I ) ) )
                                                   => ( ( k3_funcop_1 @ J @ K @ L )
                                                      = ( k11_finseq_1 @ ( k2_binop_1 @ A @ B @ C @ J @ D @ G ) @ ( k2_binop_1 @ A @ B @ C @ J @ E @ H ) @ ( k2_binop_1 @ A @ B @ C @ J @ F @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(2112,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ D @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_enumset1) ).

thf(12873,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ D @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2112]) ).

thf(1928,axiom,
    ( ( k3_tarski @ k1_xboole_0 )
    = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfmisc_1) ).

thf(11855,plain,
    ( ( k3_tarski @ k1_xboole_0 )
    = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1928]) ).

thf(1149,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( r1_tarski @ ( k6_relat_1 @ B ) @ C )
       => ( ( r1_tarski @ B @ ( k4_relset_1 @ A @ B @ C ) )
          & ( B
            = ( k5_relset_1 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_relset_1) ).

thf(8096,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( r1_tarski @ ( k6_relat_1 @ B ) @ C )
       => ( ( r1_tarski @ B @ ( k4_relset_1 @ A @ B @ C ) )
          & ( B
            = ( k5_relset_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).

thf(1494,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( ( k3_cat_5 @ A @ B @ C )
        = ( k2_mcart_1 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_cat_5) ).

thf(9578,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( ( k3_cat_5 @ A @ B @ C )
        = ( k2_mcart_1 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1494]) ).

thf(1687,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_membered @ B )
     => ( ( r1_tarski @ A @ B )
       => ( v1_membered @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_membered) ).

thf(10521,plain,
    ! [A: $i,B: $i] :
      ( ( v1_membered @ B )
     => ( ( r1_tarski @ A @ B )
       => ( v1_membered @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1687]) ).

thf(2125,axiom,
    ! [A: $i] :
      ( ( v1_funct_1 @ ( k17_monoid_0 @ A ) )
      & ( v1_funct_2 @ ( k17_monoid_0 @ A ) @ ( k2_zfmisc_1 @ ( k4_partfun1 @ A @ A ) @ ( k4_partfun1 @ A @ A ) ) @ ( k4_partfun1 @ A @ A ) )
      & ( m2_relset_1 @ ( k17_monoid_0 @ A ) @ ( k2_zfmisc_1 @ ( k4_partfun1 @ A @ A ) @ ( k4_partfun1 @ A @ A ) ) @ ( k4_partfun1 @ A @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_monoid_0) ).

thf(12968,plain,
    ! [A: $i] :
      ( ( v1_funct_1 @ ( k17_monoid_0 @ A ) )
      & ( v1_funct_2 @ ( k17_monoid_0 @ A ) @ ( k2_zfmisc_1 @ ( k4_partfun1 @ A @ A ) @ ( k4_partfun1 @ A @ A ) ) @ ( k4_partfun1 @ A @ A ) )
      & ( m2_relset_1 @ ( k17_monoid_0 @ A ) @ ( k2_zfmisc_1 @ ( k4_partfun1 @ A @ A ) @ ( k4_partfun1 @ A @ A ) ) @ ( k4_partfun1 @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2125]) ).

thf(448,axiom,
    ! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_enumset1 @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_setwiseo) ).

thf(4961,plain,
    ! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_enumset1 @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(477,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
     => ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_zfmisc_1) ).

thf(5079,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(1043,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k1_funct_5 @ ( k2_xboole_0 @ A @ B ) )
        = ( k2_xboole_0 @ ( k1_funct_5 @ A ) @ ( k1_funct_5 @ B ) ) )
      & ( ( k2_funct_5 @ ( k2_xboole_0 @ A @ B ) )
        = ( k2_xboole_0 @ ( k2_funct_5 @ A ) @ ( k2_funct_5 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_5) ).

thf(7618,plain,
    ! [A: $i,B: $i] :
      ( ( ( k1_funct_5 @ ( k2_xboole_0 @ A @ B ) )
        = ( k2_xboole_0 @ ( k1_funct_5 @ A ) @ ( k1_funct_5 @ B ) ) )
      & ( ( k2_funct_5 @ ( k2_xboole_0 @ A @ B ) )
        = ( k2_xboole_0 @ ( k2_funct_5 @ A ) @ ( k2_funct_5 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).

thf(1795,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k6_classes2 @ A @ B @ C )
        = ( k4_tarski @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_classes2) ).

thf(11137,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k6_classes2 @ A @ B @ C )
        = ( k4_tarski @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1795]) ).

thf(1218,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ~ ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
             => ( D
                = ( k3_mcart_1 @ ( k5_mcart_1 @ A @ B @ C @ D ) @ ( k6_mcart_1 @ A @ B @ C @ D ) @ ( k7_mcart_1 @ A @ B @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_mcart_1) ).

thf(8364,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ~ ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
             => ( D
                = ( k3_mcart_1 @ ( k5_mcart_1 @ A @ B @ C @ D ) @ ( k6_mcart_1 @ A @ B @ C @ D ) @ ( k7_mcart_1 @ A @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).

thf(961,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_enumset1 @ A @ B @ C )
      = ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_enumset1) ).

thf(7228,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k1_enumset1 @ A @ B @ C )
      = ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finset_1 @ A ) )
     => ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc17_finseq_1) ).

thf(2689,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finset_1 @ A ) )
     => ( v1_finset_1 @ ( k1_relat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(322,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ A )
                        & ( m2_relset_1 @ E @ B @ A ) )
                     => ( ( ( v3_binop_1 @ C @ A )
                          & ( v1_binop_1 @ C @ A )
                          & ( v2_binop_1 @ C @ A )
                          & ( v1_setwiseo @ C @ A ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                           => ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ D @ ( k2_setwiseo @ B @ F ) ) @ E )
                              = ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ D @ E ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_setwiseo) ).

thf(4314,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ A )
                        & ( m2_relset_1 @ E @ B @ A ) )
                     => ( ( ( v3_binop_1 @ C @ A )
                          & ( v1_binop_1 @ C @ A )
                          & ( v2_binop_1 @ C @ A )
                          & ( v1_setwiseo @ C @ A ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                           => ( ( k7_setwiseo @ B @ A @ C @ ( k5_setwiseo @ B @ D @ ( k2_setwiseo @ B @ F ) ) @ E )
                              = ( k2_binop_1 @ A @ A @ A @ C @ ( k7_setwiseo @ B @ A @ C @ D @ E ) @ ( k8_funct_2 @ B @ A @ E @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(1773,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_classes2 @ B ) )
     => ( ( B
          = ( k15_classes2 @ A ) )
      <=> ( ( r1_tarski @ A @ B )
          & ! [C: $i] :
              ( ( ~ ( v1_xboole_0 @ C )
                & ( v1_classes2 @ C ) )
             => ( ( r1_tarski @ A @ C )
               => ( r1_tarski @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_classes2) ).

thf(11022,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_classes2 @ B ) )
     => ( ( ( B
            = ( k15_classes2 @ A ) )
         => ( ( r1_tarski @ A @ B )
            & ! [C: $i] :
                ( ( ~ ( v1_xboole_0 @ C )
                  & ( v1_classes2 @ C ) )
               => ( ( r1_tarski @ A @ C )
                 => ( r1_tarski @ B @ C ) ) ) ) )
        & ( ( ( r1_tarski @ A @ B )
            & ! [C: $i] :
                ( ( ~ ( v1_xboole_0 @ C )
                  & ( v1_classes2 @ C ) )
               => ( ( r1_tarski @ A @ C )
                 => ( r1_tarski @ B @ C ) ) ) )
         => ( B
            = ( k15_classes2 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1773]) ).

thf(2159,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( k7_funct_2 @ A @ B @ B @ D @ ( k7_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
                        = ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funcop_1) ).

thf(13149,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ( ( k7_funct_2 @ A @ B @ B @ D @ ( k7_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ E ) )
                        = ( k7_funcop_1 @ B @ A @ C @ D @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2159]) ).

thf(1080,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( v1_xboole_0 @ C )
     => ! [D: $i] :
          ( ~ ( v1_xboole_0 @ D )
         => ! [E: $i] :
              ( ( m2_finseq_1 @ E @ C )
             => ! [F: $i] :
                  ( ( ( v1_funct_1 @ F )
                    & ( v1_funct_2 @ F @ C @ D )
                    & ( m2_relset_1 @ F @ C @ D ) )
                 => ( ( E
                      = ( k10_finseq_1 @ A @ B ) )
                   => ( ( k1_partfun1 @ k5_numbers @ C @ C @ D @ E @ F )
                      = ( k10_finseq_1 @ ( k1_funct_1 @ F @ A ) @ ( k1_funct_1 @ F @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_finseq_2) ).

thf(7769,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( v1_xboole_0 @ C )
     => ! [D: $i] :
          ( ~ ( v1_xboole_0 @ D )
         => ! [E: $i] :
              ( ( m2_finseq_1 @ E @ C )
             => ! [F: $i] :
                  ( ( ( v1_funct_1 @ F )
                    & ( v1_funct_2 @ F @ C @ D )
                    & ( m2_relset_1 @ F @ C @ D ) )
                 => ( ( E
                      = ( k10_finseq_1 @ A @ B ) )
                   => ( ( k1_partfun1 @ k5_numbers @ C @ C @ D @ E @ F )
                      = ( k10_finseq_1 @ ( k1_funct_1 @ F @ A ) @ ( k1_funct_1 @ F @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).

thf(987,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( v1_xboole_0 @ D )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ A @ D )
            & ( m2_relset_1 @ E @ A @ D ) )
         => ( ( ( r1_tarski @ B @ A )
              & ( r1_tarski @ ( k2_funct_2 @ A @ D @ E @ B ) @ C ) )
           => ( ( v1_funct_1 @ ( k2_partfun1 @ A @ D @ E @ B ) )
              & ( v1_funct_2 @ ( k2_partfun1 @ A @ D @ E @ B ) @ B @ C )
              & ( m2_relset_1 @ ( k2_partfun1 @ A @ D @ E @ B ) @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_cat_1) ).

thf(7351,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( v1_xboole_0 @ D )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ A @ D )
            & ( m2_relset_1 @ E @ A @ D ) )
         => ( ( ( r1_tarski @ B @ A )
              & ( r1_tarski @ ( k2_funct_2 @ A @ D @ E @ B ) @ C ) )
           => ( ( v1_funct_1 @ ( k2_partfun1 @ A @ D @ E @ B ) )
              & ( v1_funct_2 @ ( k2_partfun1 @ A @ D @ E @ B ) @ B @ C )
              & ( m2_relset_1 @ ( k2_partfun1 @ A @ D @ E @ B ) @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

thf(2574,axiom,
    ! [A: $i] :
      ( ( r2_hidden @ A @ a_0_18_fraenkel )
    <=> ? [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s10_fraenkel )
          & ( A = B )
          & ( p1_s10_fraenkel @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_18_fraenkel) ).

thf(14832,plain,
    ! [A: $i] :
      ( ( ( r2_hidden @ A @ a_0_18_fraenkel )
       => ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s10_fraenkel )
            & ( A = B )
            & ( p1_s10_fraenkel @ B ) ) )
      & ( ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s10_fraenkel )
            & ( A = B )
            & ( p1_s10_fraenkel @ B ) )
       => ( r2_hidden @ A @ a_0_18_fraenkel ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2574]) ).

thf(1098,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( r1_partfun1 @ k1_xboole_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_partfun1) ).

thf(7847,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( r1_partfun1 @ k1_xboole_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).

thf(1683,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( C != k1_xboole_0 )
       => ( ( k2_funct_4 @ ( k2_funct_4 @ D ) )
          = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_4) ).

thf(10509,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( C != k1_xboole_0 )
       => ( ( k2_funct_4 @ ( k2_funct_4 @ D ) )
          = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1683]) ).

thf(2545,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( m2_relset_1 @ D @ A @ B )
             => ( ( k10_relset_1 @ A @ B @ D @ C )
                = ( k3_tarski @ ( a_4_0_relset_2 @ A @ B @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_relset_2) ).

thf(14707,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( m2_relset_1 @ D @ A @ B )
             => ( ( k10_relset_1 @ A @ B @ D @ C )
                = ( k3_tarski @ ( a_4_0_relset_2 @ A @ B @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2545]) ).

thf(67,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ~ ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
             => ( ( C
                 != ( k1_mcart_1 @ C ) )
                & ( C
                 != ( k2_mcart_1 @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_mcart_1) ).

thf(3019,plain,
    ! [A: $i,B: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ~ ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
             => ( ( C
                 != ( k1_mcart_1 @ C ) )
                & ( C
                 != ( k2_mcart_1 @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(34,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k7_relat_1 @ C @ A ) ) )
       => ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
          = ( k1_funct_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).

thf(2747,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k7_relat_1 @ C @ A ) ) )
       => ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
          = ( k1_funct_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(778,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( k9_funcop_1 @ ( k2_zfmisc_1 @ A @ B ) @ B @ A @ ( k6_pralg_1 @ A @ B ) )
            = ( k2_zfmisc_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_pralg_1) ).

thf(6389,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( k9_funcop_1 @ ( k2_zfmisc_1 @ A @ B ) @ B @ A @ ( k6_pralg_1 @ A @ B ) )
            = ( k2_zfmisc_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(2451,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( m1_subset_1 @ ( k14_domain_1 @ A @ B @ C @ D ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_domain_1) ).

thf(14272,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( m1_subset_1 @ ( k14_domain_1 @ A @ B @ C @ D ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2451]) ).

thf(1781,axiom,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) )
     => ( ( v1_membered @ A )
        & ( v2_membered @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_membered) ).

thf(11066,plain,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) )
     => ( ( v1_membered @ A )
        & ( v2_membered @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1781]) ).

thf(994,axiom,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
      = ( k4_xboole_0 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_xboole_1) ).

thf(7388,plain,
    ! [A: $i,B: $i] :
      ( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
      = ( k4_xboole_0 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).

thf(2493,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
          <=> ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_orders_1) ).

thf(14491,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
             => ( r2_hidden @ A @ ( k1_orders_1 @ B ) ) )
            & ( ( r2_hidden @ A @ ( k1_orders_1 @ B ) )
             => ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2493]) ).

thf(1226,axiom,
    ( ( v1_xboole_0 @ k1_xboole_0 )
    & ( v1_relat_1 @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).

thf(8396,plain,
    ( ( v1_xboole_0 @ k1_xboole_0 )
    & ( v1_relat_1 @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).

thf(647,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ( ( ( ( k2_relat_1 @ B )
                = A )
              & ( ( k2_relat_1 @ C )
                = A ) )
           => ( ( k2_relat_1 @ ( k4_funct_2 @ A @ B @ C ) )
              = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_2) ).

thf(5767,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ( ( ( ( k2_relat_1 @ B )
                = A )
              & ( ( k2_relat_1 @ C )
                = A ) )
           => ( ( k2_relat_1 @ ( k4_funct_2 @ A @ B @ C ) )
              = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(562,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ( k18_group_2 @ A @ B )
        = ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k18_group_2) ).

thf(5431,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ( k18_group_2 @ A @ B )
        = ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(1243,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ ( k5_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_1) ).

thf(8498,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ ( k5_relset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).

thf(1681,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
        & ( m1_relset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ B )
        & ( m1_subset_1 @ H @ C ) )
     => ( m1_subset_1 @ ( k2_multop_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_multop_1) ).

thf(10504,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
        & ( m1_relset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ B )
        & ( m1_subset_1 @ H @ C ) )
     => ( m1_subset_1 @ ( k2_multop_1 @ A @ B @ C @ D @ E @ F @ G @ H ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1681]) ).

thf(1154,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( v1_funct_1 @ ( k2_funct_4 @ D ) )
        & ( m2_relset_1 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funct_4) ).

thf(8111,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( v1_funct_1 @ ( k2_funct_4 @ D ) )
        & ( m2_relset_1 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).

thf(245,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_pboole @ C @ ( k2_zfmisc_1 @ B @ A ) )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
         => ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
             => ! [F: $i,G: $i] :
                  ( ( ( r2_hidden @ F @ D )
                    & ( r2_hidden @ G @ E ) )
                 => ( ( k1_binop_1 @ C @ G @ F )
                    = ( k1_binop_1 @ ( k7_relat_1 @ C @ ( k12_mcart_1 @ B @ A @ E @ D ) ) @ G @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_altcat_1) ).

thf(3940,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_pboole @ C @ ( k2_zfmisc_1 @ B @ A ) )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
         => ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
             => ! [F: $i,G: $i] :
                  ( ( ( r2_hidden @ F @ D )
                    & ( r2_hidden @ G @ E ) )
                 => ( ( k1_binop_1 @ C @ G @ F )
                    = ( k1_binop_1 @ ( k7_relat_1 @ C @ ( k12_mcart_1 @ B @ A @ E @ D ) ) @ G @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(1053,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( r1_xboole_0 @ A @ B )
          & ( v2_funct_1 @ C ) )
       => ( r1_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_funct_1) ).

thf(7655,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( r1_xboole_0 @ A @ B )
          & ( v2_funct_1 @ C ) )
       => ( r1_xboole_0 @ ( k9_relat_1 @ C @ A ) @ ( k9_relat_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).

thf(701,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
        & ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ C @ D ) @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_partfun1) ).

thf(6036,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( ( v1_funct_1 @ ( k2_partfun1 @ A @ B @ C @ D ) )
        & ( m2_relset_1 @ ( k2_partfun1 @ A @ B @ C @ D ) @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(571,axiom,
    ! [A: $i] :
      ( ( k4_xboole_0 @ A @ k1_xboole_0 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).

thf(5467,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ A @ k1_xboole_0 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(1221,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ D ) @ C )
       => ( ( v1_funct_1 @ D )
          & ( m2_relset_1 @ D @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_partfun1) ).

thf(8377,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ D ) @ C )
       => ( ( v1_funct_1 @ D )
          & ( m2_relset_1 @ D @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).

thf(2431,axiom,
    ! [A: $i] :
      ( ( r2_hidden @ A @ a_0_0_card_fil )
    <=> ? [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s1_card_fil )
          & ( A = B )
          & ( p1_s1_card_fil @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_0_card_fil) ).

thf(14186,plain,
    ! [A: $i] :
      ( ( ( r2_hidden @ A @ a_0_0_card_fil )
       => ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s1_card_fil )
            & ( A = B )
            & ( p1_s1_card_fil @ B ) ) )
      & ( ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s1_card_fil )
            & ( A = B )
            & ( p1_s1_card_fil @ B ) )
       => ( r2_hidden @ A @ a_0_0_card_fil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2431]) ).

thf(1949,axiom,
    ( ( v1_funct_1 @ k36_binop_2 )
    & ( v1_funct_2 @ k36_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( m2_relset_1 @ k36_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k36_binop_2) ).

thf(11974,plain,
    ( ( v1_funct_1 @ k36_binop_2 )
    & ( v1_funct_2 @ k36_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( m2_relset_1 @ k36_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1949]) ).

thf(2331,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
      & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).

thf(13801,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
      & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2331]) ).

thf(1322,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_mcart_1 @ A @ B @ C )
      = ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_mcart_1) ).

thf(8858,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_mcart_1 @ A @ B @ C )
      = ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).

thf(117,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( m2_pua2mss1 @ B @ A )
      <=> ( ( m1_eqrel_1 @ ( k2_relat_1 @ B ) @ A )
          & ( v2_funct_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pua2mss1) ).

thf(3273,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( ( m2_pua2mss1 @ B @ A )
         => ( ( m1_eqrel_1 @ ( k2_relat_1 @ B ) @ A )
            & ( v2_funct_1 @ B ) ) )
        & ( ( ( m1_eqrel_1 @ ( k2_relat_1 @ B ) @ A )
            & ( v2_funct_1 @ B ) )
         => ( m2_pua2mss1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(2540,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_realset1 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ~ ( v1_realset1 @ B )
          & ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_tex_2) ).

thf(14692,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_realset1 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ~ ( v1_realset1 @ B )
          & ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2540]) ).

thf(1607,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k4_enumset1 @ A @ A @ B @ C @ D @ E )
      = ( k3_enumset1 @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_enumset1) ).

thf(10162,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k4_enumset1 @ A @ A @ B @ C @ D @ E )
      = ( k3_enumset1 @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1607]) ).

thf(1327,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] : ( m1_orders_1 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_orders_1) ).

thf(8873,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] : ( m1_orders_1 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).

thf(1889,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
            & ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
         => ( ( k5_partfun1 @ A @ ( k1_tarski @ B ) @ C )
            = ( k1_tarski @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t164_funct_2) ).

thf(11650,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ ( k1_tarski @ B ) )
            & ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
         => ( ( k5_partfun1 @ A @ ( k1_tarski @ B ) @ C )
            = ( k1_tarski @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1889]) ).

thf(1975,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( ( r2_hidden @ D @ A )
          & ( r2_hidden @ E @ B ) )
       => ( ( C = k1_xboole_0 )
          | ( r2_hidden @ ( k1_funct_1 @ F @ ( k4_tarski @ D @ E ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_funct_2) ).

thf(12124,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( ( r2_hidden @ D @ A )
          & ( r2_hidden @ E @ B ) )
       => ( ( C = k1_xboole_0 )
          | ( r2_hidden @ ( k1_funct_1 @ F @ ( k4_tarski @ D @ E ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1975]) ).

thf(965,axiom,
    ! [A: $i] :
      ( ( v1_fraenkel @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_fraenkel) ).

thf(7243,plain,
    ! [A: $i] :
      ( ( v1_fraenkel @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).

thf(2336,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).

thf(13823,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2336]) ).

thf(2416,axiom,
    ! [A: $i] :
      ( ( r2_hidden @ A @ a_0_39_fraenkel )
    <=> ? [B: $i,C: $i] :
          ( ( m1_subset_1 @ B @ f1_s22_fraenkel )
          & ( m1_subset_1 @ C @ f2_s22_fraenkel )
          & ( A
            = ( f5_s22_fraenkel @ B @ C ) )
          & ( r2_hidden @ B @ f3_s22_fraenkel )
          & ( r2_hidden @ C @ f4_s22_fraenkel ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_39_fraenkel) ).

thf(14130,plain,
    ! [A: $i] :
      ( ( ( r2_hidden @ A @ a_0_39_fraenkel )
       => ? [B: $i,C: $i] :
            ( ( m1_subset_1 @ B @ f1_s22_fraenkel )
            & ( m1_subset_1 @ C @ f2_s22_fraenkel )
            & ( A
              = ( f5_s22_fraenkel @ B @ C ) )
            & ( r2_hidden @ B @ f3_s22_fraenkel )
            & ( r2_hidden @ C @ f4_s22_fraenkel ) ) )
      & ( ? [B: $i,C: $i] :
            ( ( m1_subset_1 @ B @ f1_s22_fraenkel )
            & ( m1_subset_1 @ C @ f2_s22_fraenkel )
            & ( A
              = ( f5_s22_fraenkel @ B @ C ) )
            & ( r2_hidden @ B @ f3_s22_fraenkel )
            & ( r2_hidden @ C @ f4_s22_fraenkel ) )
       => ( r2_hidden @ A @ a_0_39_fraenkel ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2416]) ).

thf(2278,axiom,
    ! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finsub_1) ).

thf(13617,plain,
    ! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2278]) ).

thf(1378,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
        = ( k2_tarski @ A @ B ) )
     => ( r2_hidden @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_zfmisc_1) ).

thf(9050,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k3_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
        = ( k2_tarski @ A @ B ) )
     => ( r2_hidden @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378]) ).

thf(2212,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( r2_hidden @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ ( k11_setwiseo @ A ) @ C ) )
          <=> ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_setwiseo) ).

thf(13384,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( ( ( r2_hidden @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ ( k11_setwiseo @ A ) @ C ) )
             => ( B = C ) )
            & ( ( B = C )
             => ( r2_hidden @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ A ) @ ( k11_setwiseo @ A ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2212]) ).

thf(355,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_relat_1 @ ( k11_finseq_1 @ A @ B @ C ) )
      = ( k1_enumset1 @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_finseq_2) ).

thf(4549,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_relat_1 @ ( k11_finseq_1 @ A @ B @ C ) )
      = ( k1_enumset1 @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(1018,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ! [D: $i] :
              ( ( k5_relat_1 @ ( k6_partfun1 @ B ) @ ( k5_funcop_1 @ C @ D @ A ) )
              = ( k5_funcop_1 @ C @ D @ ( k7_relat_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funcop_1) ).

thf(7522,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ! [D: $i] :
              ( ( k5_relat_1 @ ( k6_partfun1 @ B ) @ ( k5_funcop_1 @ C @ D @ A ) )
              = ( k5_funcop_1 @ C @ D @ ( k7_relat_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(102,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_relset_1 @ B @ k5_numbers @ A )
      & ( v1_relat_1 @ B )
      & ( v1_funct_1 @ B )
      & ( v1_finset_1 @ B )
      & ( v1_finseq_1 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_finseq_1) ).

thf(3202,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_relset_1 @ B @ k5_numbers @ A )
      & ( v1_relat_1 @ B )
      & ( v1_funct_1 @ B )
      & ( v1_finset_1 @ B )
      & ( v1_finseq_1 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(2453,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ~ ( v1_xboole_0 @ E )
        & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
        & ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
        & ( m1_subset_1 @ I @ ( k1_zfmisc_1 @ E ) ) )
     => ( ( r2_hidden @ A @ ( a_8_0_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) )
      <=> ? [J: $i,K: $i,L: $i,M: $i] :
            ( ( m1_subset_1 @ J @ B )
            & ( m1_subset_1 @ K @ C )
            & ( m1_subset_1 @ L @ D )
            & ( m1_subset_1 @ M @ E )
            & ( A
              = ( k5_domain_1 @ B @ C @ D @ E @ J @ K @ L @ M ) )
            & ( r2_hidden @ J @ F )
            & ( r2_hidden @ K @ G )
            & ( r2_hidden @ L @ H )
            & ( r2_hidden @ M @ I ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_8_0_domain_1) ).

thf(14279,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ~ ( v1_xboole_0 @ E )
        & ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ C ) )
        & ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ D ) )
        & ( m1_subset_1 @ I @ ( k1_zfmisc_1 @ E ) ) )
     => ( ( ( r2_hidden @ A @ ( a_8_0_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) )
         => ? [J: $i,K: $i,L: $i,M: $i] :
              ( ( m1_subset_1 @ J @ B )
              & ( m1_subset_1 @ K @ C )
              & ( m1_subset_1 @ L @ D )
              & ( m1_subset_1 @ M @ E )
              & ( A
                = ( k5_domain_1 @ B @ C @ D @ E @ J @ K @ L @ M ) )
              & ( r2_hidden @ J @ F )
              & ( r2_hidden @ K @ G )
              & ( r2_hidden @ L @ H )
              & ( r2_hidden @ M @ I ) ) )
        & ( ? [J: $i,K: $i,L: $i,M: $i] :
              ( ( m1_subset_1 @ J @ B )
              & ( m1_subset_1 @ K @ C )
              & ( m1_subset_1 @ L @ D )
              & ( m1_subset_1 @ M @ E )
              & ( A
                = ( k5_domain_1 @ B @ C @ D @ E @ J @ K @ L @ M ) )
              & ( r2_hidden @ J @ F )
              & ( r2_hidden @ K @ G )
              & ( r2_hidden @ L @ H )
              & ( r2_hidden @ M @ I ) )
         => ( r2_hidden @ A @ ( a_8_0_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2453]) ).

thf(523,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( ( k5_relat_1 @ ( k5_relat_1 @ A @ B ) @ C )
                = ( k5_relat_1 @ A @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_relat_1) ).

thf(5276,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ! [C: $i] :
              ( ( v1_relat_1 @ C )
             => ( ( k5_relat_1 @ ( k5_relat_1 @ A @ B ) @ C )
                = ( k5_relat_1 @ A @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(1673,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
        = ( k4_zfmisc_1 @ E @ F @ G @ H ) )
     => ( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
          = k1_xboole_0 )
        | ( ( A = E )
          & ( B = F )
          & ( C = G )
          & ( D = H ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_mcart_1) ).

thf(10466,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
        = ( k4_zfmisc_1 @ E @ F @ G @ H ) )
     => ( ( ( k4_zfmisc_1 @ A @ B @ C @ D )
          = k1_xboole_0 )
        | ( ( A = E )
          & ( B = F )
          & ( C = G )
          & ( D = H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1673]) ).

thf(1089,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k9_funct_2 @ A @ B @ C )
      = ( k3_cqc_lang @ ( k4_tarski @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_altcat_1) ).

thf(7796,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k9_funct_2 @ A @ B @ C )
      = ( k3_cqc_lang @ ( k4_tarski @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).

thf(1123,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( ( k1_setfam_1 @ ( k2_xboole_0 @ A @ B ) )
         != ( k3_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_setfam_1) ).

thf(7988,plain,
    ! [A: $i,B: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( ( k1_setfam_1 @ ( k2_xboole_0 @ A @ B ) )
         != ( k3_xboole_0 @ ( k1_setfam_1 @ A ) @ ( k1_setfam_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).

thf(2079,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_enumset1 @ A @ A @ A @ A @ B @ C )
      = ( k1_enumset1 @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_enumset1) ).

thf(12733,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_enumset1 @ A @ A @ A @ A @ B @ C )
      = ( k1_enumset1 @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2079]) ).

thf(194,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( ( ( k1_relat_1 @ A )
            = k1_xboole_0 )
          | ( ( k2_relat_1 @ A )
            = k1_xboole_0 ) )
       => ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).

thf(3655,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( ( ( k1_relat_1 @ A )
            = k1_xboole_0 )
          | ( ( k2_relat_1 @ A )
            = k1_xboole_0 ) )
       => ( A = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(1183,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( v1_partfun1 @ D @ A @ B )
           => ( ( k1_funct_4 @ C @ D )
              = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_4) ).

thf(8216,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( v1_partfun1 @ D @ A @ B )
           => ( ( k1_funct_4 @ C @ D )
              = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).

thf(683,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ D ) @ ( k4_relset_1 @ A @ B @ C ) )
              & ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) )
           => ( r1_tarski @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_funct_2) ).

thf(5948,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ D ) @ ( k4_relset_1 @ A @ B @ C ) )
              & ( r1_tarski @ ( k5_partfun1 @ A @ B @ C ) @ ( k5_partfun1 @ A @ B @ D ) ) )
           => ( r1_tarski @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(813,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ B @ A )
            & ( m2_relset_1 @ D @ B @ A ) )
         => ( ( ( ( k2_relat_1 @ C )
                = B )
              & ( v2_funct_1 @ C )
              & ! [E: $i,F: $i] :
                  ( ( ( ( r2_hidden @ E @ B )
                      & ( ( k1_funct_1 @ D @ E )
                        = F ) )
                   => ( ( r2_hidden @ F @ A )
                      & ( ( k1_funct_1 @ C @ F )
                        = E ) ) )
                  & ( ( ( r2_hidden @ F @ A )
                      & ( ( k1_funct_1 @ C @ F )
                        = E ) )
                   => ( ( r2_hidden @ E @ B )
                      & ( ( k1_funct_1 @ D @ E )
                        = F ) ) ) ) )
           => ( ( A = k1_xboole_0 )
              | ( B = k1_xboole_0 )
              | ( D
                = ( k2_funct_1 @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_2) ).

thf(6513,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ B @ A )
            & ( m2_relset_1 @ D @ B @ A ) )
         => ( ( ( ( k2_relat_1 @ C )
                = B )
              & ( v2_funct_1 @ C )
              & ! [E: $i,F: $i] :
                  ( ( ( ( r2_hidden @ E @ B )
                      & ( ( k1_funct_1 @ D @ E )
                        = F ) )
                   => ( ( r2_hidden @ F @ A )
                      & ( ( k1_funct_1 @ C @ F )
                        = E ) ) )
                  & ( ( ( r2_hidden @ F @ A )
                      & ( ( k1_funct_1 @ C @ F )
                        = E ) )
                   => ( ( r2_hidden @ E @ B )
                      & ( ( k1_funct_1 @ D @ E )
                        = F ) ) ) ) )
           => ( ( A = k1_xboole_0 )
              | ( B = k1_xboole_0 )
              | ( D
                = ( k2_funct_1 @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(811,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ B ) )
     => ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).

thf(6508,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ B ) )
     => ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(464,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( k7_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
        = ( k4_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_relat_1) ).

thf(5030,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( k7_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
        = ( k4_xboole_0 @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(722,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_pboole) ).

thf(6125,plain,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(1387,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ( ( ( r1_binop_1 @ A @ C @ B )
                  & ( r2_binop_1 @ A @ D @ B ) )
               => ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_binop_1) ).

thf(9082,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ( ( ( r1_binop_1 @ A @ C @ B )
                  & ( r2_binop_1 @ A @ D @ B ) )
               => ( C = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387]) ).

thf(2133,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k3_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D )
      = ( k4_zfmisc_1 @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_mcart_1) ).

thf(12995,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k3_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C @ D )
      = ( k4_zfmisc_1 @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2133]) ).

thf(85,axiom,
    ! [A: $i] : ( v2_funct_1 @ ( k9_finseq_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_finseq_3) ).

thf(3127,plain,
    ! [A: $i] : ( v2_funct_1 @ ( k9_finseq_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(456,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( r1_tarski @ ( k5_relat_1 @ ( k7_relat_1 @ B @ A ) @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_relat_1) ).

thf(5001,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( r1_tarski @ ( k5_relat_1 @ ( k7_relat_1 @ B @ A ) @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( k4_funcop_1 @ B @ A @ C )
              = ( k3_funcop_1 @ B @ A @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funcop_1) ).

thf(2701,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( k4_funcop_1 @ B @ A @ C )
              = ( k3_funcop_1 @ B @ A @ ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(2275,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k4_partfun1 @ A @ C ) @ ( k4_partfun1 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_partfun1) ).

thf(13602,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k4_partfun1 @ A @ C ) @ ( k4_partfun1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2275]) ).

thf(307,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k4_card_3 @ ( k10_finseq_1 @ B @ C ) ) )
    <=> ? [D: $i,E: $i] :
          ( ( r2_hidden @ D @ B )
          & ( r2_hidden @ E @ C )
          & ( A
            = ( k10_finseq_1 @ D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funct_6) ).

thf(4241,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ ( k4_card_3 @ ( k10_finseq_1 @ B @ C ) ) )
       => ? [D: $i,E: $i] :
            ( ( r2_hidden @ D @ B )
            & ( r2_hidden @ E @ C )
            & ( A
              = ( k10_finseq_1 @ D @ E ) ) ) )
      & ( ? [D: $i,E: $i] :
            ( ( r2_hidden @ D @ B )
            & ( r2_hidden @ E @ C )
            & ( A
              = ( k10_finseq_1 @ D @ E ) ) )
       => ( r2_hidden @ A @ ( k4_card_3 @ ( k10_finseq_1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(2496,axiom,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s2_filter_1 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s2_filter_1 )
           => ( p1_s2_filter_1 @ ( k2_filter_1 @ f1_s2_filter_1 @ f2_s2_filter_1 @ A ) @ ( k2_filter_1 @ f1_s2_filter_1 @ f2_s2_filter_1 @ B ) ) ) )
   => ! [A: $i] :
        ( ( m2_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s2_filter_1 ) @ ( k8_eqrel_1 @ f1_s2_filter_1 @ f2_s2_filter_1 ) )
       => ! [B: $i] :
            ( ( m2_subset_1 @ B @ ( k1_zfmisc_1 @ f1_s2_filter_1 ) @ ( k8_eqrel_1 @ f1_s2_filter_1 @ f2_s2_filter_1 ) )
           => ( p1_s2_filter_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_filter_1) ).

thf(14498,plain,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s2_filter_1 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s2_filter_1 )
           => ( p1_s2_filter_1 @ ( k2_filter_1 @ f1_s2_filter_1 @ f2_s2_filter_1 @ A ) @ ( k2_filter_1 @ f1_s2_filter_1 @ f2_s2_filter_1 @ B ) ) ) )
   => ! [A: $i] :
        ( ( m2_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s2_filter_1 ) @ ( k8_eqrel_1 @ f1_s2_filter_1 @ f2_s2_filter_1 ) )
       => ! [B: $i] :
            ( ( m2_subset_1 @ B @ ( k1_zfmisc_1 @ f1_s2_filter_1 ) @ ( k8_eqrel_1 @ f1_s2_filter_1 @ f2_s2_filter_1 ) )
           => ( p1_s2_filter_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2496]) ).

thf(139,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B )
            & ( v1_finseq_1 @ B ) )
         => ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
           => ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) )
              & ( v1_funct_1 @ ( k5_relat_1 @ B @ A ) )
              & ( v1_finseq_1 @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finseq_1) ).

thf(3359,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B )
            & ( v1_finseq_1 @ B ) )
         => ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) )
           => ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) )
              & ( v1_funct_1 @ ( k5_relat_1 @ B @ A ) )
              & ( v1_finseq_1 @ ( k5_relat_1 @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(2215,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ A )
                        & ( m2_relset_1 @ E @ B @ A ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ( ! [G: $i] :
                                ( ( m1_subset_1 @ G @ B )
                               => ( ( k8_funct_2 @ B @ A @ D @ G )
                                  = ( k2_binop_1 @ A @ A @ A @ C @ F @ ( k8_funct_2 @ B @ A @ E @ G ) ) ) )
                           => ( D
                              = ( k8_funcop_1 @ A @ B @ C @ F @ E ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funcop_1) ).

thf(13403,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ B @ A )
                        & ( m2_relset_1 @ E @ B @ A ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ( ! [G: $i] :
                                ( ( m1_subset_1 @ G @ B )
                               => ( ( k8_funct_2 @ B @ A @ D @ G )
                                  = ( k2_binop_1 @ A @ A @ A @ C @ F @ ( k8_funct_2 @ B @ A @ E @ G ) ) ) )
                           => ( D
                              = ( k8_funcop_1 @ A @ B @ C @ F @ E ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2215]) ).

thf(1301,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ C @ A )
     => ( ( r1_tarski @ ( k2_relat_1 @ D ) @ B )
       => ( m2_relset_1 @ D @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).

thf(8757,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ C @ A )
     => ( ( r1_tarski @ ( k2_relat_1 @ D ) @ B )
       => ( m2_relset_1 @ D @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).

thf(407,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ( ( ( v1_binop_1 @ C @ B )
                  & ( v2_binop_1 @ C @ B )
                  & ( v3_binop_1 @ C @ B )
                  & ( v1_setwiseo @ C @ B ) )
               => ! [D: $i] :
                    ( ( ( v1_funct_1 @ D )
                      & ( v1_funct_2 @ D @ A @ B )
                      & ( m2_relset_1 @ D @ A @ B ) )
                   => ! [E: $i] :
                        ( ( ( v1_funct_1 @ E )
                          & ( v1_funct_2 @ E @ A @ B )
                          & ( m2_relset_1 @ E @ A @ B ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k5_finsub_1 @ A ) )
                           => ! [G: $i] :
                                ( ( m1_subset_1 @ G @ ( k5_finsub_1 @ A ) )
                               => ( ( ( k8_setwiseo @ A @ B @ D @ F )
                                    = ( k8_setwiseo @ A @ B @ E @ G ) )
                                 => ( ( k7_setwiseo @ A @ B @ C @ F @ D )
                                    = ( k7_setwiseo @ A @ B @ C @ G @ E ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_setwiseo) ).

thf(4781,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ( ( ( v1_binop_1 @ C @ B )
                  & ( v2_binop_1 @ C @ B )
                  & ( v3_binop_1 @ C @ B )
                  & ( v1_setwiseo @ C @ B ) )
               => ! [D: $i] :
                    ( ( ( v1_funct_1 @ D )
                      & ( v1_funct_2 @ D @ A @ B )
                      & ( m2_relset_1 @ D @ A @ B ) )
                   => ! [E: $i] :
                        ( ( ( v1_funct_1 @ E )
                          & ( v1_funct_2 @ E @ A @ B )
                          & ( m2_relset_1 @ E @ A @ B ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ ( k5_finsub_1 @ A ) )
                           => ! [G: $i] :
                                ( ( m1_subset_1 @ G @ ( k5_finsub_1 @ A ) )
                               => ( ( ( k8_setwiseo @ A @ B @ D @ F )
                                    = ( k8_setwiseo @ A @ B @ E @ G ) )
                                 => ( ( k7_setwiseo @ A @ B @ C @ F @ D )
                                    = ( k7_setwiseo @ A @ B @ C @ G @ E ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(1547,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_funct_1 @ ( k1_cat_1 @ A @ B @ C ) )
      & ( m2_relset_1 @ ( k1_cat_1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_cat_1) ).

thf(9911,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_funct_1 @ ( k1_cat_1 @ A @ B @ C ) )
      & ( m2_relset_1 @ ( k1_cat_1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1547]) ).

thf(567,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_relat_1 @ ( k3_funct_4 @ A @ B ) )
        & ( v1_funct_1 @ ( k3_funct_4 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_funct_4) ).

thf(5450,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_relat_1 @ ( k3_funct_4 @ A @ B ) )
        & ( v1_funct_1 @ ( k3_funct_4 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ( k18_mcart_1 @ A )
      = ( k2_mcart_1 @ ( k1_mcart_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_mcart_1) ).

thf(3095,plain,
    ! [A: $i] :
      ( ( k18_mcart_1 @ A )
      = ( k2_mcart_1 @ ( k1_mcart_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(1134,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( ! [G: $i] :
            ( ( m1_subset_1 @ G @ A )
           => ! [H: $i] :
                ( ( m1_subset_1 @ H @ B )
               => ! [I: $i] :
                    ( ( m1_subset_1 @ I @ C )
                   => ! [J: $i] :
                        ( ( m1_subset_1 @ J @ D )
                       => ( ( F
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( E = J ) ) ) ) ) )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 )
          | ( C = k1_xboole_0 )
          | ( D = k1_xboole_0 )
          | ( E
            = ( k11_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_mcart_1) ).

thf(8024,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( ! [G: $i] :
            ( ( m1_subset_1 @ G @ A )
           => ! [H: $i] :
                ( ( m1_subset_1 @ H @ B )
               => ! [I: $i] :
                    ( ( m1_subset_1 @ I @ C )
                   => ! [J: $i] :
                        ( ( m1_subset_1 @ J @ D )
                       => ( ( F
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( E = J ) ) ) ) ) )
       => ( ( A = k1_xboole_0 )
          | ( B = k1_xboole_0 )
          | ( C = k1_xboole_0 )
          | ( D = k1_xboole_0 )
          | ( E
            = ( k11_mcart_1 @ A @ B @ C @ D @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).

thf(864,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( ( k2_funct_2 @ A @ B @ C @ D )
        = ( k9_relat_1 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).

thf(6746,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( ( k2_funct_2 @ A @ B @ C @ D )
        = ( k9_relat_1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

thf(1764,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( r2_hidden @ k1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_orders_1) ).

thf(10973,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( r2_hidden @ k1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1764]) ).

thf(1412,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ~ ( r1_xboole_0 @ ( k3_zfmisc_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ D @ E @ F ) )
     => ( ~ ( r1_xboole_0 @ A @ D )
        & ~ ( r1_xboole_0 @ B @ E )
        & ~ ( r1_xboole_0 @ C @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_mcart_1) ).

thf(9247,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ~ ( r1_xboole_0 @ ( k3_zfmisc_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ D @ E @ F ) )
     => ( ~ ( r1_xboole_0 @ A @ D )
        & ~ ( r1_xboole_0 @ B @ E )
        & ~ ( r1_xboole_0 @ C @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412]) ).

thf(1293,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
         => ( ( ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ C )
              = ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ D ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_partfun1) ).

thf(8734,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ ( k1_tarski @ B ) ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ ( k1_tarski @ B ) ) )
         => ( ( ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ C )
              = ( k4_relset_1 @ A @ ( k1_tarski @ B ) @ D ) )
           => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).

thf(537,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
      | ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ B )
        = ( k1_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_zfmisc_1) ).

thf(5319,plain,
    ! [A: $i,B: $i] :
      ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
      | ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ B )
        = ( k1_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(798,axiom,
    ! [A: $i] :
      ( ( k3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k9_setwiseo @ A ) )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_setwiseo) ).

thf(6457,plain,
    ! [A: $i] :
      ( ( k3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k9_setwiseo @ A ) )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(162,axiom,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_finseq_2 @ C @ B @ ( k4_finseq_2 @ A @ B ) )
             => ! [D: $i] :
                  ( ( m2_finseq_2 @ D @ B @ ( k4_finseq_2 @ A @ B ) )
                 => ( ! [E: $i] :
                        ( ( m2_subset_1 @ E @ k1_numbers @ k5_numbers )
                       => ( ( r2_hidden @ E @ ( k2_finseq_1 @ A ) )
                         => ( ( k1_funct_1 @ C @ E )
                            = ( k1_funct_1 @ D @ E ) ) ) )
                   => ( C = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_finseq_2) ).

thf(3488,plain,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_finseq_2 @ C @ B @ ( k4_finseq_2 @ A @ B ) )
             => ! [D: $i] :
                  ( ( m2_finseq_2 @ D @ B @ ( k4_finseq_2 @ A @ B ) )
                 => ( ! [E: $i] :
                        ( ( m2_subset_1 @ E @ k1_numbers @ k5_numbers )
                       => ( ( r2_hidden @ E @ ( k2_finseq_1 @ A ) )
                         => ( ( k1_funct_1 @ C @ E )
                            = ( k1_funct_1 @ D @ E ) ) ) )
                   => ( C = D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(2028,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
                        & ( m2_relset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
                            & ( m2_relset_1 @ F @ ( k3_zfmisc_1 @ A @ B @ C ) @ D ) )
                         => ( ! [G: $i] :
                                ( ( m1_subset_1 @ G @ A )
                               => ! [H: $i] :
                                    ( ( m1_subset_1 @ H @ B )
                                   => ! [I: $i] :
                                        ( ( m1_subset_1 @ I @ C )
                                       => ( ( k2_multop_1 @ A @ B @ C @ D @ E @ G @ H @ I )
                                          = ( k2_multop_1 @ A @ B @ C @ D @ F @ G @ H @ I ) ) ) ) )
                           => ( E = F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_multop_1) ).

thf(12416,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
                        & ( m2_relset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
                            & ( m2_relset_1 @ F @ ( k3_zfmisc_1 @ A @ B @ C ) @ D ) )
                         => ( ! [G: $i] :
                                ( ( m1_subset_1 @ G @ A )
                               => ! [H: $i] :
                                    ( ( m1_subset_1 @ H @ B )
                                   => ! [I: $i] :
                                        ( ( m1_subset_1 @ I @ C )
                                       => ( ( k2_multop_1 @ A @ B @ C @ D @ E @ G @ H @ I )
                                          = ( k2_multop_1 @ A @ B @ C @ D @ F @ G @ H @ I ) ) ) ) )
                           => ( E = F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2028]) ).

thf(2233,axiom,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s3_funct_2 )
       => ? [B: $i] :
            ( ( m1_subset_1 @ B @ f2_s3_funct_2 )
            & ( p1_s3_funct_2 @ A @ B ) ) )
   => ? [A: $i] :
        ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
        & ( m2_relset_1 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s3_funct_2 )
           => ( p1_s3_funct_2 @ B @ ( k8_funct_2 @ f1_s3_funct_2 @ f2_s3_funct_2 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_2) ).

thf(13461,plain,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s3_funct_2 )
       => ? [B: $i] :
            ( ( m1_subset_1 @ B @ f2_s3_funct_2 )
            & ( p1_s3_funct_2 @ A @ B ) ) )
   => ? [A: $i] :
        ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
        & ( m2_relset_1 @ A @ f1_s3_funct_2 @ f2_s3_funct_2 )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s3_funct_2 )
           => ( p1_s3_funct_2 @ B @ ( k8_funct_2 @ f1_s3_funct_2 @ f2_s3_funct_2 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2233]) ).

thf(1002,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G )
      = ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k3_enumset1 @ C @ D @ E @ F @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_enumset1) ).

thf(7466,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G )
      = ( k2_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k3_enumset1 @ C @ D @ E @ F @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).

thf(1209,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( v4_finsub_1 @ B ) )
         => ( ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
            & ( v4_finsub_1 @ ( k3_xboole_0 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_finsub_1) ).

thf(8316,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( v4_finsub_1 @ B ) )
         => ( ~ ( v1_xboole_0 @ ( k3_xboole_0 @ A @ B ) )
            & ( v4_finsub_1 @ ( k3_xboole_0 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).

thf(271,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( r1_xboole_0 @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
               => ( ( k5_relat_1 @ A @ ( k1_funct_4 @ C @ B ) )
                  = ( k5_relat_1 @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_7) ).

thf(4057,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( r1_xboole_0 @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
               => ( ( k5_relat_1 @ A @ ( k1_funct_4 @ C @ B ) )
                  = ( k5_relat_1 @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(1083,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( k1_functor0 @ A @ B @ C @ D )
        = ( k2_funct_4 @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_functor0) ).

thf(7779,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( k1_functor0 @ A @ B @ C @ D )
        = ( k2_funct_4 @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).

thf(193,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
         => ( ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A )
            = ( k2_funcop_1 @ B @ ( k1_funct_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funcop_1) ).

thf(3652,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
         => ( ( k5_relat_1 @ ( k2_funcop_1 @ B @ C ) @ A )
            = ( k2_funcop_1 @ B @ ( k1_funct_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(986,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ A )
     => ( m2_relset_1 @ ( k1_toler_1 @ A @ B ) @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_toler_1) ).

thf(7348,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ A )
     => ( m2_relset_1 @ ( k1_toler_1 @ A @ B ) @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).

thf(447,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_2) ).

thf(4959,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(838,axiom,
    ? [A: $i] :
      ( ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A )
      & ( v1_finset_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_finseq_1) ).

thf(6633,plain,
    ? [A: $i] :
      ( ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A )
      & ( v1_finset_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(1817,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ! [C: $i] :
              ( ( ~ ( v1_xboole_0 @ C )
                & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
             => ( ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                   => ( ( r2_hidden @ D @ C )
                    <=> ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B ) ) )
               => ( ~ ( r2_hidden @ A @ C )
                  & ! [D: $i] :
                      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
                         => ( ( ( ( r2_hidden @ D @ C )
                                & ( r2_hidden @ E @ C ) )
                             => ( r2_hidden @ ( k4_subset_1 @ A @ D @ E ) @ C ) )
                            & ( ( ( r2_hidden @ D @ C )
                                & ( r1_tarski @ E @ D ) )
                             => ( r2_hidden @ E @ C ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_card_fil) ).

thf(11240,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ! [C: $i] :
              ( ( ~ ( v1_xboole_0 @ C )
                & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
             => ( ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                   => ( ( ( r2_hidden @ D @ C )
                       => ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B ) )
                      & ( ( r2_hidden @ ( k3_subset_1 @ A @ D ) @ B )
                       => ( r2_hidden @ D @ C ) ) ) )
               => ( ~ ( r2_hidden @ A @ C )
                  & ! [D: $i] :
                      ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                     => ! [E: $i] :
                          ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
                         => ( ( ( ( r2_hidden @ D @ C )
                                & ( r2_hidden @ E @ C ) )
                             => ( r2_hidden @ ( k4_subset_1 @ A @ D @ E ) @ C ) )
                            & ( ( ( r2_hidden @ D @ C )
                                & ( r1_tarski @ E @ D ) )
                             => ( r2_hidden @ E @ C ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1817]) ).

thf(891,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ( ( r1_partfun1 @ B @ C )
          <=> ! [D: $i] :
                ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ A @ B ) )
               => ( ( k1_funct_1 @ B @ D )
                  = ( k1_funct_1 @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_2) ).

thf(6899,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ( ( ( r1_partfun1 @ B @ C )
             => ! [D: $i] :
                  ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ A @ B ) )
                 => ( ( k1_funct_1 @ B @ D )
                    = ( k1_funct_1 @ C @ D ) ) ) )
            & ( ! [D: $i] :
                  ( ( r2_hidden @ D @ ( k4_relset_1 @ A @ A @ B ) )
                 => ( ( k1_funct_1 @ B @ D )
                    = ( k1_funct_1 @ C @ D ) ) )
             => ( r1_partfun1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).

thf(1574,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) )
             => ( m1_subset_1 @ ( k5_subset_1 @ ( k1_closure2 @ A @ B ) @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_closure2) ).

thf(10023,plain,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) )
             => ( m1_subset_1 @ ( k5_subset_1 @ ( k1_closure2 @ A @ B ) @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1574]) ).

thf(508,axiom,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k1_numbers )
     => ( ( k8_binop_2 @ ( k8_binop_2 @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k8_binop_2) ).

thf(5223,plain,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k1_numbers )
     => ( ( k8_binop_2 @ ( k8_binop_2 @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(2090,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ( ( k1_funct_4 @ C @ D )
                = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_4) ).

thf(12771,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ( ( k1_funct_4 @ C @ D )
                = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2090]) ).

thf(84,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( ( k1_relat_1 @ B )
                = ( k1_relat_1 @ C ) )
              & ( ( k2_relat_1 @ B )
                = ( k1_tarski @ A ) )
              & ( ( k2_relat_1 @ C )
                = ( k1_tarski @ A ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_1) ).

thf(3124,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( ( k1_relat_1 @ B )
                = ( k1_relat_1 @ C ) )
              & ( ( k2_relat_1 @ B )
                = ( k1_tarski @ A ) )
              & ( ( k2_relat_1 @ C )
                = ( k1_tarski @ A ) ) )
           => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(2227,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

thf(13446,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2227]) ).

thf(2096,axiom,
    ! [A: $i] :
      ~ ( ( v1_finset_1 @ A )
        & ( A != k1_xboole_0 )
        & ( v6_ordinal1 @ A )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ( ( r2_hidden @ C @ A )
                 => ( r1_tarski @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finset_1) ).

thf(12790,plain,
    ! [A: $i] :
      ~ ( ( v1_finset_1 @ A )
        & ( A != k1_xboole_0 )
        & ( v6_ordinal1 @ A )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ( ( r2_hidden @ C @ A )
                 => ( r1_tarski @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2096]) ).

thf(1690,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
      & ( v1_xboole_0 @ B )
      & ( v1_finset_1 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_setwiseo) ).

thf(10531,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
      & ( v1_xboole_0 @ B )
      & ( v1_finset_1 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1690]) ).

thf(1256,axiom,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
        & ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) )
     => ( ( A = k34_binop_2 )
      <=> ! [B: $i] :
            ( ( m1_subset_1 @ B @ k1_numbers )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ k1_numbers )
               => ( ( k2_binop_1 @ k1_numbers @ k1_numbers @ k1_numbers @ A @ B @ C )
                  = ( k10_binop_2 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_binop_2) ).

thf(8547,plain,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
        & ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) )
     => ( ( ( A = k34_binop_2 )
         => ! [B: $i] :
              ( ( m1_subset_1 @ B @ k1_numbers )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ k1_numbers )
                 => ( ( k2_binop_1 @ k1_numbers @ k1_numbers @ k1_numbers @ A @ B @ C )
                    = ( k10_binop_2 @ B @ C ) ) ) ) )
        & ( ! [B: $i] :
              ( ( m1_subset_1 @ B @ k1_numbers )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ k1_numbers )
                 => ( ( k2_binop_1 @ k1_numbers @ k1_numbers @ k1_numbers @ A @ B @ C )
                    = ( k10_binop_2 @ B @ C ) ) ) )
         => ( A = k34_binop_2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).

thf(2433,axiom,
    ! [A: $i,B: $i] :
      ( ( m2_relset_1 @ B @ A @ A )
     => ( B
        = ( k1_toler_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_yellow_0) ).

thf(14197,plain,
    ! [A: $i,B: $i] :
      ( ( m2_relset_1 @ B @ A @ A )
     => ( B
        = ( k1_toler_1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2433]) ).

thf(870,axiom,
    ! [A: $i,B: $i] :
      ( ( k5_xboole_0 @ A @ B )
      = ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t101_xboole_1) ).

thf(6803,plain,
    ! [A: $i,B: $i] :
      ( ( k5_xboole_0 @ A @ B )
      = ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(2468,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
     => ( ( k8_relset_2 @ A @ B @ C @ D )
        = ( k7_relset_2 @ A @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_relset_2) ).

thf(14359,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
     => ( ( k8_relset_2 @ A @ B @ C @ D )
        = ( k7_relset_2 @ A @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2468]) ).

thf(617,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ A @ C )
            & ( m2_relset_1 @ E @ A @ C ) )
         => ( ( k13_funct_3 @ D @ E )
            = ( k5_relat_1 @ ( k12_funct_3 @ A ) @ ( k16_funct_3 @ A @ A @ B @ C @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_funct_3) ).

thf(5613,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ A @ C )
            & ( m2_relset_1 @ E @ A @ C ) )
         => ( ( k13_funct_3 @ D @ E )
            = ( k5_relat_1 @ ( k12_funct_3 @ A ) @ ( k16_funct_3 @ A @ A @ B @ C @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(2276,axiom,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s1_funct_7 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f2_s1_funct_7 )
           => ( r2_hidden @ ( f4_s1_funct_7 @ A @ B ) @ f3_s1_funct_7 ) ) )
   => ? [A: $i] :
        ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ f1_s1_funct_7 @ f2_s1_funct_7 ) @ f3_s1_funct_7 )
        & ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ f1_s1_funct_7 @ f2_s1_funct_7 ) @ f3_s1_funct_7 )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s1_funct_7 )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ f2_s1_funct_7 )
               => ( ( k8_funct_2 @ ( k2_zfmisc_1 @ f1_s1_funct_7 @ f2_s1_funct_7 ) @ f3_s1_funct_7 @ A @ ( k1_domain_1 @ f1_s1_funct_7 @ f2_s1_funct_7 @ B @ C ) )
                  = ( f4_s1_funct_7 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_7) ).

thf(13605,plain,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s1_funct_7 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f2_s1_funct_7 )
           => ( r2_hidden @ ( f4_s1_funct_7 @ A @ B ) @ f3_s1_funct_7 ) ) )
   => ? [A: $i] :
        ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ f1_s1_funct_7 @ f2_s1_funct_7 ) @ f3_s1_funct_7 )
        & ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ f1_s1_funct_7 @ f2_s1_funct_7 ) @ f3_s1_funct_7 )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s1_funct_7 )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ f2_s1_funct_7 )
               => ( ( k8_funct_2 @ ( k2_zfmisc_1 @ f1_s1_funct_7 @ f2_s1_funct_7 ) @ f3_s1_funct_7 @ A @ ( k1_domain_1 @ f1_s1_funct_7 @ f2_s1_funct_7 @ B @ C ) )
                  = ( f4_s1_funct_7 @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2276]) ).

thf(772,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
     => ( ( k1_funct_1 @ ( k1_funct_3 @ ( k9_funct_3 @ B @ C ) ) @ A )
        = ( k2_funct_2 @ ( k2_zfmisc_1 @ B @ C ) @ B @ ( k9_funct_3 @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_borsuk_1) ).

thf(6369,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
     => ( ( k1_funct_1 @ ( k1_funct_3 @ ( k9_funct_3 @ B @ C ) ) @ A )
        = ( k2_funct_2 @ ( k2_zfmisc_1 @ B @ C ) @ B @ ( k9_funct_3 @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(2308,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k7_subset_1 @ A @ B @ C )
                = ( a_3_6_domain_1 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_domain_1) ).

thf(13724,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k7_subset_1 @ A @ B @ C )
                = ( a_3_6_domain_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2308]) ).

thf(2111,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i,D: $i] :
          ( ( ( r1_tarski @ C @ B )
            & ( r1_tarski @ D @ A ) )
         => ( ( ( k1_funct_2 @ C @ D )
              = k1_xboole_0 )
            | ! [E: $i] :
                ( ( m1_subset_1 @ E @ ( k1_funct_2 @ C @ D ) )
               => ( ( v1_funct_1 @ E )
                  & ( m2_relset_1 @ E @ B @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_fraenkel) ).

thf(12868,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i,D: $i] :
          ( ( ( r1_tarski @ C @ B )
            & ( r1_tarski @ D @ A ) )
         => ( ( ( k1_funct_2 @ C @ D )
              = k1_xboole_0 )
            | ! [E: $i] :
                ( ( m1_subset_1 @ E @ ( k1_funct_2 @ C @ D ) )
               => ( ( v1_funct_1 @ E )
                  & ( m2_relset_1 @ E @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2111]) ).

thf(54,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( r1_xboole_0 @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( ( k5_relat_1 @ A @ B )
              = k1_xboole_0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_relat_1) ).

thf(2975,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( r1_xboole_0 @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( ( k5_relat_1 @ A @ B )
              = k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(995,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( ( k10_relset_1 @ A @ B @ C @ A )
          = ( k5_relset_1 @ A @ B @ C ) )
        & ( ( k11_relset_1 @ A @ B @ C @ B )
          = ( k4_relset_1 @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_relset_1) ).

thf(7391,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( ( k10_relset_1 @ A @ B @ C @ A )
          = ( k5_relset_1 @ A @ B @ C ) )
        & ( ( k11_relset_1 @ A @ B @ C @ B )
          = ( k4_relset_1 @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(2166,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ~ ( v1_xboole_0 @ E )
     => ! [F: $i] :
          ( ~ ( v1_xboole_0 @ F )
         => ! [G: $i] :
              ( ( ( v1_funct_1 @ G )
                & ( v1_funct_2 @ G @ ( k2_zfmisc_1 @ A @ B ) @ E )
                & ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ B ) @ E ) )
             => ! [H: $i] :
                  ( ( ( v1_funct_1 @ H )
                    & ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ C @ D ) @ F )
                    & ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ C @ D ) @ F ) )
                 => ( ( v1_funct_1 @ ( k3_funct_4 @ G @ H ) )
                    & ( v1_funct_2 @ ( k3_funct_4 @ G @ H ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) @ ( k2_zfmisc_1 @ E @ F ) )
                    & ( m2_relset_1 @ ( k3_funct_4 @ G @ H ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) @ ( k2_zfmisc_1 @ E @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_4) ).

thf(13175,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ~ ( v1_xboole_0 @ E )
     => ! [F: $i] :
          ( ~ ( v1_xboole_0 @ F )
         => ! [G: $i] :
              ( ( ( v1_funct_1 @ G )
                & ( v1_funct_2 @ G @ ( k2_zfmisc_1 @ A @ B ) @ E )
                & ( m2_relset_1 @ G @ ( k2_zfmisc_1 @ A @ B ) @ E ) )
             => ! [H: $i] :
                  ( ( ( v1_funct_1 @ H )
                    & ( v1_funct_2 @ H @ ( k2_zfmisc_1 @ C @ D ) @ F )
                    & ( m2_relset_1 @ H @ ( k2_zfmisc_1 @ C @ D ) @ F ) )
                 => ( ( v1_funct_1 @ ( k3_funct_4 @ G @ H ) )
                    & ( v1_funct_2 @ ( k3_funct_4 @ G @ H ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) @ ( k2_zfmisc_1 @ E @ F ) )
                    & ( m2_relset_1 @ ( k3_funct_4 @ G @ H ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) @ ( k2_zfmisc_1 @ E @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2166]) ).

thf(1415,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m2_finseq_1 @ B @ A )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k4_finseq_1 @ B ) @ ( k4_finseq_1 @ B ) )
                & ( m2_relset_1 @ C @ ( k4_finseq_1 @ B ) @ ( k4_finseq_1 @ B ) ) )
             => ( m2_finseq_1 @ ( k1_partfun1 @ ( k4_finseq_1 @ B ) @ ( k4_finseq_1 @ B ) @ k5_numbers @ A @ C @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_finseq_2) ).

thf(9257,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m2_finseq_1 @ B @ A )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k4_finseq_1 @ B ) @ ( k4_finseq_1 @ B ) )
                & ( m2_relset_1 @ C @ ( k4_finseq_1 @ B ) @ ( k4_finseq_1 @ B ) ) )
             => ( m2_finseq_1 @ ( k1_partfun1 @ ( k4_finseq_1 @ B ) @ ( k4_finseq_1 @ B ) @ k5_numbers @ A @ C @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415]) ).

thf(286,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_relat_1 @ E )
        & ( v1_funct_1 @ E ) )
     => ! [F: $i] :
          ( ( ( v1_relat_1 @ F )
            & ( v1_funct_1 @ F ) )
         => ( ( ( r1_tarski @ ( k1_relat_1 @ E ) @ ( k2_zfmisc_1 @ A @ B ) )
              & ( r1_tarski @ ( k1_relat_1 @ F ) @ ( k2_zfmisc_1 @ C @ D ) ) )
           => ( r1_tarski @ ( k1_relat_1 @ ( k3_funct_4 @ E @ F ) ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funct_4) ).

thf(4106,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_relat_1 @ E )
        & ( v1_funct_1 @ E ) )
     => ! [F: $i] :
          ( ( ( v1_relat_1 @ F )
            & ( v1_funct_1 @ F ) )
         => ( ( ( r1_tarski @ ( k1_relat_1 @ E ) @ ( k2_zfmisc_1 @ A @ B ) )
              & ( r1_tarski @ ( k1_relat_1 @ F ) @ ( k2_zfmisc_1 @ C @ D ) ) )
           => ( r1_tarski @ ( k1_relat_1 @ ( k3_funct_4 @ E @ F ) ) @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(2579,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_tex_2) ).

thf(14868,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2579]) ).

thf(1576,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i,D: $i] :
          ( ( ( r2_hidden @ C @ ( k2_cantor_1 @ A @ B ) )
            & ( r2_hidden @ D @ ( k2_cantor_1 @ A @ B ) ) )
         => ( r2_hidden @ ( k3_xboole_0 @ C @ D ) @ ( k2_cantor_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_cantor_1) ).

thf(10028,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i,D: $i] :
          ( ( ( r2_hidden @ C @ ( k2_cantor_1 @ A @ B ) )
            & ( r2_hidden @ D @ ( k2_cantor_1 @ A @ B ) ) )
         => ( r2_hidden @ ( k3_xboole_0 @ C @ D ) @ ( k2_cantor_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1576]) ).

thf(2519,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k7_subset_1 @ A @ B @ C )
                = ( a_3_7_domain_1 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_domain_1) ).

thf(14631,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k7_subset_1 @ A @ B @ C )
                = ( a_3_7_domain_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2519]) ).

thf(568,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( k5_relat_1 @ A @ ( k1_funct_4 @ B @ C ) )
                = ( k1_funct_4 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funct_7) ).

thf(5453,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( k5_relat_1 @ A @ ( k1_funct_4 @ B @ C ) )
                = ( k1_funct_4 @ ( k5_relat_1 @ A @ B ) @ ( k5_relat_1 @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(1266,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ A @ C )
            & ( m2_relset_1 @ E @ A @ C ) )
         => ( r1_tarski @ ( k2_relat_1 @ ( k13_funct_3 @ D @ E ) ) @ ( k2_zfmisc_1 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_funct_3) ).

thf(8602,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ A @ C )
            & ( m2_relset_1 @ E @ A @ C ) )
         => ( r1_tarski @ ( k2_relat_1 @ ( k13_funct_3 @ D @ E ) ) @ ( k2_zfmisc_1 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).

thf(1833,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( C != k1_xboole_0 )
       => ( ( v1_funct_1 @ ( k2_funct_4 @ D ) )
          & ( v1_funct_2 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C )
          & ( m2_relset_1 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_funct_4) ).

thf(11334,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( C != k1_xboole_0 )
       => ( ( v1_funct_1 @ ( k2_funct_4 @ D ) )
          & ( v1_funct_2 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C )
          & ( m2_relset_1 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1833]) ).

thf(147,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ A @ C )
     => ( ( r1_tarski @ ( k1_relat_1 @ D ) @ B )
       => ( m2_relset_1 @ D @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_relset_1) ).

thf(3388,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ A @ C )
     => ( ( r1_tarski @ ( k1_relat_1 @ D ) @ B )
       => ( m2_relset_1 @ D @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(1554,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                 => ( ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ A )
                           => ( ( ( r2_hidden @ E @ D )
                                & ( ( k8_funct_2 @ A @ B @ C @ E )
                                  = ( k8_funct_2 @ A @ B @ C @ F ) ) )
                             => ( r2_hidden @ F @ D ) ) ) )
                   => ( ( k3_funct_2 @ A @ B @ C @ ( k2_funct_2 @ A @ B @ C @ D ) )
                      = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_t_0topsp) ).

thf(9930,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                 => ( ! [E: $i] :
                        ( ( m1_subset_1 @ E @ A )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ A )
                           => ( ( ( r2_hidden @ E @ D )
                                & ( ( k8_funct_2 @ A @ B @ C @ E )
                                  = ( k8_funct_2 @ A @ B @ C @ F ) ) )
                             => ( r2_hidden @ F @ D ) ) ) )
                   => ( ( k3_funct_2 @ A @ B @ C @ ( k2_funct_2 @ A @ B @ C @ D ) )
                      = D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1554]) ).

thf(305,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
       => ( r1_tarski @ ( k2_funcop_1 @ ( k1_tarski @ A ) @ ( k1_funct_1 @ B @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_4) ).

thf(4235,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
       => ( r1_tarski @ ( k2_funcop_1 @ ( k1_tarski @ A ) @ ( k1_funct_1 @ B @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(1461,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ~ ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ B )
                 => ( ( E
                      = ( k6_mcart_1 @ A @ B @ C @ D ) )
                  <=> ! [F: $i,G: $i,H: $i] :
                        ( ( D
                          = ( k3_mcart_1 @ F @ G @ H ) )
                       => ( E = G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_mcart_1) ).

thf(9442,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ~ ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ B )
                 => ( ( ( E
                        = ( k6_mcart_1 @ A @ B @ C @ D ) )
                     => ! [F: $i,G: $i,H: $i] :
                          ( ( D
                            = ( k3_mcart_1 @ F @ G @ H ) )
                         => ( E = G ) ) )
                    & ( ! [F: $i,G: $i,H: $i] :
                          ( ( D
                            = ( k3_mcart_1 @ F @ G @ H ) )
                         => ( E = G ) )
                     => ( E
                        = ( k6_mcart_1 @ A @ B @ C @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461]) ).

thf(1636,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( k3_zfmisc_1 @ A @ B @ C )
        = ( k3_zfmisc_1 @ D @ E @ F ) )
     => ( ( ( k3_zfmisc_1 @ A @ B @ C )
          = k1_xboole_0 )
        | ( ( A = D )
          & ( B = E )
          & ( C = F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_mcart_1) ).

thf(10283,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( k3_zfmisc_1 @ A @ B @ C )
        = ( k3_zfmisc_1 @ D @ E @ F ) )
     => ( ( ( k3_zfmisc_1 @ A @ B @ C )
          = k1_xboole_0 )
        | ( ( A = D )
          & ( B = E )
          & ( C = F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1636]) ).

thf(509,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
     => ( r1_xboole_0 @ B @ ( k4_xboole_0 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_xboole_1) ).

thf(5226,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
     => ( r1_xboole_0 @ B @ ( k4_xboole_0 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(712,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( r2_hidden @ A @ ( k2_zfmisc_1 @ D @ E ) ) )
     => ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k3_xboole_0 @ B @ D ) @ ( k3_xboole_0 @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_zfmisc_1) ).

thf(6086,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( r2_hidden @ A @ ( k2_zfmisc_1 @ D @ E ) ) )
     => ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k3_xboole_0 @ B @ D ) @ ( k3_xboole_0 @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(1153,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) @ ( k2_tarski @ D @ E ) )
      = ( k2_enumset1 @ ( k3_mcart_1 @ A @ B @ D ) @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ A @ B @ E ) @ ( k3_mcart_1 @ A @ C @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_mcart_1) ).

thf(8108,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k3_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) @ ( k2_tarski @ D @ E ) )
      = ( k2_enumset1 @ ( k3_mcart_1 @ A @ B @ D ) @ ( k3_mcart_1 @ A @ C @ D ) @ ( k3_mcart_1 @ A @ B @ E ) @ ( k3_mcart_1 @ A @ C @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).

thf(2403,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k9_classes2 @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_classes2) ).

thf(14073,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k9_classes2 @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2403]) ).

thf(25,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( r1_tarski @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) @ ( k9_relat_1 @ ( k4_relat_1 @ B ) @ ( k9_relat_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t163_relat_1) ).

thf(2722,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( r1_tarski @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) @ ( k9_relat_1 @ ( k4_relat_1 @ B ) @ ( k9_relat_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(246,axiom,
    ! [A: $i] : ( v2_funct_2 @ ( k6_partfun1 @ A ) @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_functor1) ).

thf(3943,plain,
    ! [A: $i] : ( v2_funct_2 @ ( k6_partfun1 @ A ) @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(329,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_xboole_0 @ A @ B )
       => ( ( r1_xboole_0 @ ( k1_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ ( k2_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) )
          & ( r1_xboole_0 @ ( k1_relat_1 @ ( k3_xboole_0 @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) ) ) @ ( k2_relat_1 @ ( k3_xboole_0 @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_sysrel) ).

thf(4342,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_xboole_0 @ A @ B )
       => ( ( r1_xboole_0 @ ( k1_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) @ ( k2_relat_1 @ ( k3_xboole_0 @ C @ ( k2_zfmisc_1 @ A @ B ) ) ) )
          & ( r1_xboole_0 @ ( k1_relat_1 @ ( k3_xboole_0 @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) ) ) @ ( k2_relat_1 @ ( k3_xboole_0 @ ( k4_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(2070,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ! [C: $i] :
          ( ( m1_relset_1 @ C @ A @ B )
         => ( ( ( v1_funct_1 @ C )
              & ( v1_funct_2 @ C @ A @ B ) )
           => ( ( v1_funct_1 @ C )
              & ~ ( v1_xboole_0 @ C )
              & ( v1_partfun1 @ C @ A @ B )
              & ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_funct_2) ).

thf(12652,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ! [C: $i] :
          ( ( m1_relset_1 @ C @ A @ B )
         => ( ( ( v1_funct_1 @ C )
              & ( v1_funct_2 @ C @ A @ B ) )
           => ( ( v1_funct_1 @ C )
              & ~ ( v1_xboole_0 @ C )
              & ( v1_partfun1 @ C @ A @ B )
              & ( v1_funct_2 @ C @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2070]) ).

thf(2565,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k1_borsuk_1 @ A @ B @ C )
        = ( k2_funcop_1 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_borsuk_1) ).

thf(14781,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k1_borsuk_1 @ A @ B @ C )
        = ( k2_funcop_1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2565]) ).

thf(2107,axiom,
    ! [A: $i] :
      ( ! [B: $i] :
          ( ( r2_hidden @ B @ A )
         => ( v1_membered @ B ) )
     => ( v1_membered @ ( k3_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_membered) ).

thf(12856,plain,
    ! [A: $i] :
      ( ! [B: $i] :
          ( ( r2_hidden @ B @ A )
         => ( v1_membered @ B ) )
     => ( v1_membered @ ( k3_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2107]) ).

thf(896,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t105_zfmisc_1) ).

thf(6917,plain,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).

thf(2418,axiom,
    m1_subset_1 @ a_0_1_domain_1 @ ( k1_zfmisc_1 @ f2_s8_domain_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s8_domain_1) ).

thf(14145,plain,
    m1_subset_1 @ a_0_1_domain_1 @ ( k1_zfmisc_1 @ f2_s8_domain_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2418]) ).

thf(1886,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( ( B = k1_xboole_0 )
             => ( A = k1_xboole_0 ) )
           => ( ( k1_funct_4 @ C @ D )
              = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_4) ).

thf(11636,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( ( B = k1_xboole_0 )
             => ( A = k1_xboole_0 ) )
           => ( ( k1_funct_4 @ C @ D )
              = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1886]) ).

thf(1137,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
        = A )
    <=> ~ ( r2_hidden @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).

thf(8043,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
          = A )
       => ~ ( r2_hidden @ B @ A ) )
      & ( ~ ( r2_hidden @ B @ A )
       => ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).

thf(1663,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( v1_classes2 @ B ) )
         => ( ( r1_tarski @ A @ B )
            | ( r2_hidden @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_classes2) ).

thf(10436,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( v1_classes2 @ B ) )
         => ( ( r1_tarski @ A @ B )
            | ( r2_hidden @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663]) ).

thf(1085,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( r1_tarski @ ( k2_relat_1 @ ( k13_funct_3 @ A @ B ) ) @ ( k2_zfmisc_1 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_funct_3) ).

thf(7784,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( r1_tarski @ ( k2_relat_1 @ ( k13_funct_3 @ A @ B ) ) @ ( k2_zfmisc_1 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).

thf(2338,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( v1_xboole_0 @ ( k2_yellow21 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_yellow21) ).

thf(13831,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( v1_xboole_0 @ ( k2_yellow21 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2338]) ).

thf(1946,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).

thf(11957,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1946]) ).

thf(2153,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ~ ( ( r2_hidden @ D @ B )
                  <=> ( r2_hidden @ D @ C ) ) )
           => ( B
              = ( k3_subset_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_subset_1) ).

thf(13119,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ~ ( ( ( r2_hidden @ D @ B )
                     => ( r2_hidden @ D @ C ) )
                    & ( ( r2_hidden @ D @ C )
                     => ( r2_hidden @ D @ B ) ) ) )
           => ( B
              = ( k3_subset_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2153]) ).

thf(1445,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
        & ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
     => ( ( B != k1_xboole_0 )
       => ( ( k2_relat_1 @ C )
          = ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_2) ).

thf(9374,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k1_tarski @ A ) @ B )
        & ( m2_relset_1 @ C @ ( k1_tarski @ A ) @ B ) )
     => ( ( B != k1_xboole_0 )
       => ( ( k2_relat_1 @ C )
          = ( k1_tarski @ ( k1_funct_1 @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445]) ).

thf(734,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
     != k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_zfmisc_1) ).

thf(6161,plain,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ ( k1_tarski @ A ) @ B )
     != k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(238,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ( ( ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ B )
                       => ( ( k7_setwiseo @ B @ A @ C @ ( k2_setwiseo @ B @ E ) @ D )
                          = ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_setwiseo) ).

thf(3914,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ( ( ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ B )
                       => ( ( k7_setwiseo @ B @ A @ C @ ( k2_setwiseo @ B @ E ) @ D )
                          = ( k8_funct_2 @ B @ A @ D @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(1012,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ B @ C )
            & ( m2_relset_1 @ E @ B @ C ) )
         => ( ( ( ( k2_relat_1 @ D )
                = B )
              & ( ( k2_relat_1 @ E )
                = C ) )
           => ( ( B = k1_xboole_0 )
              | ( C = k1_xboole_0 )
              | ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
                = C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funct_2) ).

thf(7498,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ B @ C )
            & ( m2_relset_1 @ E @ B @ C ) )
         => ( ( ( ( k2_relat_1 @ D )
                = B )
              & ( ( k2_relat_1 @ E )
                = C ) )
           => ( ( B = k1_xboole_0 )
              | ( C = k1_xboole_0 )
              | ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
                = C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).

thf(1931,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_subset_1) ).

thf(11879,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1931]) ).

thf(2557,axiom,
    ~ ( v1_xboole_0 @ k3_qc_lang1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_qc_lang1) ).

thf(14749,plain,
    ~ ( v1_xboole_0 @ k3_qc_lang1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2557]) ).

thf(1259,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( k1_funct_1 @ ( k1_funct_3 @ A ) @ k1_xboole_0 )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_3) ).

thf(8565,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( k1_funct_1 @ ( k1_funct_3 @ A ) @ k1_xboole_0 )
        = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).

thf(1938,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
                    & ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
                 => ( m2_relset_1 @ ( k2_relat_1 @ D ) @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funcop_1) ).

thf(11906,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
                    & ( m2_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
                 => ( m2_relset_1 @ ( k2_relat_1 @ D ) @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1938]) ).

thf(1323,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ B ) )
        = ( k1_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_zfmisc_1) ).

thf(8861,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ B ) )
        = ( k1_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).

thf(676,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k2_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_zfmisc_1) ).

thf(5895,plain,
    ! [A: $i,B: $i] : ( r1_tarski @ ( k1_zfmisc_1 @ ( k4_xboole_0 @ A @ B ) ) @ ( k2_xboole_0 @ ( k1_tarski @ k1_xboole_0 ) @ ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(2492,axiom,
    ! [A: $i] :
      ( ( r2_hidden @ A @ a_0_38_fraenkel )
    <=> ? [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s21_fraenkel )
          & ( A
            = ( f3_s21_fraenkel @ B ) )
          & ( r2_hidden @ B @ f2_s21_fraenkel ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_38_fraenkel) ).

thf(14482,plain,
    ! [A: $i] :
      ( ( ( r2_hidden @ A @ a_0_38_fraenkel )
       => ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s21_fraenkel )
            & ( A
              = ( f3_s21_fraenkel @ B ) )
            & ( r2_hidden @ B @ f2_s21_fraenkel ) ) )
      & ( ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s21_fraenkel )
            & ( A
              = ( f3_s21_fraenkel @ B ) )
            & ( r2_hidden @ B @ f2_s21_fraenkel ) )
       => ( r2_hidden @ A @ a_0_38_fraenkel ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2492]) ).

thf(310,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_funct_1 @ A )
        & ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_partfun1) ).

thf(4257,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_funct_1 @ A )
        & ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(1854,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ( ( A != k1_xboole_0 )
               => ( m1_subset_1 @ ( k1_enumset1 @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_subset_1) ).

thf(11465,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ( ( A != k1_xboole_0 )
               => ( m1_subset_1 @ ( k1_enumset1 @ B @ C @ D ) @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1854]) ).

thf(913,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_pboole @ B @ A )
         => ! [C: $i] :
              ( ( m1_pboole @ C @ A )
             => ( ( k1_funct_4 @ B @ C )
                = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_closure3) ).

thf(6992,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_pboole @ B @ A )
         => ! [C: $i] :
              ( ( m1_pboole @ C @ A )
             => ( ( k1_funct_4 @ B @ C )
                = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).

thf(2495,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k5_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).

thf(14496,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k5_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2495]) ).

thf(1501,axiom,
    ( ( k1_zfmisc_1 @ k1_xboole_0 )
    = ( k1_tarski @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).

thf(9601,plain,
    ( ( k1_zfmisc_1 @ k1_xboole_0 )
    = ( k1_tarski @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1501]) ).

thf(343,axiom,
    ( ( v1_funct_1 @ k35_binop_2 )
    & ( v1_funct_2 @ k35_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( v1_binop_1 @ k35_binop_2 @ k1_numbers )
    & ( v2_binop_1 @ k35_binop_2 @ k1_numbers )
    & ( v1_setwiseo @ k35_binop_2 @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc17_binop_2) ).

thf(4414,plain,
    ( ( v1_funct_1 @ k35_binop_2 )
    & ( v1_funct_2 @ k35_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( v1_binop_1 @ k35_binop_2 @ k1_numbers )
    & ( v2_binop_1 @ k35_binop_2 @ k1_numbers )
    & ( v1_setwiseo @ k35_binop_2 @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(199,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ ( k4_card_3 @ ( k9_finseq_1 @ B ) ) )
    <=> ? [C: $i] :
          ( ( r2_hidden @ C @ B )
          & ( A
            = ( k9_finseq_1 @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funct_6) ).

thf(3684,plain,
    ! [A: $i,B: $i] :
      ( ( ( r2_hidden @ A @ ( k4_card_3 @ ( k9_finseq_1 @ B ) ) )
       => ? [C: $i] :
            ( ( r2_hidden @ C @ B )
            & ( A
              = ( k9_finseq_1 @ C ) ) ) )
      & ( ? [C: $i] :
            ( ( r2_hidden @ C @ B )
            & ( A
              = ( k9_finseq_1 @ C ) ) )
       => ( r2_hidden @ A @ ( k4_card_3 @ ( k9_finseq_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(1567,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                     => ! [F: $i] :
                          ( ( m2_finseq_1 @ F @ B )
                         => ( m2_finseq_1 @ ( k5_funcop_1 @ E @ D @ F ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_finseq_2) ).

thf(9995,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                     => ! [F: $i] :
                          ( ( m2_finseq_1 @ F @ B )
                         => ( m2_finseq_1 @ ( k5_funcop_1 @ E @ D @ F ) @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567]) ).

thf(1204,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ A @ B )
      = ( k2_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_xboole_1) ).

thf(8299,plain,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ A @ B )
      = ( k2_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).

thf(963,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ ( k2_xboole_0 @ A @ ( k1_tarski @ B ) ) @ C )
    <=> ( ( r2_hidden @ B @ C )
        & ( r1_tarski @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_setwiseo) ).

thf(7234,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ ( k2_xboole_0 @ A @ ( k1_tarski @ B ) ) @ C )
       => ( ( r2_hidden @ B @ C )
          & ( r1_tarski @ A @ C ) ) )
      & ( ( ( r2_hidden @ B @ C )
          & ( r1_tarski @ A @ C ) )
       => ( r1_tarski @ ( k2_xboole_0 @ A @ ( k1_tarski @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).

thf(2502,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A ) )
     => ( ( k10_domain_1 @ A @ B @ C @ D @ E @ F )
        = ( k3_enumset1 @ B @ C @ D @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_domain_1) ).

thf(14554,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A ) )
     => ( ( k10_domain_1 @ A @ B @ C @ D @ E @ F )
        = ( k3_enumset1 @ B @ C @ D @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2502]) ).

thf(159,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k2_ens_1 @ A ) @ ( k2_ens_1 @ A ) ) @ ( k2_ens_1 @ A ) ) )
         => ( ( B
              = ( k10_ens_1 @ A ) )
          <=> ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ ( k2_ens_1 @ A ) )
                     => ( ( r2_hidden @ ( k1_domain_1 @ ( k2_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ C @ D ) @ ( k1_relat_1 @ B ) )
                      <=> ( ( k3_ens_1 @ A @ C )
                          = ( k4_ens_1 @ A @ D ) ) ) ) )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
                 => ! [D: $i] :
                      ( ( m1_subset_1 @ D @ ( k2_ens_1 @ A ) )
                     => ( ( ( k3_ens_1 @ A @ C )
                          = ( k4_ens_1 @ A @ D ) )
                       => ( ( k1_funct_1 @ B @ ( k1_domain_1 @ ( k2_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ C @ D ) )
                          = ( k6_ens_1 @ A @ D @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_ens_1) ).

thf(3452,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ ( k2_ens_1 @ A ) @ ( k2_ens_1 @ A ) ) @ ( k2_ens_1 @ A ) ) )
         => ( ( ( B
                = ( k10_ens_1 @ A ) )
             => ( ! [C: $i] :
                    ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
                   => ! [D: $i] :
                        ( ( m1_subset_1 @ D @ ( k2_ens_1 @ A ) )
                       => ( ( ( r2_hidden @ ( k1_domain_1 @ ( k2_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ C @ D ) @ ( k1_relat_1 @ B ) )
                           => ( ( k3_ens_1 @ A @ C )
                              = ( k4_ens_1 @ A @ D ) ) )
                          & ( ( ( k3_ens_1 @ A @ C )
                              = ( k4_ens_1 @ A @ D ) )
                           => ( r2_hidden @ ( k1_domain_1 @ ( k2_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ C @ D ) @ ( k1_relat_1 @ B ) ) ) ) ) )
                & ! [C: $i] :
                    ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
                   => ! [D: $i] :
                        ( ( m1_subset_1 @ D @ ( k2_ens_1 @ A ) )
                       => ( ( ( k3_ens_1 @ A @ C )
                            = ( k4_ens_1 @ A @ D ) )
                         => ( ( k1_funct_1 @ B @ ( k1_domain_1 @ ( k2_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ C @ D ) )
                            = ( k6_ens_1 @ A @ D @ C ) ) ) ) ) ) )
            & ( ( ! [C: $i] :
                    ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
                   => ! [D: $i] :
                        ( ( m1_subset_1 @ D @ ( k2_ens_1 @ A ) )
                       => ( ( ( r2_hidden @ ( k1_domain_1 @ ( k2_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ C @ D ) @ ( k1_relat_1 @ B ) )
                           => ( ( k3_ens_1 @ A @ C )
                              = ( k4_ens_1 @ A @ D ) ) )
                          & ( ( ( k3_ens_1 @ A @ C )
                              = ( k4_ens_1 @ A @ D ) )
                           => ( r2_hidden @ ( k1_domain_1 @ ( k2_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ C @ D ) @ ( k1_relat_1 @ B ) ) ) ) ) )
                & ! [C: $i] :
                    ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
                   => ! [D: $i] :
                        ( ( m1_subset_1 @ D @ ( k2_ens_1 @ A ) )
                       => ( ( ( k3_ens_1 @ A @ C )
                            = ( k4_ens_1 @ A @ D ) )
                         => ( ( k1_funct_1 @ B @ ( k1_domain_1 @ ( k2_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ C @ D ) )
                            = ( k6_ens_1 @ A @ D @ C ) ) ) ) ) )
             => ( B
                = ( k10_ens_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(1950,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ~ ( v1_xboole_0 @ ( k1_ens_1 @ A ) )
        & ( v1_fraenkel @ ( k1_ens_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ens_1) ).

thf(11978,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ~ ( v1_xboole_0 @ ( k1_ens_1 @ A ) )
        & ( v1_fraenkel @ ( k1_ens_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1950]) ).

thf(1110,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ( ( ( k6_ens_1 @ A @ ( k5_ens_1 @ A @ ( k3_ens_1 @ A @ B ) ) @ B )
              = B )
            & ( ( k6_ens_1 @ A @ B @ ( k5_ens_1 @ A @ ( k4_ens_1 @ A @ B ) ) )
              = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_ens_1) ).

thf(7904,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ( ( ( k6_ens_1 @ A @ ( k5_ens_1 @ A @ ( k3_ens_1 @ A @ B ) ) @ B )
              = B )
            & ( ( k6_ens_1 @ A @ B @ ( k5_ens_1 @ A @ ( k4_ens_1 @ A @ B ) ) )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).

thf(2207,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] : ( m1_card_fil @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_card_fil) ).

thf(13357,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] : ( m1_card_fil @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2207]) ).

thf(1977,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( r2_hidden @ D @ C )
        & ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
        & ! [E: $i] :
            ( ( m1_subset_1 @ E @ A )
           => ! [F: $i] :
                ( ( m1_subset_1 @ F @ B )
               => ( D
                 != ( k4_tarski @ E @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_grcat_1) ).

thf(12130,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( r2_hidden @ D @ C )
        & ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
        & ! [E: $i] :
            ( ( m1_subset_1 @ E @ A )
           => ! [F: $i] :
                ( ( m1_subset_1 @ F @ B )
               => ( D
                 != ( k4_tarski @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1977]) ).

thf(577,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
     => ( ( k2_tarski @ A @ B )
        = ( k1_tarski @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_zfmisc_1) ).

thf(5485,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
     => ( ( k2_tarski @ A @ B )
        = ( k1_tarski @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(242,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B )
        & ( v1_finseq_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k1_tarski @ A ) ) @ ( k1_relat_1 @ C ) )
           => ( ( v1_relat_1 @ ( k4_funcop_1 @ C @ B @ A ) )
              & ( v1_funct_1 @ ( k4_funcop_1 @ C @ B @ A ) )
              & ( v1_finseq_1 @ ( k4_funcop_1 @ C @ B @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_finseq_2) ).

thf(3929,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B )
        & ( v1_finseq_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k1_tarski @ A ) ) @ ( k1_relat_1 @ C ) )
           => ( ( v1_relat_1 @ ( k4_funcop_1 @ C @ B @ A ) )
              & ( v1_funct_1 @ ( k4_funcop_1 @ C @ B @ A ) )
              & ( v1_finseq_1 @ ( k4_funcop_1 @ C @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(662,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( ( k2_tarski @ A @ B )
          = ( k2_tarski @ C @ D ) )
        & ( A != C )
        & ( A != D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).

thf(5832,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( ( k2_tarski @ A @ B )
          = ( k2_tarski @ C @ D ) )
        & ( A != C )
        & ( A != D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(1312,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( r2_hidden @ ( k3_mcart_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ D @ E @ F ) )
    <=> ( ( r2_hidden @ A @ D )
        & ( r2_hidden @ B @ E )
        & ( r2_hidden @ C @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_mcart_1) ).

thf(8812,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( r2_hidden @ ( k3_mcart_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ D @ E @ F ) )
       => ( ( r2_hidden @ A @ D )
          & ( r2_hidden @ B @ E )
          & ( r2_hidden @ C @ F ) ) )
      & ( ( ( r2_hidden @ A @ D )
          & ( r2_hidden @ B @ E )
          & ( r2_hidden @ C @ F ) )
       => ( r2_hidden @ ( k3_mcart_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ D @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).

thf(648,axiom,
    ! [A: $i,B: $i] :
      ( ( k3_cqc_lang @ A @ B )
      = ( k2_funcop_1 @ ( k1_tarski @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_cqc_lang) ).

thf(5771,plain,
    ! [A: $i,B: $i] :
      ( ( k3_cqc_lang @ A @ B )
      = ( k2_funcop_1 @ ( k1_tarski @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(758,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ ( k2_xboole_0 @ B @ ( k1_tarski @ C ) ) )
    <=> ( ( r2_hidden @ A @ B )
        | ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_setwiseo) ).

thf(6284,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ ( k2_xboole_0 @ B @ ( k1_tarski @ C ) ) )
       => ( ( r2_hidden @ A @ B )
          | ( A = C ) ) )
      & ( ( ( r2_hidden @ A @ B )
          | ( A = C ) )
       => ( r2_hidden @ A @ ( k2_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(1644,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ~ ( v1_xboole_0 @ E )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
                     => ( ( A
                          = ( k10_mcart_1 @ B @ C @ D @ E @ F ) )
                      <=> ! [G: $i] :
                            ( ( m1_subset_1 @ G @ B )
                           => ! [H: $i] :
                                ( ( m1_subset_1 @ H @ C )
                               => ! [I: $i] :
                                    ( ( m1_subset_1 @ I @ D )
                                   => ! [J: $i] :
                                        ( ( m1_subset_1 @ J @ E )
                                       => ( ( F
                                            = ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
                                         => ( A = I ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_domain_1) ).

thf(10332,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ~ ( v1_xboole_0 @ E )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
                     => ( ( ( A
                            = ( k10_mcart_1 @ B @ C @ D @ E @ F ) )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ C )
                                 => ! [I: $i] :
                                      ( ( m1_subset_1 @ I @ D )
                                     => ! [J: $i] :
                                          ( ( m1_subset_1 @ J @ E )
                                         => ( ( F
                                              = ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
                                           => ( A = I ) ) ) ) ) ) )
                        & ( ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ C )
                                 => ! [I: $i] :
                                      ( ( m1_subset_1 @ I @ D )
                                     => ! [J: $i] :
                                          ( ( m1_subset_1 @ J @ E )
                                         => ( ( F
                                              = ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
                                           => ( A = I ) ) ) ) ) )
                         => ( A
                            = ( k10_mcart_1 @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644]) ).

thf(1217,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ( ( ( r6_binop_1 @ A @ C @ D )
                              & ( r6_binop_1 @ B @ E @ F ) )
                          <=> ( r6_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_filter_1) ).

thf(8360,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ( ( ( ( r6_binop_1 @ A @ C @ D )
                                & ( r6_binop_1 @ B @ E @ F ) )
                             => ( r6_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) )
                            & ( ( r6_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) )
                             => ( ( r6_binop_1 @ A @ C @ D )
                                & ( r6_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).

thf(1314,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
      & ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_finset_1) ).

thf(8830,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
      & ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314]) ).

thf(900,axiom,
    ! [A: $i,B: $i] :
      ( ( k4_tarski @ A @ B )
      = ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

thf(6928,plain,
    ! [A: $i,B: $i] :
      ( ( k4_tarski @ A @ B )
      = ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(2265,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_enumset1 @ A @ A @ B @ C )
      = ( k1_enumset1 @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_enumset1) ).

thf(13566,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_enumset1 @ A @ A @ B @ C )
      = ( k1_enumset1 @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2265]) ).

thf(1678,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ D )
        & ( r2_hidden @ D @ E )
        & ( r2_hidden @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_ordinal1) ).

thf(10496,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ D )
        & ( r2_hidden @ D @ E )
        & ( r2_hidden @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1678]) ).

thf(1355,axiom,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_xboole_0 @ A )
      & ( v1_funct_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).

thf(8973,plain,
    ? [A: $i] :
      ( ( v1_relat_1 @ A )
      & ( v1_xboole_0 @ A )
      & ( v1_funct_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).

thf(88,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ( ( ( v1_binop_1 @ C @ B )
                  & ( v2_binop_1 @ C @ B )
                  & ( v3_binop_1 @ C @ B ) )
               => ! [D: $i] :
                    ( ~ ( v1_xboole_0 @ D )
                   => ! [E: $i] :
                        ( ( ( v1_funct_1 @ E )
                          & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D )
                          & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D ) )
                       => ( ( ( v1_binop_1 @ E @ D )
                            & ( v2_binop_1 @ E @ D )
                            & ( v3_binop_1 @ E @ D ) )
                         => ! [F: $i] :
                              ( ( ( v1_funct_1 @ F )
                                & ( v1_funct_2 @ F @ A @ B )
                                & ( m2_relset_1 @ F @ A @ B ) )
                             => ! [G: $i] :
                                  ( ( ( v1_funct_1 @ G )
                                    & ( v1_funct_2 @ G @ B @ D )
                                    & ( m2_relset_1 @ G @ B @ D ) )
                                 => ( ! [H: $i] :
                                        ( ( m1_subset_1 @ H @ B )
                                       => ! [I: $i] :
                                            ( ( m1_subset_1 @ I @ B )
                                           => ( ( k8_funct_2 @ B @ D @ G @ ( k2_binop_1 @ B @ B @ B @ C @ H @ I ) )
                                              = ( k2_binop_1 @ D @ D @ D @ E @ ( k8_funct_2 @ B @ D @ G @ H ) @ ( k8_funct_2 @ B @ D @ G @ I ) ) ) ) )
                                   => ! [H: $i] :
                                        ( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
                                       => ( ( H != k1_xboole_0 )
                                         => ( ( k8_funct_2 @ B @ D @ G @ ( k7_setwiseo @ A @ B @ C @ H @ F ) )
                                            = ( k7_setwiseo @ A @ D @ E @ H @ ( k7_funct_2 @ A @ B @ D @ F @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_setwiseo) ).

thf(3139,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ( ( ( v1_binop_1 @ C @ B )
                  & ( v2_binop_1 @ C @ B )
                  & ( v3_binop_1 @ C @ B ) )
               => ! [D: $i] :
                    ( ~ ( v1_xboole_0 @ D )
                   => ! [E: $i] :
                        ( ( ( v1_funct_1 @ E )
                          & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D )
                          & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ D @ D ) @ D ) )
                       => ( ( ( v1_binop_1 @ E @ D )
                            & ( v2_binop_1 @ E @ D )
                            & ( v3_binop_1 @ E @ D ) )
                         => ! [F: $i] :
                              ( ( ( v1_funct_1 @ F )
                                & ( v1_funct_2 @ F @ A @ B )
                                & ( m2_relset_1 @ F @ A @ B ) )
                             => ! [G: $i] :
                                  ( ( ( v1_funct_1 @ G )
                                    & ( v1_funct_2 @ G @ B @ D )
                                    & ( m2_relset_1 @ G @ B @ D ) )
                                 => ( ! [H: $i] :
                                        ( ( m1_subset_1 @ H @ B )
                                       => ! [I: $i] :
                                            ( ( m1_subset_1 @ I @ B )
                                           => ( ( k8_funct_2 @ B @ D @ G @ ( k2_binop_1 @ B @ B @ B @ C @ H @ I ) )
                                              = ( k2_binop_1 @ D @ D @ D @ E @ ( k8_funct_2 @ B @ D @ G @ H ) @ ( k8_funct_2 @ B @ D @ G @ I ) ) ) ) )
                                   => ! [H: $i] :
                                        ( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
                                       => ( ( H != k1_xboole_0 )
                                         => ( ( k8_funct_2 @ B @ D @ G @ ( k7_setwiseo @ A @ B @ C @ H @ F ) )
                                            = ( k7_setwiseo @ A @ D @ E @ H @ ( k7_funct_2 @ A @ B @ D @ F @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(189,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
       => ( r1_tarski @ ( k1_relat_1 @ ( k2_funct_4 @ C ) ) @ ( k2_zfmisc_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_4) ).

thf(3620,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
       => ( r1_tarski @ ( k1_relat_1 @ ( k2_funct_4 @ C ) ) @ ( k2_zfmisc_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(950,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( r2_hidden @ C @ A )
         => ( m1_subset_1 @ ( k1_funct_1 @ B @ C ) @ ( k2_relat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_pboole) ).

thf(7146,plain,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( r2_hidden @ C @ A )
         => ( m1_subset_1 @ ( k1_funct_1 @ B @ C ) @ ( k2_relat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).

thf(2247,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_finset_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).

thf(13509,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_finset_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2247]) ).

thf(1318,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_xboole_0 @ A @ B )
        | ( r1_xboole_0 @ C @ D ) )
     => ( r1_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).

thf(8844,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_xboole_0 @ A @ B )
        | ( r1_xboole_0 @ C @ D ) )
     => ( r1_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).

thf(790,axiom,
    ! [A: $i] :
      ( ( k3_xboole_0 @ A @ k1_xboole_0 )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).

thf(6425,plain,
    ! [A: $i] :
      ( ( k3_xboole_0 @ A @ k1_xboole_0 )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(906,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ A )
                & ( m2_relset_1 @ D @ A @ A ) )
             => ( ( ( r1_partfun1 @ B @ D )
                  & ( r1_partfun1 @ C @ D ) )
               => ( r1_partfun1 @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t152_funct_2) ).

thf(6965,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ A )
                & ( m2_relset_1 @ D @ A @ A ) )
             => ( ( ( r1_partfun1 @ B @ D )
                  & ( r1_partfun1 @ C @ D ) )
               => ( r1_partfun1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(422,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ~ ( ? [B: $i] :
              ( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
              & ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_finseq_1 @ B ) ) )
          & ! [B: $i] :
              ( ( ( v1_relat_1 @ B )
                & ( v1_funct_1 @ B )
                & ( v1_finseq_1 @ B ) )
             => ~ ( r1_tarski @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finseq_1) ).

thf(4851,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ~ ( ? [B: $i] :
              ( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
              & ( r1_tarski @ ( k1_relat_1 @ A ) @ ( k2_finseq_1 @ B ) ) )
          & ! [B: $i] :
              ( ( ( v1_relat_1 @ B )
                & ( v1_funct_1 @ B )
                & ( v1_finseq_1 @ B ) )
             => ~ ( r1_tarski @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(1359,axiom,
    ! [A: $i,B: $i] :
      ( ( k1_funct_1 @ ( k3_cqc_lang @ A @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_cqc_lang) ).

thf(8987,plain,
    ! [A: $i,B: $i] :
      ( ( k1_funct_1 @ ( k3_cqc_lang @ A @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).

thf(398,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( v1_setwiseo @ B @ A )
          <=> ? [C: $i] :
                ( ( m1_subset_1 @ C @ A )
                & ( r3_binop_1 @ A @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_setwiseo) ).

thf(4727,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( v1_setwiseo @ B @ A )
             => ? [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                  & ( r3_binop_1 @ A @ C @ B ) ) )
            & ( ? [C: $i] :
                  ( ( m1_subset_1 @ C @ A )
                  & ( r3_binop_1 @ A @ C @ B ) )
             => ( v1_setwiseo @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(180,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ B @ C )
                    & ( m2_relset_1 @ E @ B @ C ) )
                 => ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
                    & ( v1_funct_2 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ ( k1_relat_1 @ D ) @ C )
                    & ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ ( k1_relat_1 @ D ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_msualg_1) ).

thf(3589,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ B @ C )
                    & ( m2_relset_1 @ E @ B @ C ) )
                 => ( ( v1_funct_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
                    & ( v1_funct_2 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ ( k1_relat_1 @ D ) @ C )
                    & ( m2_relset_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) @ ( k1_relat_1 @ D ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(73,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ( ( ( v3_binop_1 @ C @ A )
                      & ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ B )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                           => ! [G: $i] :
                                ( ( m1_subset_1 @ G @ B )
                               => ( ( k7_setwiseo @ B @ A @ C @ ( k4_setwiseo @ B @ E @ F @ G ) @ D )
                                  = ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ ( k8_funct_2 @ B @ A @ D @ F ) ) @ ( k8_funct_2 @ B @ A @ D @ G ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_setwiseo) ).

thf(3092,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ( ( ( v3_binop_1 @ C @ A )
                      & ( v1_binop_1 @ C @ A )
                      & ( v2_binop_1 @ C @ A ) )
                   => ! [E: $i] :
                        ( ( m1_subset_1 @ E @ B )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                           => ! [G: $i] :
                                ( ( m1_subset_1 @ G @ B )
                               => ( ( k7_setwiseo @ B @ A @ C @ ( k4_setwiseo @ B @ E @ F @ G ) @ D )
                                  = ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ E ) @ ( k8_funct_2 @ B @ A @ D @ F ) ) @ ( k8_funct_2 @ B @ A @ D @ G ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(2546,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k8_classes2 @ A @ B @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k8_classes2) ).

thf(14710,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k8_classes2 @ A @ B @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2546]) ).

thf(2176,axiom,
    ! [A: $i] :
      ( ( v1_finset_1 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
         => ? [C: $i] :
              ( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ A ) @ B )
              & ! [D: $i] :
                  ( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ A ) @ B )
                 => ( ( r1_tarski @ D @ C )
                   => ( D = C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_7) ).

thf(13211,plain,
    ! [A: $i] :
      ( ( v1_finset_1 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
         => ? [C: $i] :
              ( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ A ) @ B )
              & ! [D: $i] :
                  ( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ A ) @ B )
                 => ( ( r1_tarski @ D @ C )
                   => ( D = C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2176]) ).

thf(2016,axiom,
    ! [A: $i] : ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_relset_1) ).

thf(12360,plain,
    ! [A: $i] : ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2016]) ).

thf(70,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
              & ( ( k2_relat_1 @ B )
                = ( k1_relat_1 @ A ) ) )
           => ( ( v2_funct_1 @ B )
              & ( v2_funct_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_funct_1) ).

thf(3067,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
              & ( ( k2_relat_1 @ B )
                = ( k1_relat_1 @ A ) ) )
           => ( ( v2_funct_1 @ B )
              & ( v2_funct_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(1738,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
          & ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ B @ C @ D @ A ) )
          & ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ C @ D @ A @ B ) )
          & ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ D @ A @ B @ C ) ) )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_mcart_1) ).

thf(10806,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
          & ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ B @ C @ D @ A ) )
          & ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ C @ D @ A @ B ) )
          & ~ ( r1_tarski @ A @ ( k4_zfmisc_1 @ D @ A @ B @ C ) ) )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1738]) ).

thf(1707,axiom,
    ( ( v1_funct_1 @ k35_binop_2 )
    & ( v1_funct_2 @ k35_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( m2_relset_1 @ k35_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k35_binop_2) ).

thf(10595,plain,
    ( ( v1_funct_1 @ k35_binop_2 )
    & ( v1_funct_2 @ k35_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
    & ( m2_relset_1 @ k35_binop_2 @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1707]) ).

thf(1672,axiom,
    ~ ( v1_xboole_0 @ k1_numbers ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_numbers) ).

thf(10464,plain,
    ~ ( v1_xboole_0 @ k1_numbers ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1672]) ).

thf(1079,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ ( k15_classes2 @ A ) )
      & ( v1_classes2 @ ( k15_classes2 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_classes2) ).

thf(7764,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ ( k15_classes2 @ A ) )
      & ( v1_classes2 @ ( k15_classes2 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).

thf(784,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v2_membered @ A )
        & ( v2_membered @ B ) )
     => ( ( v1_membered @ ( k2_xboole_0 @ A @ B ) )
        & ( v2_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc23_membered) ).

thf(6408,plain,
    ! [A: $i,B: $i] :
      ( ( ( v2_membered @ A )
        & ( v2_membered @ B ) )
     => ( ( v1_membered @ ( k2_xboole_0 @ A @ B ) )
        & ( v2_membered @ ( k2_xboole_0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(702,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
     => ~ ( ( A != k1_xboole_0 )
          & ( B != k1_xboole_0 )
          & ( C != k1_xboole_0 )
          & ? [E: $i,F: $i,G: $i] :
              ( ( D
                = ( k3_mcart_1 @ E @ F @ G ) )
              & ~ ( ( ( k5_mcart_1 @ A @ B @ C @ D )
                    = E )
                  & ( ( k6_mcart_1 @ A @ B @ C @ D )
                    = F )
                  & ( ( k7_mcart_1 @ A @ B @ C @ D )
                    = G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_mcart_1) ).

thf(6041,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
     => ~ ( ( A != k1_xboole_0 )
          & ( B != k1_xboole_0 )
          & ( C != k1_xboole_0 )
          & ? [E: $i,F: $i,G: $i] :
              ( ( D
                = ( k3_mcart_1 @ E @ F @ G ) )
              & ~ ( ( ( k5_mcart_1 @ A @ B @ C @ D )
                    = E )
                  & ( ( k6_mcart_1 @ A @ B @ C @ D )
                    = F )
                  & ( ( k7_mcart_1 @ A @ B @ C @ D )
                    = G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(1593,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G )
      = ( k2_xboole_0 @ ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) @ ( k1_tarski @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_enumset1) ).

thf(10114,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G )
      = ( k2_xboole_0 @ ( k4_enumset1 @ A @ B @ C @ D @ E @ F ) @ ( k1_tarski @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1593]) ).

thf(593,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ( ( k10_setwiseo @ A @ B @ ( k1_setwiseo @ A ) @ C )
            = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_setwiseo) ).

thf(5536,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ( ( k10_setwiseo @ A @ B @ ( k1_setwiseo @ A ) @ C )
            = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(1448,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_eqrel_1 @ B @ A )
     => ! [C: $i] :
          ( ( m2_finseq_1 @ C @ A )
         => ? [D: $i] :
              ( ( m2_finseq_1 @ D @ B )
              & ( r2_hidden @ C @ ( k4_card_3 @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_pua2mss1) ).

thf(9389,plain,
    ! [A: $i,B: $i] :
      ( ( m1_eqrel_1 @ B @ A )
     => ! [C: $i] :
          ( ( m2_finseq_1 @ C @ A )
         => ? [D: $i] :
              ( ( m2_finseq_1 @ D @ B )
              & ( r2_hidden @ C @ ( k4_card_3 @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448]) ).

thf(51,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_relat_1 @ D )
        & ( v1_funct_1 @ D ) )
     => ( ( ( ( k1_relat_1 @ D )
            = ( k1_tarski @ A ) )
          & ( r2_hidden @ A @ B )
          & ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
       => ( ( v1_funct_1 @ D )
          & ( m2_relset_1 @ D @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_partfun1) ).

thf(2960,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_relat_1 @ D )
        & ( v1_funct_1 @ D ) )
     => ( ( ( ( k1_relat_1 @ D )
            = ( k1_tarski @ A ) )
          & ( r2_hidden @ A @ B )
          & ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
       => ( ( v1_funct_1 @ D )
          & ( m2_relset_1 @ D @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(1956,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D )
        & ( r1_tarski @ E @ F ) )
     => ( r1_tarski @ ( k3_zfmisc_1 @ A @ C @ E ) @ ( k3_zfmisc_1 @ B @ D @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_mcart_1) ).

thf(12027,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D )
        & ( r1_tarski @ E @ F ) )
     => ( r1_tarski @ ( k3_zfmisc_1 @ A @ C @ E ) @ ( k3_zfmisc_1 @ B @ D @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1956]) ).

thf(1578,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k2_zfmisc_1 @ A @ A )
        = ( k2_zfmisc_1 @ B @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).

thf(10033,plain,
    ! [A: $i,B: $i] :
      ( ( ( k2_zfmisc_1 @ A @ A )
        = ( k2_zfmisc_1 @ B @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1578]) ).

thf(1803,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ D ) ) )
    <=> ( ( r2_hidden @ A @ C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_zfmisc_1) ).

thf(11176,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ D ) ) )
       => ( ( r2_hidden @ A @ C )
          & ( B = D ) ) )
      & ( ( ( r2_hidden @ A @ C )
          & ( B = D ) )
       => ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1803]) ).

thf(382,axiom,
    ! [A: $i] :
      ( ( k2_funct_1 @ ( k6_relat_1 @ A ) )
      = ( k6_relat_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_1) ).

thf(4656,plain,
    ! [A: $i] :
      ( ( k2_funct_1 @ ( k6_relat_1 @ A ) )
      = ( k6_relat_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(2390,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v5_grcat_1 @ A ) )
     => ! [B: $i] :
          ( ( m3_grcat_1 @ B @ A )
        <=> ( m1_subset_1 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m3_grcat_1) ).

thf(14037,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v5_grcat_1 @ A ) )
     => ! [B: $i] :
          ( ( ( m3_grcat_1 @ B @ A )
           => ( m1_subset_1 @ B @ A ) )
          & ( ( m1_subset_1 @ B @ A )
           => ( m3_grcat_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2390]) ).

thf(1025,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_funct_4 @ ( k10_pboole @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
      = ( k10_pboole @ ( k2_zfmisc_1 @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_functor0) ).

thf(7547,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_funct_4 @ ( k10_pboole @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
      = ( k10_pboole @ ( k2_zfmisc_1 @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).

thf(2448,axiom,
    ! [A: $i] :
      ( ( r2_hidden @ A @ a_0_1_domain_1 )
    <=> ? [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s8_domain_1 )
          & ( A
            = ( f3_s8_domain_1 @ B ) )
          & ( p1_s8_domain_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_1_domain_1) ).

thf(14257,plain,
    ! [A: $i] :
      ( ( ( r2_hidden @ A @ a_0_1_domain_1 )
       => ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s8_domain_1 )
            & ( A
              = ( f3_s8_domain_1 @ B ) )
            & ( p1_s8_domain_1 @ B ) ) )
      & ( ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s8_domain_1 )
            & ( A
              = ( f3_s8_domain_1 @ B ) )
            & ( p1_s8_domain_1 @ B ) )
       => ( r2_hidden @ A @ a_0_1_domain_1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2448]) ).

thf(1252,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) ) )
     => ( ( v1_relat_1 @ ( k2_mcart_1 @ B ) )
        & ( v1_funct_1 @ ( k2_mcart_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ens_1) ).

thf(8533,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) ) )
     => ( ( v1_relat_1 @ ( k2_mcart_1 @ B ) )
        & ( v1_funct_1 @ ( k2_mcart_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).

thf(1899,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k3_zfmisc_1 @ A @ A @ A )
        = ( k3_zfmisc_1 @ B @ B @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_mcart_1) ).

thf(11681,plain,
    ! [A: $i,B: $i] :
      ( ( ( k3_zfmisc_1 @ A @ A @ A )
        = ( k3_zfmisc_1 @ B @ B @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1899]) ).

thf(1606,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ ( k3_zfmisc_1 @ A @ A @ A ) )
     => ! [C: $i] :
          ( ( m1_pboole @ C @ ( k3_zfmisc_1 @ A @ A @ A ) )
         => ( ! [D: $i,E: $i,F: $i] :
                ( ( ( r2_hidden @ D @ A )
                  & ( r2_hidden @ E @ A )
                  & ( r2_hidden @ F @ A ) )
               => ( ( k1_multop_1 @ B @ D @ E @ F )
                  = ( k1_multop_1 @ C @ D @ E @ F ) ) )
           => ( r6_pboole @ ( k3_zfmisc_1 @ A @ A @ A ) @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_altcat_1) ).

thf(10156,plain,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ ( k3_zfmisc_1 @ A @ A @ A ) )
     => ! [C: $i] :
          ( ( m1_pboole @ C @ ( k3_zfmisc_1 @ A @ A @ A ) )
         => ( ! [D: $i,E: $i,F: $i] :
                ( ( ( r2_hidden @ D @ A )
                  & ( r2_hidden @ E @ A )
                  & ( r2_hidden @ F @ A ) )
               => ( ( k1_multop_1 @ B @ D @ E @ F )
                  = ( k1_multop_1 @ C @ D @ E @ F ) ) )
           => ( r6_pboole @ ( k3_zfmisc_1 @ A @ A @ A ) @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1606]) ).

thf(1351,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( r2_hidden @ A @ B )
        & ~ ( r2_hidden @ C @ B )
        & ~ ( r1_xboole_0 @ ( k2_tarski @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_zfmisc_1) ).

thf(8962,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( r2_hidden @ A @ B )
        & ~ ( r2_hidden @ C @ B )
        & ~ ( r1_xboole_0 @ ( k2_tarski @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).

thf(169,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ( ( ( v1_binop_1 @ C @ B )
                          & ( v2_binop_1 @ C @ B )
                          & ( v3_binop_1 @ C @ B ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                           => ( ( ( k2_funct_2 @ A @ B @ E @ D )
                                = ( k2_setwiseo @ B @ F ) )
                             => ( ( k7_setwiseo @ A @ B @ C @ D @ E )
                                = F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_setwiseo) ).

thf(3548,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ( ( ( v1_binop_1 @ C @ B )
                          & ( v2_binop_1 @ C @ B )
                          & ( v3_binop_1 @ C @ B ) )
                       => ! [F: $i] :
                            ( ( m1_subset_1 @ F @ B )
                           => ( ( ( k2_funct_2 @ A @ B @ E @ D )
                                = ( k2_setwiseo @ B @ F ) )
                             => ( ( k7_setwiseo @ A @ B @ C @ D @ E )
                                = F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(358,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) @ k1_numbers )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ B ) )
     => ( ( k1_metric_1 @ A @ B @ C @ D @ E )
        = ( k1_binop_1 @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_metric_1) ).

thf(4559,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) @ k1_numbers )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ B ) )
     => ( ( k1_metric_1 @ A @ B @ C @ D @ E )
        = ( k1_binop_1 @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(489,axiom,
    ! [A: $i,B: $i] :
      ( ( k3_xboole_0 @ A @ B )
      = ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_xboole_1) ).

thf(5115,plain,
    ! [A: $i,B: $i] :
      ( ( k3_xboole_0 @ A @ B )
      = ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(191,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( ( ( k1_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
            = ( k1_relat_1 @ A ) )
          & ( ( k2_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
            = ( k1_relat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_funct_1) ).

thf(3625,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( ( ( k1_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
            = ( k1_relat_1 @ A ) )
          & ( ( k2_relat_1 @ ( k5_relat_1 @ A @ ( k2_funct_1 @ A ) ) )
            = ( k1_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(379,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( r1_tarski @ ( k1_relat_1 @ A ) @ C )
                & ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ C ) )
             => ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ C )
                = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funct_4) ).

thf(4646,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( r1_tarski @ ( k1_relat_1 @ A ) @ C )
                & ( r1_xboole_0 @ ( k1_relat_1 @ B ) @ C ) )
             => ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ C )
                = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(1224,axiom,
    ( ( k2_funct_4 @ k1_xboole_0 )
    = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funct_5) ).

thf(8392,plain,
    ( ( k2_funct_4 @ k1_xboole_0 )
    = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).

thf(534,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_xboole_1) ).

thf(5308,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(849,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_xboole_0 @ A @ C ) )
     => ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_xboole_1) ).

thf(6674,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_xboole_0 @ A @ C ) )
     => ( r1_tarski @ A @ ( k4_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(1715,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( r1_tarski @ ( k1_funct_5 @ A ) @ ( k1_funct_5 @ B ) )
        & ( r1_tarski @ ( k2_funct_5 @ A ) @ ( k2_funct_5 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_funct_5) ).

thf(10637,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( r1_tarski @ ( k1_funct_5 @ A ) @ ( k1_funct_5 @ B ) )
        & ( r1_tarski @ ( k2_funct_5 @ A ) @ ( k2_funct_5 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1715]) ).

thf(1775,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ~ ( r2_hidden @ k1_xboole_0 @ A )
       => ! [B: $i] :
            ( ( ( v1_funct_1 @ B )
              & ( v1_funct_2 @ B @ A @ ( k3_tarski @ A ) )
              & ( m2_relset_1 @ B @ A @ ( k3_tarski @ A ) ) )
           => ( ( m1_orders_1 @ B @ A )
            <=> ! [C: $i] :
                  ( ( r2_hidden @ C @ A )
                 => ( r2_hidden @ ( k1_funct_1 @ B @ C ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_orders_1) ).

thf(11044,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ~ ( r2_hidden @ k1_xboole_0 @ A )
       => ! [B: $i] :
            ( ( ( v1_funct_1 @ B )
              & ( v1_funct_2 @ B @ A @ ( k3_tarski @ A ) )
              & ( m2_relset_1 @ B @ A @ ( k3_tarski @ A ) ) )
           => ( ( ( m1_orders_1 @ B @ A )
               => ! [C: $i] :
                    ( ( r2_hidden @ C @ A )
                   => ( r2_hidden @ ( k1_funct_1 @ B @ C ) @ C ) ) )
              & ( ! [C: $i] :
                    ( ( r2_hidden @ C @ A )
                   => ( r2_hidden @ ( k1_funct_1 @ B @ C ) @ C ) )
               => ( m1_orders_1 @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1775]) ).

thf(259,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( k2_funct_2 @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) @ ( k1_relat_1 @ A ) @ ( k9_funct_3 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) @ A )
        = ( k1_relat_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_funct_3) ).

thf(4006,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( k2_funct_2 @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) @ ( k1_relat_1 @ A ) @ ( k9_funct_3 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) @ A )
        = ( k1_relat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(2059,axiom,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s13_funct_2 )
       => ( m1_subset_1 @ ( f3_s13_funct_2 @ A ) @ f2_s13_funct_2 ) )
   => ? [A: $i] :
        ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
        & ( m2_relset_1 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s13_funct_2 )
           => ( ( k8_funct_2 @ f1_s13_funct_2 @ f2_s13_funct_2 @ A @ B )
              = ( f3_s13_funct_2 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s13_funct_2) ).

thf(12563,plain,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s13_funct_2 )
       => ( m1_subset_1 @ ( f3_s13_funct_2 @ A ) @ f2_s13_funct_2 ) )
   => ? [A: $i] :
        ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
        & ( m2_relset_1 @ A @ f1_s13_funct_2 @ f2_s13_funct_2 )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s13_funct_2 )
           => ( ( k8_funct_2 @ f1_s13_funct_2 @ f2_s13_funct_2 @ A @ B )
              = ( f3_s13_funct_2 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2059]) ).

thf(296,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
       => ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_relat_1) ).

thf(4170,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k1_relat_1 @ B ) @ A )
       => ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ? [B: $i] :
            ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B )
            & ( ( k5_relat_1 @ A @ B )
              = ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
       => ( v2_funct_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funct_1) ).

thf(2792,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ? [B: $i] :
            ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B )
            & ( ( k5_relat_1 @ A @ B )
              = ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
       => ( v2_funct_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(1160,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( r1_tarski @ ( k2_relat_1 @ ( k1_funct_4 @ A @ B ) ) @ ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_4) ).

thf(8134,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( r1_tarski @ ( k2_relat_1 @ ( k1_funct_4 @ A @ B ) ) @ ( k2_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).

thf(502,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) ) )
     => ( ( k8_setwiseo @ A @ B @ C @ D )
        = ( k9_relat_1 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_setwiseo) ).

thf(5184,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) ) )
     => ( ( k8_setwiseo @ A @ B @ C @ D )
        = ( k9_relat_1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(2506,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
        & ( v1_xboole_0 @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

thf(14571,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
        & ( v1_xboole_0 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2506]) ).

thf(874,axiom,
    ! [A: $i,B: $i] :
      ( ( k6_enumset1 @ A @ A @ A @ A @ A @ A @ A @ B )
      = ( k2_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_enumset1) ).

thf(6814,plain,
    ! [A: $i,B: $i] :
      ( ( k6_enumset1 @ A @ A @ A @ A @ A @ A @ A @ B )
      = ( k2_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(197,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
           => ( ( C
                = ( k1_funct_1 @ A @ B ) )
            <=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) ) )
          & ( ~ ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
           => ( ( C
                = ( k1_funct_1 @ A @ B ) )
            <=> ( C = k1_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).

thf(3665,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
           => ( ( ( C
                  = ( k1_funct_1 @ A @ B ) )
               => ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) )
              & ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
               => ( C
                  = ( k1_funct_1 @ A @ B ) ) ) ) )
          & ( ~ ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
           => ( ( ( C
                  = ( k1_funct_1 @ A @ B ) )
               => ( C = k1_xboole_0 ) )
              & ( ( C = k1_xboole_0 )
               => ( C
                  = ( k1_funct_1 @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(857,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ C )
        = ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ C ) ) )
      & ( ( k2_zfmisc_1 @ C @ ( k2_tarski @ A @ B ) )
        = ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_zfmisc_1) ).

thf(6711,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ C )
        = ( k2_xboole_0 @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ B ) @ C ) ) )
      & ( ( k2_zfmisc_1 @ C @ ( k2_tarski @ A @ B ) )
        = ( k2_xboole_0 @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ A ) ) @ ( k2_zfmisc_1 @ C @ ( k1_tarski @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(181,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( r1_tarski @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
       => ( A
          = ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_sysrel) ).

thf(3593,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( r1_tarski @ A @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) )
       => ( A
          = ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(945,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                         => ! [G: $i] :
                              ( ( m2_finseq_1 @ G @ A )
                             => ! [H: $i] :
                                  ( ( m2_finseq_1 @ H @ B )
                                 => ( ( ( G
                                        = ( k12_finseq_1 @ A @ D ) )
                                      & ( H
                                        = ( k12_finseq_1 @ B @ E ) ) )
                                   => ( ( k3_funcop_1 @ F @ G @ H )
                                      = ( k12_finseq_1 @ C @ ( k2_binop_1 @ A @ B @ C @ F @ D @ E ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_finseq_2) ).

thf(7131,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
                         => ! [G: $i] :
                              ( ( m2_finseq_1 @ G @ A )
                             => ! [H: $i] :
                                  ( ( m2_finseq_1 @ H @ B )
                                 => ( ( ( G
                                        = ( k12_finseq_1 @ A @ D ) )
                                      & ( H
                                        = ( k12_finseq_1 @ B @ E ) ) )
                                   => ( ( k3_funcop_1 @ F @ G @ H )
                                      = ( k12_finseq_1 @ C @ ( k2_binop_1 @ A @ B @ C @ F @ D @ E ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(1916,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m1_relset_1 @ E @ A @ B )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ C @ D )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( r4_nattra_1 @ A @ B @ C @ D @ E @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r4_nattra_1) ).

thf(11745,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m1_relset_1 @ E @ A @ B )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ C @ D )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( r4_nattra_1 @ A @ B @ C @ D @ E @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1916]) ).

thf(866,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
                  ( ( ( r2_hidden @ C @ D )
                    & ( r2_hidden @ D @ E )
                    & ( r2_hidden @ E @ F )
                    & ( r2_hidden @ F @ G )
                    & ( r2_hidden @ G @ B ) )
                 => ( r1_xboole_0 @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_mcart_1) ).

thf(6753,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
                  ( ( ( r2_hidden @ C @ D )
                    & ( r2_hidden @ D @ E )
                    & ( r2_hidden @ E @ F )
                    & ( r2_hidden @ F @ G )
                    & ( r2_hidden @ G @ B ) )
                 => ( r1_xboole_0 @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(831,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ~ ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
             => ( ( ( k5_mcart_1 @ A @ B @ C @ D )
                  = ( k1_mcart_1 @ ( k1_mcart_1 @ D ) ) )
                & ( ( k6_mcart_1 @ A @ B @ C @ D )
                  = ( k2_mcart_1 @ ( k1_mcart_1 @ D ) ) )
                & ( ( k7_mcart_1 @ A @ B @ C @ D )
                  = ( k2_mcart_1 @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_mcart_1) ).

thf(6607,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ~ ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
             => ( ( ( k5_mcart_1 @ A @ B @ C @ D )
                  = ( k1_mcart_1 @ ( k1_mcart_1 @ D ) ) )
                & ( ( k6_mcart_1 @ A @ B @ C @ D )
                  = ( k2_mcart_1 @ ( k1_mcart_1 @ D ) ) )
                & ( ( k7_mcart_1 @ A @ B @ C @ D )
                  = ( k2_mcart_1 @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(131,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k2_zfmisc_1 @ A @ B )
       != k1_xboole_0 )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
         => ( ( C
             != ( k1_mcart_1 @ C ) )
            & ( C
             != ( k2_mcart_1 @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_mcart_1) ).

thf(3336,plain,
    ! [A: $i,B: $i] :
      ( ( ( k2_zfmisc_1 @ A @ B )
       != k1_xboole_0 )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k2_zfmisc_1 @ A @ B ) )
         => ( ( C
             != ( k1_mcart_1 @ C ) )
            & ( C
             != ( k2_mcart_1 @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(957,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( B
          = ( k6_relat_1 @ A ) )
      <=> ! [C: $i,D: $i] :
            ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
          <=> ( ( r2_hidden @ C @ A )
              & ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).

thf(7167,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( ( B
            = ( k6_relat_1 @ A ) )
         => ! [C: $i,D: $i] :
              ( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
               => ( ( r2_hidden @ C @ A )
                  & ( C = D ) ) )
              & ( ( ( r2_hidden @ C @ A )
                  & ( C = D ) )
               => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) )
        & ( ! [C: $i,D: $i] :
              ( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
               => ( ( r2_hidden @ C @ A )
                  & ( C = D ) ) )
              & ( ( ( r2_hidden @ C @ A )
                  & ( C = D ) )
               => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
         => ( B
            = ( k6_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).

thf(1849,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
             => ( ! [E: $i] :
                    ( ( m1_subset_1 @ E @ A )
                   => ( ( r2_hidden @ E @ B )
                    <=> ( ( r2_hidden @ E @ C )
                        & ~ ( r2_hidden @ E @ D ) ) ) )
               => ( B
                  = ( k6_subset_1 @ A @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_subset_1) ).

thf(11433,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
             => ( ! [E: $i] :
                    ( ( m1_subset_1 @ E @ A )
                   => ( ( ( r2_hidden @ E @ B )
                       => ( ( r2_hidden @ E @ C )
                          & ~ ( r2_hidden @ E @ D ) ) )
                      & ( ( ( r2_hidden @ E @ C )
                          & ~ ( r2_hidden @ E @ D ) )
                       => ( r2_hidden @ E @ B ) ) ) )
               => ( B
                  = ( k6_subset_1 @ A @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1849]) ).

thf(827,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ A @ C ) )
     => ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).

thf(6584,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ A @ C ) )
     => ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(2050,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
    <=> ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).

thf(12527,plain,
    ! [A: $i] :
      ( ( ( v1_xboole_0 @ A )
       => ( A = k1_xboole_0 ) )
      & ( ( A = k1_xboole_0 )
       => ( v1_xboole_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2050]) ).

thf(1008,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ B )
     => ( ( ( r2_hidden @ C @ B )
          & ( A != C ) )
        | ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
          = ( k1_tarski @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_zfmisc_1) ).

thf(7483,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ A @ B )
     => ( ( ( r2_hidden @ C @ B )
          & ( A != C ) )
        | ( ( k3_xboole_0 @ ( k2_tarski @ A @ C ) @ B )
          = ( k1_tarski @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).

thf(1520,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ C @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_enumset1) ).

thf(9755,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ C @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1520]) ).

thf(1072,axiom,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
        & ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) )
     => ( ( A = k33_binop_2 )
      <=> ! [B: $i] :
            ( ( m1_subset_1 @ B @ k1_numbers )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ k1_numbers )
               => ( ( k2_binop_1 @ k1_numbers @ k1_numbers @ k1_numbers @ A @ B @ C )
                  = ( k9_binop_2 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_binop_2) ).

thf(7732,plain,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers )
        & ( m2_relset_1 @ A @ ( k2_zfmisc_1 @ k1_numbers @ k1_numbers ) @ k1_numbers ) )
     => ( ( ( A = k33_binop_2 )
         => ! [B: $i] :
              ( ( m1_subset_1 @ B @ k1_numbers )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ k1_numbers )
                 => ( ( k2_binop_1 @ k1_numbers @ k1_numbers @ k1_numbers @ A @ B @ C )
                    = ( k9_binop_2 @ B @ C ) ) ) ) )
        & ( ! [B: $i] :
              ( ( m1_subset_1 @ B @ k1_numbers )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ k1_numbers )
                 => ( ( k2_binop_1 @ k1_numbers @ k1_numbers @ k1_numbers @ A @ B @ C )
                    = ( k9_binop_2 @ B @ C ) ) ) )
         => ( A = k33_binop_2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).

thf(921,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ? [D: $i] :
            ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
            & ? [E: $i,F: $i,G: $i] :
                ( ( D
                  = ( k3_mcart_1 @ E @ F @ G ) )
                & ~ ( ( ( k5_mcart_1 @ A @ B @ C @ D )
                      = E )
                    & ( ( k6_mcart_1 @ A @ B @ C @ D )
                      = F )
                    & ( ( k7_mcart_1 @ A @ B @ C @ D )
                      = G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_mcart_1) ).

thf(7034,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ? [D: $i] :
            ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
            & ? [E: $i,F: $i,G: $i] :
                ( ( D
                  = ( k3_mcart_1 @ E @ F @ G ) )
                & ~ ( ( ( k5_mcart_1 @ A @ B @ C @ D )
                      = E )
                    & ( ( k6_mcart_1 @ A @ B @ C @ D )
                      = F )
                    & ( ( k7_mcart_1 @ A @ B @ C @ D )
                      = G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).

thf(209,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k2_tarski @ B @ C ) @ ( k2_tarski @ D @ E ) ) )
     => ( ( ( ( k1_mcart_1 @ A )
            = B )
          | ( ( k1_mcart_1 @ A )
            = C ) )
        & ( ( ( k2_mcart_1 @ A )
            = D )
          | ( ( k2_mcart_1 @ A )
            = E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_mcart_1) ).

thf(3729,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k2_tarski @ B @ C ) @ ( k2_tarski @ D @ E ) ) )
     => ( ( ( ( k1_mcart_1 @ A )
            = B )
          | ( ( k1_mcart_1 @ A )
            = C ) )
        & ( ( ( k2_mcart_1 @ A )
            = D )
          | ( ( k2_mcart_1 @ A )
            = E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(2405,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k4_classes2 @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_classes2) ).

thf(14083,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k4_classes2 @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2405]) ).

thf(1601,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) ) )
     => ( m1_subset_1 @ ( k8_setwiseo @ A @ B @ C @ D ) @ ( k5_finsub_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_setwiseo) ).

thf(10135,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) ) )
     => ( m1_subset_1 @ ( k8_setwiseo @ A @ B @ C @ D ) @ ( k5_finsub_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1601]) ).

thf(22,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( ( k1_relat_1 @ C )
            = A )
          & ! [D: $i] :
              ( ( r2_hidden @ D @ A )
             => ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
       => ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ A @ B )
          & ( m2_relset_1 @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_funct_2) ).

thf(2707,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( ( k1_relat_1 @ C )
            = A )
          & ! [D: $i] :
              ( ( r2_hidden @ D @ A )
             => ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ B ) ) )
       => ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ A @ B )
          & ( m2_relset_1 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(1619,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k1_finsub_1 @ A @ B @ C )
        = ( k1_finsub_1 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k1_finsub_1) ).

thf(10220,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k1_finsub_1 @ A @ B @ C )
        = ( k1_finsub_1 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1619]) ).

thf(1185,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ B @ A )
            & ( m2_relset_1 @ D @ B @ A ) )
         => ( ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
              = ( k6_partfun1 @ A ) )
           => ( ( B = k1_xboole_0 )
              | ( ( v2_funct_1 @ C )
                & ( ( k2_relat_1 @ D )
                  = A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_funct_2) ).

thf(8221,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ B @ A )
            & ( m2_relset_1 @ D @ B @ A ) )
         => ( ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
              = ( k6_partfun1 @ A ) )
           => ( ( B = k1_xboole_0 )
              | ( ( v2_funct_1 @ C )
                & ( ( k2_relat_1 @ D )
                  = A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).

thf(393,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( ( k2_funct_1 @ A )
          = ( k4_relat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).

thf(4710,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( ( k2_funct_1 @ A )
          = ( k4_relat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(1983,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D ) )
     => ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).

thf(12157,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D ) )
     => ( r1_tarski @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1983]) ).

thf(1408,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( k9_relat_1 @ ( k3_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
            = ( k3_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_relset_2) ).

thf(9234,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( k9_relat_1 @ ( k3_xboole_0 @ B @ C ) @ ( k1_tarski @ A ) )
            = ( k3_xboole_0 @ ( k9_relat_1 @ B @ ( k1_tarski @ A ) ) @ ( k9_relat_1 @ C @ ( k1_tarski @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408]) ).

thf(2368,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k5_classes2 @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_classes2) ).

thf(13959,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k5_classes2 @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2368]) ).

thf(1858,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( r2_hidden @ B @ ( k1_ens_1 @ A ) )
        <=> ? [C: $i] :
              ( ( m1_subset_1 @ C @ A )
              & ? [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                  & ( ( D = k1_xboole_0 )
                   => ( C = k1_xboole_0 ) )
                  & ( v1_funct_1 @ B )
                  & ( v1_funct_2 @ B @ C @ D )
                  & ( m2_relset_1 @ B @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_ens_1) ).

thf(11482,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( r2_hidden @ B @ ( k1_ens_1 @ A ) )
           => ? [C: $i] :
                ( ( m1_subset_1 @ C @ A )
                & ? [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                    & ( ( D = k1_xboole_0 )
                     => ( C = k1_xboole_0 ) )
                    & ( v1_funct_1 @ B )
                    & ( v1_funct_2 @ B @ C @ D )
                    & ( m2_relset_1 @ B @ C @ D ) ) ) )
          & ( ? [C: $i] :
                ( ( m1_subset_1 @ C @ A )
                & ? [D: $i] :
                    ( ( m1_subset_1 @ D @ A )
                    & ( ( D = k1_xboole_0 )
                     => ( C = k1_xboole_0 ) )
                    & ( v1_funct_1 @ B )
                    & ( v1_funct_2 @ B @ C @ D )
                    & ( m2_relset_1 @ B @ C @ D ) ) )
           => ( r2_hidden @ B @ ( k1_ens_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1858]) ).

thf(806,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ~ ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
             => ! [F: $i] :
                  ( ( m1_subset_1 @ F @ D )
                 => ( ( F
                      = ( k11_mcart_1 @ A @ B @ C @ D @ E ) )
                  <=> ! [G: $i,H: $i,I: $i,J: $i] :
                        ( ( E
                          = ( k4_mcart_1 @ G @ H @ I @ J ) )
                       => ( F = J ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_mcart_1) ).

thf(6489,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ~ ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
             => ! [F: $i] :
                  ( ( m1_subset_1 @ F @ D )
                 => ( ( ( F
                        = ( k11_mcart_1 @ A @ B @ C @ D @ E ) )
                     => ! [G: $i,H: $i,I: $i,J: $i] :
                          ( ( E
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( F = J ) ) )
                    & ( ! [G: $i,H: $i,I: $i,J: $i] :
                          ( ( E
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( F = J ) )
                     => ( F
                        = ( k11_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(1987,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_xboole_0 @ ( k2_funct_5 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_yellow_3) ).

thf(12166,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_xboole_0 @ ( k2_funct_5 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1987]) ).

thf(2580,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ( r1_cat_2 @ ( k12_ens_1 @ B ) @ ( k12_ens_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_ens_1) ).

thf(14872,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ( r1_cat_2 @ ( k12_ens_1 @ B ) @ ( k12_ens_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2580]) ).

thf(459,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ! [D: $i] :
            ~ ( ( r2_hidden @ D @ B )
              & ! [E: $i] :
                  ~ ( ( r2_hidden @ E @ A )
                    & ( D
                      = ( k1_funct_1 @ C @ E ) ) ) )
       => ( ( B = k1_xboole_0 )
          | ( ( k2_relat_1 @ C )
            = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_2) ).

thf(5008,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ! [D: $i] :
            ~ ( ( r2_hidden @ D @ B )
              & ! [E: $i] :
                  ~ ( ( r2_hidden @ E @ A )
                    & ( D
                      = ( k1_funct_1 @ C @ E ) ) ) )
       => ( ( B = k1_xboole_0 )
          | ( ( k2_relat_1 @ C )
            = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(2386,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
         => ( ( k7_setfam_1 @ A @ B )
            = ( a_2_0_card_fil @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_card_fil) ).

thf(14026,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
         => ( ( k7_setfam_1 @ A @ B )
            = ( a_2_0_card_fil @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2386]) ).

thf(2359,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_card_fil) ).

thf(13919,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2359]) ).

thf(346,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( ( k2_xboole_0 @ A @ B )
              = ( k1_funct_4 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_funct_4) ).

thf(4468,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( ( k2_xboole_0 @ A @ B )
              = ( k1_funct_4 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(387,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A != B )
        & ( B != C )
        & ( C != A ) )
    <=> ( v2_funct_1 @ ( k11_finseq_1 @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_finseq_3) ).

thf(4681,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( A != B )
          & ( B != C )
          & ( C != A ) )
       => ( v2_funct_1 @ ( k11_finseq_1 @ A @ B @ C ) ) )
      & ( ( v2_funct_1 @ ( k11_finseq_1 @ A @ B @ C ) )
       => ( ( A != B )
          & ( B != C )
          & ( C != A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(1621,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B )
        & ( v1_finset_1 @ C )
        & ( v1_finset_1 @ D ) )
     => ( v1_finset_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc16_finset_1) ).

thf(10225,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B )
        & ( v1_finset_1 @ C )
        & ( v1_finset_1 @ D ) )
     => ( v1_finset_1 @ ( k4_zfmisc_1 @ A @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1621]) ).

thf(2061,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
     => ( ( ( k2_zfmisc_1 @ A @ B )
          = k1_xboole_0 )
        | ( ( r1_tarski @ A @ C )
          & ( r1_tarski @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).

thf(12574,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( r1_tarski @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
     => ( ( ( k2_zfmisc_1 @ A @ B )
          = k1_xboole_0 )
        | ( ( r1_tarski @ A @ C )
          & ( r1_tarski @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2061]) ).

thf(839,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i,D: $i] :
          ( ( k1_multop_1 @ A @ B @ C @ D )
          = ( k1_funct_1 @ A @ ( k3_mcart_1 @ B @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_multop_1) ).

thf(6639,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i,C: $i,D: $i] :
          ( ( k1_multop_1 @ A @ B @ C @ D )
          = ( k1_funct_1 @ A @ ( k3_mcart_1 @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(2083,axiom,
    ( ( v1_funct_1 @ k32_binop_2 )
    & ( v1_funct_2 @ k32_binop_2 @ k1_numbers @ k1_numbers )
    & ( m2_relset_1 @ k32_binop_2 @ k1_numbers @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k32_binop_2) ).

thf(12743,plain,
    ( ( v1_funct_1 @ k32_binop_2 )
    & ( v1_funct_2 @ k32_binop_2 @ k1_numbers @ k1_numbers )
    & ( m2_relset_1 @ k32_binop_2 @ k1_numbers @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2083]) ).

thf(308,axiom,
    ( ( v1_relat_1 @ k1_xboole_0 )
    & ( v1_funct_1 @ k1_xboole_0 )
    & ( v1_finseq_1 @ k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finseq_1) ).

thf(4250,plain,
    ( ( v1_relat_1 @ k1_xboole_0 )
    & ( v1_funct_1 @ k1_xboole_0 )
    & ( v1_finseq_1 @ k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(1262,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_eqrel_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                   => ( ( r2_hidden @ D @ B )
                     => ( ( r1_xboole_0 @ D @ C )
                        | ( r1_tarski @ D @ C ) ) ) )
               => ( C
                  = ( k3_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ ( k2_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_borsuk_1) ).

thf(8584,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_eqrel_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                   => ( ( r2_hidden @ D @ B )
                     => ( ( r1_xboole_0 @ D @ C )
                        | ( r1_tarski @ D @ C ) ) ) )
               => ( C
                  = ( k3_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ ( k2_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).

thf(1178,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_xboole_0 @ A @ B )
     => ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_xboole_1) ).

thf(8197,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_xboole_0 @ A @ B )
     => ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).

thf(1966,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ( ( v1_funct_1 @ ( k6_pralg_1 @ A @ B ) )
        & ( v1_funct_2 @ ( k6_pralg_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) )
        & ( m2_relset_1 @ ( k6_pralg_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pralg_1) ).

thf(12061,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ( ( v1_funct_1 @ ( k6_pralg_1 @ A @ B ) )
        & ( v1_funct_2 @ ( k6_pralg_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) )
        & ( m2_relset_1 @ ( k6_pralg_1 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1966]) ).

thf(2018,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( k6_relat_1 @ A )
       != k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relset_1) ).

thf(12370,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( k6_relat_1 @ A )
       != k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2018]) ).

thf(2048,axiom,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s14_funct_2 )
       => ? [B: $i] :
            ( ( m1_subset_1 @ B @ f2_s14_funct_2 )
            & ( p1_s14_funct_2 @ A @ B ) ) )
   => ? [A: $i] :
        ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
        & ( m2_relset_1 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s14_funct_2 )
           => ( p1_s14_funct_2 @ B @ ( k8_funct_2 @ f1_s14_funct_2 @ f2_s14_funct_2 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s14_funct_2) ).

thf(12516,plain,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s14_funct_2 )
       => ? [B: $i] :
            ( ( m1_subset_1 @ B @ f2_s14_funct_2 )
            & ( p1_s14_funct_2 @ A @ B ) ) )
   => ? [A: $i] :
        ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
        & ( m2_relset_1 @ A @ f1_s14_funct_2 @ f2_s14_funct_2 )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s14_funct_2 )
           => ( p1_s14_funct_2 @ B @ ( k8_funct_2 @ f1_s14_funct_2 @ f2_s14_funct_2 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2048]) ).

thf(2516,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_card_fil @ B @ A )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ~ ( v1_xboole_0 @ ( k3_card_fil @ A @ B @ C ) )
        & ( m1_subset_1 @ ( k3_card_fil @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_card_fil) ).

thf(14618,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_card_fil @ B @ A )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ~ ( v1_xboole_0 @ ( k3_card_fil @ A @ B @ C ) )
        & ( m1_subset_1 @ ( k3_card_fil @ A @ B @ C ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2516]) ).

thf(410,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C )
        & ( v2_funct_1 @ C ) )
     => ! [D: $i] :
          ( ( v1_relat_1 @ D )
         => ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ ( k5_relat_1 @ C @ D ) @ ( k2_funct_1 @ C ) ) )
          <=> ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
              & ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
              & ( r2_hidden @ ( k4_tarski @ ( k1_funct_1 @ C @ A ) @ ( k1_funct_1 @ C @ B ) ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow21) ).

thf(4791,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C )
        & ( v2_funct_1 @ C ) )
     => ! [D: $i] :
          ( ( v1_relat_1 @ D )
         => ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ ( k5_relat_1 @ C @ D ) @ ( k2_funct_1 @ C ) ) )
             => ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
                & ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
                & ( r2_hidden @ ( k4_tarski @ ( k1_funct_1 @ C @ A ) @ ( k1_funct_1 @ C @ B ) ) @ D ) ) )
            & ( ( ( r2_hidden @ A @ ( k1_relat_1 @ C ) )
                & ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
                & ( r2_hidden @ ( k4_tarski @ ( k1_funct_1 @ C @ A ) @ ( k1_funct_1 @ C @ B ) ) @ D ) )
             => ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ ( k5_relat_1 @ C @ D ) @ ( k2_funct_1 @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(2489,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ~ ( v1_xboole_0 @ E ) )
     => ( ( r2_hidden @ A @ ( a_4_2_domain_1 @ B @ C @ D @ E ) )
      <=> ? [F: $i,G: $i,H: $i,I: $i] :
            ( ( m1_subset_1 @ F @ B )
            & ( m1_subset_1 @ G @ C )
            & ( m1_subset_1 @ H @ D )
            & ( m1_subset_1 @ I @ E )
            & ( A
              = ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) )
            & ( p1_s4_domain_1 @ F @ G @ H @ I ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_2_domain_1) ).

thf(14457,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ~ ( v1_xboole_0 @ E ) )
     => ( ( ( r2_hidden @ A @ ( a_4_2_domain_1 @ B @ C @ D @ E ) )
         => ? [F: $i,G: $i,H: $i,I: $i] :
              ( ( m1_subset_1 @ F @ B )
              & ( m1_subset_1 @ G @ C )
              & ( m1_subset_1 @ H @ D )
              & ( m1_subset_1 @ I @ E )
              & ( A
                = ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) )
              & ( p1_s4_domain_1 @ F @ G @ H @ I ) ) )
        & ( ? [F: $i,G: $i,H: $i,I: $i] :
              ( ( m1_subset_1 @ F @ B )
              & ( m1_subset_1 @ G @ C )
              & ( m1_subset_1 @ H @ D )
              & ( m1_subset_1 @ I @ E )
              & ( A
                = ( k5_domain_1 @ B @ C @ D @ E @ F @ G @ H @ I ) )
              & ( p1_s4_domain_1 @ F @ G @ H @ I ) )
         => ( r2_hidden @ A @ ( a_4_2_domain_1 @ B @ C @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2489]) ).

thf(510,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
     => ( ( k7_filter_1 @ A @ B @ C @ D )
        = ( k3_funct_4 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_filter_1) ).

thf(5228,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
     => ( ( k7_filter_1 @ A @ B @ C @ D )
        = ( k3_funct_4 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(192,axiom,
    ! [A: $i,B: $i] :
      ~ ( ~ ( ( A = k1_xboole_0 )
            & ( B != k1_xboole_0 ) )
        & ! [C: $i] :
            ( ( ( v1_relat_1 @ C )
              & ( v1_funct_1 @ C ) )
           => ~ ( ( B
                  = ( k1_relat_1 @ C ) )
                & ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_1) ).

thf(3630,plain,
    ! [A: $i,B: $i] :
      ~ ( ~ ( ( A = k1_xboole_0 )
            & ( B != k1_xboole_0 ) )
        & ! [C: $i] :
            ( ( ( v1_relat_1 @ C )
              & ( v1_funct_1 @ C ) )
           => ~ ( ( B
                  = ( k1_relat_1 @ C ) )
                & ( r1_tarski @ ( k2_relat_1 @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(1927,axiom,
    ! [A: $i] :
      ( ( ( v1_finset_1 @ A )
        & ! [B: $i] :
            ( ( r2_hidden @ B @ A )
           => ( v1_finset_1 @ B ) ) )
    <=> ( v1_finset_1 @ ( k3_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finset_1) ).

thf(11847,plain,
    ! [A: $i] :
      ( ( ( ( v1_finset_1 @ A )
          & ! [B: $i] :
              ( ( r2_hidden @ B @ A )
             => ( v1_finset_1 @ B ) ) )
       => ( v1_finset_1 @ ( k3_tarski @ A ) ) )
      & ( ( v1_finset_1 @ ( k3_tarski @ A ) )
       => ( ( v1_finset_1 @ A )
          & ! [B: $i] :
              ( ( r2_hidden @ B @ A )
             => ( v1_finset_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1927]) ).

thf(2281,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( ( k1_funct_7 @ A @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_7) ).

thf(13625,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( ( k1_funct_7 @ A @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2281]) ).

thf(165,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
       => ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
          = ( k1_funct_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_funct_1) ).

thf(3501,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ C ) @ A ) )
       => ( ( k1_funct_1 @ ( k7_relat_1 @ C @ A ) @ B )
          = ( k1_funct_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(61,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
           => ( ( k1_funct_1 @ ( k1_funct_4 @ C @ B ) @ A )
              = ( k1_funct_1 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_4) ).

thf(3003,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
           => ( ( k1_funct_1 @ ( k1_funct_4 @ C @ B ) @ A )
              = ( k1_funct_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(37,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( r6_binop_1 @ A @ B @ C )
          <=> ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ! [E: $i] :
                    ( ( m1_subset_1 @ E @ A )
                   => ! [F: $i] :
                        ( ( m1_subset_1 @ F @ A )
                       => ( ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
                            = ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) )
                          & ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
                            = ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_binop_1) ).

thf(2764,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( r6_binop_1 @ A @ B @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ( ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
                              = ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) )
                            & ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
                              = ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) ) )
            & ( ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ A )
                         => ( ( ( k1_binop_1 @ B @ D @ ( k1_binop_1 @ C @ E @ F ) )
                              = ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ E ) @ ( k1_binop_1 @ B @ D @ F ) ) )
                            & ( ( k1_binop_1 @ B @ ( k1_binop_1 @ C @ D @ E ) @ F )
                              = ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) )
             => ( r6_binop_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(1534,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( r1_realset1 @ A @ B @ C )
          <=> ! [D: $i] :
                ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
               => ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_realset1) ).

thf(9824,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( ( r1_realset1 @ A @ B @ C )
             => ! [D: $i] :
                  ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
                 => ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) ) )
            & ( ! [D: $i] :
                  ( ( r2_hidden @ D @ ( k2_zfmisc_1 @ C @ C ) )
                 => ( r2_hidden @ ( k1_funct_1 @ B @ D ) @ C ) )
             => ( r1_realset1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534]) ).

thf(2307,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
                         => ( ( k13_mcart_1 @ A @ B @ C @ D @ E @ F )
                            = ( a_6_0_domain_1 @ A @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_domain_1) ).

thf(13721,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ C ) )
                         => ( ( k13_mcart_1 @ A @ B @ C @ D @ E @ F )
                            = ( a_6_0_domain_1 @ A @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2307]) ).

thf(480,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ B @ C )
            & ( m2_relset_1 @ E @ B @ C ) )
         => ( ( ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
                = C )
              & ( v2_funct_1 @ E ) )
           => ( ( C = k1_xboole_0 )
              | ( ( k2_relat_1 @ D )
                = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_funct_2) ).

thf(5087,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ B @ C )
            & ( m2_relset_1 @ E @ B @ C ) )
         => ( ( ( ( k2_relat_1 @ ( k1_partfun1 @ A @ B @ B @ C @ D @ E ) )
                = C )
              & ( v2_funct_1 @ E ) )
           => ( ( C = k1_xboole_0 )
              | ( ( k2_relat_1 @ D )
                = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(391,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ ( k1_relat_1 @ A ) )
              = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_4) ).

thf(4705,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ ( k1_relat_1 @ A ) )
              = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(833,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k2_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_relat_1) ).

thf(6618,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( r1_tarski @ ( k4_xboole_0 @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ B ) ) @ ( k2_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(1747,axiom,
    ! [A: $i] :
      ( ( v1_realset1 @ A )
    <=> ~ ( ~ ( v1_xboole_0 @ A )
          & ! [B: $i] :
              ( A
             != ( k1_tarski @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_realset1) ).

thf(10870,plain,
    ! [A: $i] :
      ( ( ( v1_realset1 @ A )
       => ~ ( ~ ( v1_xboole_0 @ A )
            & ! [B: $i] :
                ( A
               != ( k1_tarski @ B ) ) ) )
      & ( ~ ( ~ ( v1_xboole_0 @ A )
            & ! [B: $i] :
                ( A
               != ( k1_tarski @ B ) ) )
       => ( v1_realset1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1747]) ).

thf(486,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( v1_partfun1 @ C @ A @ B )
          & ( B = k1_xboole_0 ) )
       => ( A = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_partfun1) ).

thf(5104,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( v1_partfun1 @ C @ A @ B )
          & ( B = k1_xboole_0 ) )
       => ( A = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(1145,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k7_domain_1 @ A @ B @ C )
        = ( k2_tarski @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_domain_1) ).

thf(8083,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k7_domain_1 @ A @ B @ C )
        = ( k2_tarski @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).

thf(1290,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B )
        & ( v1_finseq_1 @ B ) )
     => ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
          & ! [C: $i] :
              ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
             => ~ ( ( r2_hidden @ C @ ( k4_finseq_1 @ B ) )
                  & ( ( k1_funct_1 @ B @ C )
                    = A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_finseq_2) ).

thf(8716,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B )
        & ( v1_finseq_1 @ B ) )
     => ~ ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
          & ! [C: $i] :
              ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
             => ~ ( ( r2_hidden @ C @ ( k4_finseq_1 @ B ) )
                  & ( ( k1_funct_1 @ B @ C )
                    = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290]) ).

thf(2525,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( ( k2_cantor_1 @ A @ B )
        = ( k1_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_yellow_9) ).

thf(14646,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) )
     => ( ( k2_cantor_1 @ A @ B )
        = ( k1_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2525]) ).

thf(2372,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_setfam_1 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) ) )
     => ? [C: $i] :
          ( ( m1_subset_1 @ C @ B )
          & ~ ( v1_xboole_0 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_triang_1) ).

thf(13969,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_setfam_1 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) ) )
     => ? [C: $i] :
          ( ( m1_subset_1 @ C @ B )
          & ~ ( v1_xboole_0 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2372]) ).

thf(1962,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k7_classes2 @ A @ B @ C )
        = ( k2_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_classes2) ).

thf(12050,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k7_classes2 @ A @ B @ C )
        = ( k2_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1962]) ).

thf(196,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( k9_relat_1 @ B @ A )
        = ( k9_relat_1 @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_relat_1) ).

thf(3662,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( k9_relat_1 @ B @ A )
        = ( k9_relat_1 @ B @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(1996,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ B @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_enumset1) ).

thf(12268,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ B @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1996]) ).

thf(2428,axiom,
    m1_subset_1 @ k4_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_urysohn1) ).

thf(14177,plain,
    m1_subset_1 @ k4_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2428]) ).

thf(2452,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
     => ! [D: $i] :
          ( ( m1_nat_lat @ D @ A @ B @ C )
        <=> ( m1_subset_1 @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_nat_lat) ).

thf(14274,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) ) )
     => ! [D: $i] :
          ( ( ( m1_nat_lat @ D @ A @ B @ C )
           => ( m1_subset_1 @ D @ C ) )
          & ( ( m1_subset_1 @ D @ C )
           => ( m1_nat_lat @ D @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2452]) ).

thf(2562,axiom,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s5_filter_1 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s5_filter_1 )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ f2_s5_filter_1 )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ f2_s5_filter_1 )
                   => ( p1_s5_filter_1 @ ( k1_domain_1 @ f1_s5_filter_1 @ f2_s5_filter_1 @ A @ C ) @ ( k1_domain_1 @ f1_s5_filter_1 @ f2_s5_filter_1 @ B @ D ) ) ) ) ) )
   => ! [A: $i] :
        ( ( m1_subset_1 @ A @ ( k2_zfmisc_1 @ f1_s5_filter_1 @ f2_s5_filter_1 ) )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ ( k2_zfmisc_1 @ f1_s5_filter_1 @ f2_s5_filter_1 ) )
           => ( p1_s5_filter_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s5_filter_1) ).

thf(14770,plain,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s5_filter_1 )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s5_filter_1 )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ f2_s5_filter_1 )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ f2_s5_filter_1 )
                   => ( p1_s5_filter_1 @ ( k1_domain_1 @ f1_s5_filter_1 @ f2_s5_filter_1 @ A @ C ) @ ( k1_domain_1 @ f1_s5_filter_1 @ f2_s5_filter_1 @ B @ D ) ) ) ) ) )
   => ! [A: $i] :
        ( ( m1_subset_1 @ A @ ( k2_zfmisc_1 @ f1_s5_filter_1 @ f2_s5_filter_1 ) )
       => ! [B: $i] :
            ( ( m1_subset_1 @ B @ ( k2_zfmisc_1 @ f1_s5_filter_1 @ f2_s5_filter_1 ) )
           => ( p1_s5_filter_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2562]) ).

thf(1371,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( ( k2_funct_3 @ A @ B @ C )
        = ( k1_funct_3 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_3) ).

thf(9028,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B ) )
     => ( ( k2_funct_3 @ A @ B @ C )
        = ( k1_funct_3 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).

thf(1585,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ( r2_hidden @ B @ ( k2_zfmisc_1 @ A @ A ) )
       => ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_realset1) ).

thf(10077,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ( r2_hidden @ B @ ( k2_zfmisc_1 @ A @ A ) )
       => ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1585]) ).

thf(1298,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
      = ( k2_xboole_0 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_xboole_1) ).

thf(8749,plain,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ A @ ( k2_xboole_0 @ A @ B ) )
      = ( k2_xboole_0 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).

thf(2510,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k4_finsub_1 @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_finsub_1) ).

thf(14596,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k4_finsub_1 @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2510]) ).

thf(1362,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).

thf(8997,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ ( k3_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362]) ).

thf(804,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( k1_funct_3 @ ( k5_relat_1 @ A @ B ) )
            = ( k5_relat_1 @ ( k1_funct_3 @ A ) @ ( k1_funct_3 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funct_3) ).

thf(6484,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( k1_funct_3 @ ( k5_relat_1 @ A @ B ) )
            = ( k5_relat_1 @ ( k1_funct_3 @ A ) @ ( k1_funct_3 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(116,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( v1_finseq_1 @ A )
      <=> ? [B: $i] :
            ( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
            & ( ( k1_relat_1 @ A )
              = ( k2_finseq_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_finseq_1) ).

thf(3267,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( ( v1_finseq_1 @ A )
         => ? [B: $i] :
              ( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
              & ( ( k1_relat_1 @ A )
                = ( k2_finseq_1 @ B ) ) ) )
        & ( ? [B: $i] :
              ( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
              & ( ( k1_relat_1 @ A )
                = ( k2_finseq_1 @ B ) ) )
         => ( v1_finseq_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(555,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
     => ( ( k9_relat_1 @ C @ B )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_partfun1) ).

thf(5409,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
     => ( ( k9_relat_1 @ C @ B )
        = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(1528,axiom,
    ? [A: $i] :
      ( ( v1_funct_1 @ A )
      & ( v1_funct_2 @ A @ f1_s1_setwiseo @ ( k5_finsub_1 @ f1_s1_setwiseo ) )
      & ( m2_relset_1 @ A @ f1_s1_setwiseo @ ( k5_finsub_1 @ f1_s1_setwiseo ) )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s1_setwiseo )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ f1_s1_setwiseo )
             => ( ( r2_hidden @ C @ ( k8_funct_2 @ f1_s1_setwiseo @ ( k5_finsub_1 @ f1_s1_setwiseo ) @ A @ B ) )
              <=> ( ( r2_hidden @ C @ f2_s1_setwiseo )
                  & ( p1_s1_setwiseo @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_setwiseo) ).

thf(9799,plain,
    ? [A: $i] :
      ( ( v1_funct_1 @ A )
      & ( v1_funct_2 @ A @ f1_s1_setwiseo @ ( k5_finsub_1 @ f1_s1_setwiseo ) )
      & ( m2_relset_1 @ A @ f1_s1_setwiseo @ ( k5_finsub_1 @ f1_s1_setwiseo ) )
      & ! [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s1_setwiseo )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ f1_s1_setwiseo )
             => ( ( ( r2_hidden @ C @ ( k8_funct_2 @ f1_s1_setwiseo @ ( k5_finsub_1 @ f1_s1_setwiseo ) @ A @ B ) )
                 => ( ( r2_hidden @ C @ f2_s1_setwiseo )
                    & ( p1_s1_setwiseo @ C @ B ) ) )
                & ( ( ( r2_hidden @ C @ f2_s1_setwiseo )
                    & ( p1_s1_setwiseo @ C @ B ) )
                 => ( r2_hidden @ C @ ( k8_funct_2 @ f1_s1_setwiseo @ ( k5_finsub_1 @ f1_s1_setwiseo ) @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1528]) ).

thf(2347,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ~ ( r2_subset_1 @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_subset_1) ).

thf(13873,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ~ ( r2_subset_1 @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2347]) ).

thf(1877,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k5_enumset1 @ A @ A @ A @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_enumset1) ).

thf(11599,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k5_enumset1 @ A @ A @ A @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1877]) ).

thf(2504,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_eqrel_1 @ B @ A )
     => ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_eqrel_1) ).

thf(14560,plain,
    ! [A: $i,B: $i] :
      ( ( m1_eqrel_1 @ B @ A )
     => ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2504]) ).

thf(2223,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_qc_lang1) ).

thf(13438,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( m1_subset_1 @ C @ A )
         => ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ B ) @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2223]) ).

thf(1859,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( v2_pre_topc @ ( g1_pre_topc @ A @ ( k1_cantor_1 @ A @ ( k2_cantor_1 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_cantor_1) ).

thf(11497,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( v2_pre_topc @ ( g1_pre_topc @ A @ ( k1_cantor_1 @ A @ ( k2_cantor_1 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1859]) ).

thf(1684,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( k2_ens_1 @ A )
        = ( k3_tarski @ ( a_1_2_ens_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_ens_1) ).

thf(10512,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( k2_ens_1 @ A )
        = ( k3_tarski @ ( a_1_2_ens_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1684]) ).

thf(1195,axiom,
    ! [A: $i,B: $i] :
      ( ( k13_funct_3 @ ( k9_funct_3 @ A @ B ) @ ( k10_funct_3 @ A @ B ) )
      = ( k6_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_3) ).

thf(8253,plain,
    ! [A: $i,B: $i] :
      ( ( k13_funct_3 @ ( k9_funct_3 @ A @ B ) @ ( k10_funct_3 @ A @ B ) )
      = ( k6_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).

thf(96,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k2_ens_1 @ A ) )
                 => ( ( ( ( k3_ens_1 @ A @ B )
                        = ( k4_ens_1 @ A @ C ) )
                      & ( ( k3_ens_1 @ A @ D )
                        = ( k4_ens_1 @ A @ B ) ) )
                   => ( ( k6_ens_1 @ A @ ( k6_ens_1 @ A @ C @ B ) @ D )
                      = ( k6_ens_1 @ A @ C @ ( k6_ens_1 @ A @ B @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_ens_1) ).

thf(3181,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k2_ens_1 @ A ) )
                 => ( ( ( ( k3_ens_1 @ A @ B )
                        = ( k4_ens_1 @ A @ C ) )
                      & ( ( k3_ens_1 @ A @ D )
                        = ( k4_ens_1 @ A @ B ) ) )
                   => ( ( k6_ens_1 @ A @ ( k6_ens_1 @ A @ C @ B ) @ D )
                      = ( k6_ens_1 @ A @ C @ ( k6_ens_1 @ A @ B @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(2531,axiom,
    ! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).

thf(14663,plain,
    ! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2531]) ).

thf(1561,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( v1_funct_1 @ ( k1_functor0 @ A @ B @ C @ D ) )
        & ( v1_funct_2 @ ( k1_functor0 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C )
        & ( m2_relset_1 @ ( k1_functor0 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_functor0) ).

thf(9972,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ( ( v1_funct_1 @ ( k1_functor0 @ A @ B @ C @ D ) )
        & ( v1_funct_2 @ ( k1_functor0 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C )
        & ( m2_relset_1 @ ( k1_functor0 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1561]) ).

thf(2298,axiom,
    ! [A: $i,B: $i] : ( m1_subset_1 @ ( k1_card_fil @ A @ B ) @ ( k1_zfmisc_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_card_fil) ).

thf(13691,plain,
    ! [A: $i,B: $i] : ( m1_subset_1 @ ( k1_card_fil @ A @ B ) @ ( k1_zfmisc_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2298]) ).

thf(2193,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ B @ ( k1_zfmisc_1 @ C ) )
        & ( m1_relset_1 @ D @ B @ ( k1_zfmisc_1 @ C ) ) )
     => ( m1_subset_1 @ ( k3_cantor_1 @ A @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_cantor_1) ).

thf(13288,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ B @ ( k1_zfmisc_1 @ C ) )
        & ( m1_relset_1 @ D @ B @ ( k1_zfmisc_1 @ C ) ) )
     => ( m1_subset_1 @ ( k3_cantor_1 @ A @ B @ C @ D @ E ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2193]) ).

thf(1580,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( r2_hidden @ D @ A )
        & ! [E: $i,F: $i] :
            ~ ( ( r2_hidden @ E @ B )
              & ( r2_hidden @ F @ C )
              & ( D
                = ( k4_tarski @ E @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).

thf(10040,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( r2_hidden @ D @ A )
        & ! [E: $i,F: $i] :
            ~ ( ( r2_hidden @ E @ B )
              & ( r2_hidden @ F @ C )
              & ( D
                = ( k4_tarski @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1580]) ).

thf(761,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( r1_tarski @ A @ C )
                  & ( r1_tarski @ B @ C ) )
               => ( r1_partfun1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_partfun1) ).

thf(6305,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( r1_tarski @ A @ C )
                  & ( r1_tarski @ B @ C ) )
               => ( r1_partfun1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(380,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( ( k1_relat_1 @ B )
                = A )
              & ( ( k1_relat_1 @ C )
                = A )
              & ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
              & ( v2_funct_1 @ B )
              & ( ( k5_relat_1 @ C @ B )
                = B ) )
           => ( C
              = ( k6_relat_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_funct_1) ).

thf(4649,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( ( k1_relat_1 @ B )
                = A )
              & ( ( k1_relat_1 @ C )
                = A )
              & ( r1_tarski @ ( k2_relat_1 @ C ) @ A )
              & ( v2_funct_1 @ B )
              & ( ( k5_relat_1 @ C @ B )
                = B ) )
           => ( C
              = ( k6_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(2491,axiom,
    ! [A: $i] :
      ( ( r2_hidden @ A @ a_0_33_fraenkel )
    <=> ? [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s18_fraenkel )
          & ( A
            = ( f3_s18_fraenkel @ B ) )
          & ( p1_s18_fraenkel @ B )
          & ~ ( r2_hidden @ ( f3_s18_fraenkel @ B ) @ f2_s18_fraenkel ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_33_fraenkel) ).

thf(14472,plain,
    ! [A: $i] :
      ( ( ( r2_hidden @ A @ a_0_33_fraenkel )
       => ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s18_fraenkel )
            & ( A
              = ( f3_s18_fraenkel @ B ) )
            & ( p1_s18_fraenkel @ B )
            & ~ ( r2_hidden @ ( f3_s18_fraenkel @ B ) @ f2_s18_fraenkel ) ) )
      & ( ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s18_fraenkel )
            & ( A
              = ( f3_s18_fraenkel @ B ) )
            & ( p1_s18_fraenkel @ B )
            & ~ ( r2_hidden @ ( f3_s18_fraenkel @ B ) @ f2_s18_fraenkel ) )
       => ( r2_hidden @ A @ a_0_33_fraenkel ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2491]) ).

thf(1869,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r2_hidden @ C @ A )
       => ( ( B = k1_xboole_0 )
          | ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_funct_2) ).

thf(11553,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( ( r2_hidden @ C @ A )
       => ( ( B = k1_xboole_0 )
          | ( r2_hidden @ ( k1_funct_1 @ D @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1869]) ).

thf(1998,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ! [E: $i] :
                ( ( m1_subset_1 @ E @ A )
               => ( ( k1_funct_1 @ C @ E )
                  = ( k1_funct_1 @ D @ E ) ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_funct_2) ).

thf(12273,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ B )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ! [E: $i] :
                ( ( m1_subset_1 @ E @ A )
               => ( ( k1_funct_1 @ C @ E )
                  = ( k1_funct_1 @ D @ E ) ) )
           => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1998]) ).

thf(1991,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( I
        = ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H ) )
    <=> ! [J: $i] :
          ( ( r2_hidden @ J @ I )
        <=> ~ ( ( J != A )
              & ( J != B )
              & ( J != C )
              & ( J != D )
              & ( J != E )
              & ( J != F )
              & ( J != G )
              & ( J != H ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_enumset1) ).

thf(12176,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
      ( ( ( I
          = ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H ) )
       => ! [J: $i] :
            ( ( ( r2_hidden @ J @ I )
             => ~ ( ( J != A )
                  & ( J != B )
                  & ( J != C )
                  & ( J != D )
                  & ( J != E )
                  & ( J != F )
                  & ( J != G )
                  & ( J != H ) ) )
            & ( ~ ( ( J != A )
                  & ( J != B )
                  & ( J != C )
                  & ( J != D )
                  & ( J != E )
                  & ( J != F )
                  & ( J != G )
                  & ( J != H ) )
             => ( r2_hidden @ J @ I ) ) ) )
      & ( ! [J: $i] :
            ( ( ( r2_hidden @ J @ I )
             => ~ ( ( J != A )
                  & ( J != B )
                  & ( J != C )
                  & ( J != D )
                  & ( J != E )
                  & ( J != F )
                  & ( J != G )
                  & ( J != H ) ) )
            & ( ~ ( ( J != A )
                  & ( J != B )
                  & ( J != C )
                  & ( J != D )
                  & ( J != E )
                  & ( J != F )
                  & ( J != G )
                  & ( J != H ) )
             => ( r2_hidden @ J @ I ) ) )
       => ( I
          = ( k6_enumset1 @ A @ B @ C @ D @ E @ F @ G @ H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1991]) ).

thf(2445,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) )
      <=> ? [C: $i] :
            ( ( m1_subset_1 @ C @ B )
            & ( A = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).

thf(14246,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) )
         => ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A = C ) ) )
        & ( ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A = C ) )
         => ( r2_hidden @ A @ ( a_1_0_domain_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2445]) ).

thf(368,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
              & ( r1_tarski @ C @ B ) )
           => ( r1_tarski @ C @ ( k7_relat_1 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t186_relat_1) ).

thf(4591,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ! [C: $i] :
          ( ( v1_relat_1 @ C )
         => ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
              & ( r1_tarski @ C @ B ) )
           => ( r1_tarski @ C @ ( k7_relat_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(2340,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k3_card_fil @ A @ B @ C )
                = ( a_3_0_card_fil @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_card_fil) ).

thf(13846,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k3_card_fil @ A @ B @ C )
                = ( a_3_0_card_fil @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2340]) ).

thf(1067,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r1_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
        & ( r2_hidden @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_zfmisc_1) ).

thf(7715,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r1_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
        & ( r2_hidden @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).

thf(650,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( ( v1_finset_1 @ ( k1_funct_2 @ A @ B ) )
        & ( v1_fraenkel @ ( k1_funct_2 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_fraenkel) ).

thf(5781,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( ( v1_finset_1 @ ( k1_funct_2 @ A @ B ) )
        & ( v1_fraenkel @ ( k1_funct_2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(1180,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( v1_xboole_0 @ D )
     => ! [E: $i] :
          ( ~ ( v1_xboole_0 @ E )
         => ! [F: $i] :
              ( ( m2_finseq_1 @ F @ D )
             => ! [G: $i] :
                  ( ( ( v1_funct_1 @ G )
                    & ( v1_funct_2 @ G @ D @ E )
                    & ( m2_relset_1 @ G @ D @ E ) )
                 => ( ( F
                      = ( k11_finseq_1 @ A @ B @ C ) )
                   => ( ( k1_partfun1 @ k5_numbers @ D @ D @ E @ F @ G )
                      = ( k11_finseq_1 @ ( k1_funct_1 @ G @ A ) @ ( k1_funct_1 @ G @ B ) @ ( k1_funct_1 @ G @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_finseq_2) ).

thf(8203,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ~ ( v1_xboole_0 @ D )
     => ! [E: $i] :
          ( ~ ( v1_xboole_0 @ E )
         => ! [F: $i] :
              ( ( m2_finseq_1 @ F @ D )
             => ! [G: $i] :
                  ( ( ( v1_funct_1 @ G )
                    & ( v1_funct_2 @ G @ D @ E )
                    & ( m2_relset_1 @ G @ D @ E ) )
                 => ( ( F
                      = ( k11_finseq_1 @ A @ B @ C ) )
                   => ( ( k1_partfun1 @ k5_numbers @ D @ D @ E @ F @ G )
                      = ( k11_finseq_1 @ ( k1_funct_1 @ G @ A ) @ ( k1_funct_1 @ G @ B ) @ ( k1_funct_1 @ G @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).

thf(819,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
        & ( r1_xboole_0 @ A @ C ) )
     => ( r1_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_xboole_1) ).

thf(6554,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ A @ ( k2_xboole_0 @ B @ C ) )
        & ( r1_xboole_0 @ A @ C ) )
     => ( r1_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(1827,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( m2_relset_1 @ C @ k1_xboole_0 @ B )
       => ( C = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_relset_1) ).

thf(11305,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( m2_relset_1 @ C @ k1_xboole_0 @ B )
       => ( C = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1827]) ).

thf(462,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_finset_1 @ A )
     => ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_finset_1) ).

thf(5023,plain,
    ! [A: $i,B: $i] :
      ( ( v1_finset_1 @ A )
     => ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(2316,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ( r2_hidden @ D @ B )
                <=> ( r2_hidden @ D @ C ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_subset_1) ).

thf(13761,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ( ( r2_hidden @ D @ B )
                   => ( r2_hidden @ D @ C ) )
                  & ( ( r2_hidden @ D @ C )
                   => ( r2_hidden @ D @ B ) ) ) )
           => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2316]) ).

thf(2306,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_realset1 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_realset1 @ B )
          & ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_tex_2) ).

thf(13716,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_realset1 @ A ) )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_realset1 @ B )
          & ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2306]) ).

thf(1844,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k4_partfun1 @ A @ B ) )
     => ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_partfun1) ).

thf(11405,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k4_partfun1 @ A @ B ) )
     => ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1844]) ).

thf(1602,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ( r1_tarski @ B @ C )
               => ( r1_tarski @ ( k8_funct_2 @ A @ A @ ( k6_partfun1 @ A ) @ B ) @ ( k8_funct_2 @ A @ A @ ( k6_partfun1 @ A ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_closure2) ).

thf(10137,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ( r1_tarski @ B @ C )
               => ( r1_tarski @ ( k8_funct_2 @ A @ A @ ( k6_partfun1 @ A ) @ B ) @ ( k8_funct_2 @ A @ A @ ( k6_partfun1 @ A ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1602]) ).

thf(1851,axiom,
    ! [A: $i] :
      ( ( v1_finset_1 @ A )
    <=> ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finset_1) ).

thf(11454,plain,
    ! [A: $i] :
      ( ( ( v1_finset_1 @ A )
       => ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) )
      & ( ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) )
       => ( v1_finset_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1851]) ).

thf(2173,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ D @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_enumset1) ).

thf(13198,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ D @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2173]) ).

thf(629,axiom,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc17_membered) ).

thf(5699,plain,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(2285,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_eqrel_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                 => ( ( D
                      = ( k3_tarski @ C ) )
                   => ( ( k3_subset_1 @ A @ D )
                      = ( k3_tarski @ ( k3_subset_1 @ B @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_borsuk_1) ).

thf(13642,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_eqrel_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                 => ( ( D
                      = ( k3_tarski @ C ) )
                   => ( ( k3_subset_1 @ A @ D )
                      = ( k3_tarski @ ( k3_subset_1 @ B @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2285]) ).

thf(602,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( m1_subset_1 @ ( k10_mcart_1 @ A @ B @ C @ D @ E ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_mcart_1) ).

thf(5568,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( m1_subset_1 @ ( k10_mcart_1 @ A @ B @ C @ D @ E ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(707,axiom,
    ! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_xboole_1) ).

thf(6062,plain,
    ! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(1814,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_card_fil @ B @ A ) )
     => ( m2_card_fil @ ( k2_card_fil @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_card_fil) ).

thf(11227,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_card_fil @ B @ A ) )
     => ( m2_card_fil @ ( k2_card_fil @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1814]) ).

thf(1227,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
      = ( k3_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_xboole_1) ).

thf(8399,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ C @ B ) )
      = ( k3_xboole_0 @ ( k4_xboole_0 @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).

thf(2425,axiom,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k2_qc_lang1 )
     => ( m1_subset_1 @ ( k23_qc_lang1 @ A ) @ ( k1_zfmisc_1 @ k2_qc_lang1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k23_qc_lang1) ).

thf(14165,plain,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k2_qc_lang1 )
     => ( m1_subset_1 @ ( k23_qc_lang1 @ A ) @ ( k1_zfmisc_1 @ k2_qc_lang1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2425]) ).

thf(2037,axiom,
    ! [A: $i] :
      ( ( k1_subset_1 @ A )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_subset_1) ).

thf(12448,plain,
    ! [A: $i] :
      ( ( k1_subset_1 @ A )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2037]) ).

thf(1308,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
        = k1_xboole_0 )
    <=> ( r2_hidden @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).

thf(8793,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
          = k1_xboole_0 )
       => ( r2_hidden @ A @ B ) )
      & ( ( r2_hidden @ A @ B )
       => ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
          = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
              & ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) )
           => ( v2_funct_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_funct_1) ).

thf(2680,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ ( k5_relat_1 @ B @ A ) )
              & ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ A ) ) )
           => ( v2_funct_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(1455,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( r1_tarski @ ( k1_funct_4 @ A @ B ) @ ( k2_xboole_0 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_funct_4) ).

thf(9421,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( r1_tarski @ ( k1_funct_4 @ A @ B ) @ ( k2_xboole_0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455]) ).

thf(1396,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( k4_xboole_0 @ A @ B ) )
    <=> ! [D: $i] :
          ( ( r2_hidden @ D @ C )
        <=> ( ( r2_hidden @ D @ A )
            & ~ ( r2_hidden @ D @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).

thf(9130,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C
          = ( k4_xboole_0 @ A @ B ) )
       => ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ( ( r2_hidden @ D @ A )
                & ~ ( r2_hidden @ D @ B ) ) )
            & ( ( ( r2_hidden @ D @ A )
                & ~ ( r2_hidden @ D @ B ) )
             => ( r2_hidden @ D @ C ) ) ) )
      & ( ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ( ( r2_hidden @ D @ A )
                & ~ ( r2_hidden @ D @ B ) ) )
            & ( ( ( r2_hidden @ D @ A )
                & ~ ( r2_hidden @ D @ B ) )
             => ( r2_hidden @ D @ C ) ) )
       => ( C
          = ( k4_xboole_0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396]) ).

thf(828,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( ( k2_mcart_1 @ ( k5_ens_1 @ A @ B ) )
              = ( k6_partfun1 @ B ) )
            & ( ( k3_ens_1 @ A @ ( k5_ens_1 @ A @ B ) )
              = B )
            & ( ( k4_ens_1 @ A @ ( k5_ens_1 @ A @ B ) )
              = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_ens_1) ).

thf(6586,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ A )
         => ( ( ( k2_mcart_1 @ ( k5_ens_1 @ A @ B ) )
              = ( k6_partfun1 @ B ) )
            & ( ( k3_ens_1 @ A @ ( k5_ens_1 @ A @ B ) )
              = B )
            & ( ( k4_ens_1 @ A @ ( k5_ens_1 @ A @ B ) )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(1958,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
            & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
         => ( ! [F: $i] :
                ( ( m1_subset_1 @ F @ A )
               => ! [G: $i] :
                    ( ( m1_subset_1 @ G @ B )
                   => ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
                      = ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
           => ( D = E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_funct_2) ).

thf(12031,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
        & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
     => ! [E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C )
            & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
         => ( ! [F: $i] :
                ( ( m1_subset_1 @ F @ A )
               => ! [G: $i] :
                    ( ( m1_subset_1 @ G @ B )
                   => ( ( k1_funct_1 @ D @ ( k4_tarski @ F @ G ) )
                      = ( k1_funct_1 @ E @ ( k4_tarski @ F @ G ) ) ) ) )
           => ( D = E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1958]) ).

thf(2393,axiom,
    m1_subset_1 @ k5_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_urysohn1) ).

thf(14047,plain,
    m1_subset_1 @ k5_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2393]) ).

thf(917,axiom,
    ! [A: $i,B: $i] :
      ( ( k1_card_fil @ A @ B )
      = ( k4_xboole_0 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_card_fil) ).

thf(7017,plain,
    ! [A: $i,B: $i] :
      ( ( k1_card_fil @ A @ B )
      = ( k4_xboole_0 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).

thf(476,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( ~ ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
          & ( r1_xboole_0 @ A @ B )
          & ( r1_xboole_0 @ A @ C ) )
      & ~ ( ~ ( ( r1_xboole_0 @ A @ B )
              & ( r1_xboole_0 @ A @ C ) )
          & ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_xboole_1) ).

thf(5072,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( ~ ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
          & ( r1_xboole_0 @ A @ B )
          & ( r1_xboole_0 @ A @ C ) )
      & ~ ( ~ ( ( r1_xboole_0 @ A @ B )
              & ( r1_xboole_0 @ A @ C ) )
          & ( r1_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(256,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( v1_classes2 @ B ) )
         => ( ( ( r2_hidden @ ( k1_relat_1 @ A ) @ B )
              & ( r1_tarski @ ( k2_relat_1 @ A ) @ B ) )
           => ( r2_hidden @ ( k2_relat_1 @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_zfrefle1) ).

thf(3993,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( v1_classes2 @ B ) )
         => ( ( ( r2_hidden @ ( k1_relat_1 @ A ) @ B )
              & ( r1_tarski @ ( k2_relat_1 @ A ) @ B ) )
           => ( r2_hidden @ ( k2_relat_1 @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(1900,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( B != k1_xboole_0 )
       => ( ( k6_subset_1 @ A @ ( k2_subset_1 @ A ) @ ( k5_setfam_1 @ A @ B ) )
          = ( k6_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_setfam_1) ).

thf(11685,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( B != k1_xboole_0 )
       => ( ( k6_subset_1 @ A @ ( k2_subset_1 @ A ) @ ( k5_setfam_1 @ A @ B ) )
          = ( k6_setfam_1 @ A @ ( k7_setfam_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1900]) ).

thf(777,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( k5_relat_1 @ B @ A )
            = ( k5_relat_1 @ B @ ( k7_relat_1 @ A @ ( k2_relat_1 @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funct_4) ).

thf(6386,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( k5_relat_1 @ B @ A )
            = ( k5_relat_1 @ B @ ( k7_relat_1 @ A @ ( k2_relat_1 @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(1406,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( B
            = ( k2_relat_1 @ A ) )
        <=> ! [C: $i] :
              ( ( r2_hidden @ C @ B )
            <=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).

thf(9211,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( ( B
              = ( k2_relat_1 @ A ) )
           => ! [C: $i] :
                ( ( ( r2_hidden @ C @ B )
                 => ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
                & ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
                 => ( r2_hidden @ C @ B ) ) ) )
          & ( ! [C: $i] :
                ( ( ( r2_hidden @ C @ B )
                 => ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
                & ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
                 => ( r2_hidden @ C @ B ) ) )
           => ( B
              = ( k2_relat_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406]) ).

thf(1291,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_tarski @ A @ B )
       => ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
          = ( k7_relat_1 @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_relat_1) ).

thf(8721,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_tarski @ A @ B )
       => ( ( k7_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
          = ( k7_relat_1 @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).

thf(1033,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ~ ( r2_hidden @ D @ A )
        <=> ( ( r2_hidden @ D @ B )
          <=> ( r2_hidden @ D @ C ) ) )
     => ( A
        = ( k5_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_0) ).

thf(7574,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( ~ ( r2_hidden @ D @ A )
           => ( ( ( r2_hidden @ D @ B )
               => ( r2_hidden @ D @ C ) )
              & ( ( r2_hidden @ D @ C )
               => ( r2_hidden @ D @ B ) ) ) )
          & ( ( ( ( r2_hidden @ D @ B )
               => ( r2_hidden @ D @ C ) )
              & ( ( r2_hidden @ D @ C )
               => ( r2_hidden @ D @ B ) ) )
           => ~ ( r2_hidden @ D @ A ) ) )
     => ( A
        = ( k5_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).

thf(1426,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_xboole_0 @ A @ ( k4_xboole_0 @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_xboole_1) ).

thf(9289,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_xboole_0 @ A @ ( k4_xboole_0 @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1426]) ).

thf(1890,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ B ) )
     => ( ( k1_domain_1 @ A @ B @ C @ D )
        = ( k4_tarski @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).

thf(11653,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ B ) )
     => ( ( k1_domain_1 @ A @ B @ C @ D )
        = ( k4_tarski @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1890]) ).

thf(492,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ! [D: $i] :
            ~ ( ( r2_hidden @ D @ B )
              & ! [E: $i] :
                  ~ ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) )
      <=> ( ( k5_relset_1 @ A @ B @ C )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relset_1) ).

thf(5128,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( ! [D: $i] :
              ~ ( ( r2_hidden @ D @ B )
                & ! [E: $i] :
                    ~ ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) )
         => ( ( k5_relset_1 @ A @ B @ C )
            = B ) )
        & ( ( ( k5_relset_1 @ A @ B @ C )
            = B )
         => ! [D: $i] :
              ~ ( ( r2_hidden @ D @ B )
                & ! [E: $i] :
                    ~ ( r2_hidden @ ( k4_tarski @ E @ D ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(1050,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_relat_1 @ ( k15_funct_3 @ A @ B ) )
        & ( v1_funct_1 @ ( k15_funct_3 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_funct_3) ).

thf(7644,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( v1_relat_1 @ ( k15_funct_3 @ A @ B ) )
        & ( v1_funct_1 @ ( k15_funct_3 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).

thf(32,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
       => ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_sysrel) ).

thf(2739,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
       => ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(283,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ ( k2_funct_1 @ A ) )
        & ( v1_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).

thf(4098,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_relat_1 @ ( k2_funct_1 @ A ) )
        & ( v1_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(998,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ( ( r1_partfun1 @ B @ C )
           => ( r2_hidden @ C @ ( k5_partfun1 @ A @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_funct_2) ).

thf(7406,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) )
         => ( ( r1_partfun1 @ B @ C )
           => ( r2_hidden @ C @ ( k5_partfun1 @ A @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).

thf(1525,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ( ( k10_setwiseo @ A @ B @ ( k3_setwiseo @ A @ D @ E ) @ C )
                    = ( k5_setwiseo @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_setwiseo) ).

thf(9787,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ( ( k10_setwiseo @ A @ B @ ( k3_setwiseo @ A @ D @ E ) @ C )
                    = ( k5_setwiseo @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525]) ).

thf(2343,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k4_partfun1 @ A @ B ) ) ) )
     => ? [D: $i] : ( m1_pua2mss1 @ D @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_pua2mss1) ).

thf(13855,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k4_partfun1 @ A @ B ) ) ) )
     => ? [D: $i] : ( m1_pua2mss1 @ D @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2343]) ).

thf(217,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ( ( ( v3_binop_1 @ C @ B )
                          & ( v1_binop_1 @ C @ B )
                          & ( v2_binop_1 @ C @ B ) )
                       => ( ( ( D = k1_xboole_0 )
                            & ~ ( v1_setwiseo @ C @ B ) )
                          | ! [F: $i] :
                              ( ( m1_subset_1 @ F @ B )
                             => ( ( F
                                  = ( k7_setwiseo @ A @ B @ C @ D @ E ) )
                              <=> ? [G: $i] :
                                    ( ( v1_funct_1 @ G )
                                    & ( v1_funct_2 @ G @ ( k5_finsub_1 @ A ) @ B )
                                    & ( m2_relset_1 @ G @ ( k5_finsub_1 @ A ) @ B )
                                    & ( F
                                      = ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ D ) )
                                    & ! [H: $i] :
                                        ( ( m1_subset_1 @ H @ B )
                                       => ( ( r3_binop_1 @ B @ H @ C )
                                         => ( ( k1_funct_1 @ G @ k1_xboole_0 )
                                            = H ) ) )
                                    & ! [H: $i] :
                                        ( ( m1_subset_1 @ H @ A )
                                       => ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k2_setwiseo @ A @ H ) )
                                          = ( k8_funct_2 @ A @ B @ E @ H ) ) )
                                    & ! [H: $i] :
                                        ( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
                                       => ( ( r1_tarski @ H @ D )
                                         => ( ( H = k1_xboole_0 )
                                            | ! [I: $i] :
                                                ( ( m1_subset_1 @ I @ A )
                                               => ( ( r2_hidden @ I @ D )
                                                 => ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k5_setwiseo @ A @ H @ ( k2_setwiseo @ A @ I ) ) )
                                                    = ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ H ) @ ( k8_funct_2 @ A @ B @ E @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_setwiseo) ).

thf(3761,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k5_finsub_1 @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ( ( ( v3_binop_1 @ C @ B )
                          & ( v1_binop_1 @ C @ B )
                          & ( v2_binop_1 @ C @ B ) )
                       => ( ( ( D = k1_xboole_0 )
                            & ~ ( v1_setwiseo @ C @ B ) )
                          | ! [F: $i] :
                              ( ( m1_subset_1 @ F @ B )
                             => ( ( ( F
                                    = ( k7_setwiseo @ A @ B @ C @ D @ E ) )
                                 => ? [G: $i] :
                                      ( ( v1_funct_1 @ G )
                                      & ( v1_funct_2 @ G @ ( k5_finsub_1 @ A ) @ B )
                                      & ( m2_relset_1 @ G @ ( k5_finsub_1 @ A ) @ B )
                                      & ( F
                                        = ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ D ) )
                                      & ! [H: $i] :
                                          ( ( m1_subset_1 @ H @ B )
                                         => ( ( r3_binop_1 @ B @ H @ C )
                                           => ( ( k1_funct_1 @ G @ k1_xboole_0 )
                                              = H ) ) )
                                      & ! [H: $i] :
                                          ( ( m1_subset_1 @ H @ A )
                                         => ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k2_setwiseo @ A @ H ) )
                                            = ( k8_funct_2 @ A @ B @ E @ H ) ) )
                                      & ! [H: $i] :
                                          ( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
                                         => ( ( r1_tarski @ H @ D )
                                           => ( ( H = k1_xboole_0 )
                                              | ! [I: $i] :
                                                  ( ( m1_subset_1 @ I @ A )
                                                 => ( ( r2_hidden @ I @ D )
                                                   => ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k5_setwiseo @ A @ H @ ( k2_setwiseo @ A @ I ) ) )
                                                      = ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ H ) @ ( k8_funct_2 @ A @ B @ E @ I ) ) ) ) ) ) ) ) ) )
                                & ( ? [G: $i] :
                                      ( ( v1_funct_1 @ G )
                                      & ( v1_funct_2 @ G @ ( k5_finsub_1 @ A ) @ B )
                                      & ( m2_relset_1 @ G @ ( k5_finsub_1 @ A ) @ B )
                                      & ( F
                                        = ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ D ) )
                                      & ! [H: $i] :
                                          ( ( m1_subset_1 @ H @ B )
                                         => ( ( r3_binop_1 @ B @ H @ C )
                                           => ( ( k1_funct_1 @ G @ k1_xboole_0 )
                                              = H ) ) )
                                      & ! [H: $i] :
                                          ( ( m1_subset_1 @ H @ A )
                                         => ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k2_setwiseo @ A @ H ) )
                                            = ( k8_funct_2 @ A @ B @ E @ H ) ) )
                                      & ! [H: $i] :
                                          ( ( m1_subset_1 @ H @ ( k5_finsub_1 @ A ) )
                                         => ( ( r1_tarski @ H @ D )
                                           => ( ( H = k1_xboole_0 )
                                              | ! [I: $i] :
                                                  ( ( m1_subset_1 @ I @ A )
                                                 => ( ( r2_hidden @ I @ D )
                                                   => ( ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ ( k5_setwiseo @ A @ H @ ( k2_setwiseo @ A @ I ) ) )
                                                      = ( k2_binop_1 @ B @ B @ B @ C @ ( k8_funct_2 @ ( k5_finsub_1 @ A ) @ B @ G @ H ) @ ( k8_funct_2 @ A @ B @ E @ I ) ) ) ) ) ) ) ) )
                                 => ( F
                                    = ( k7_setwiseo @ A @ B @ C @ D @ E ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(1248,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ( m2_finseq_1 @ D @ B )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ B @ C )
                    & ( m2_relset_1 @ E @ B @ C ) )
                 => ( ( D
                      = ( k9_finseq_1 @ A ) )
                   => ( ( k1_partfun1 @ k5_numbers @ B @ B @ C @ D @ E )
                      = ( k9_finseq_1 @ ( k1_funct_1 @ E @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_finseq_2) ).

thf(8520,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ( m2_finseq_1 @ D @ B )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ B @ C )
                    & ( m2_relset_1 @ E @ B @ C ) )
                 => ( ( D
                      = ( k9_finseq_1 @ A ) )
                   => ( ( k1_partfun1 @ k5_numbers @ B @ B @ C @ D @ E )
                      = ( k9_finseq_1 @ ( k1_funct_1 @ E @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).

thf(1879,axiom,
    r1_xboole_0 @ a_0_33_fraenkel @ f2_s18_fraenkel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s18_fraenkel) ).

thf(11604,plain,
    r1_xboole_0 @ a_0_33_fraenkel @ f2_s18_fraenkel,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1879]) ).

thf(1905,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k6_enumset1 @ A @ A @ A @ A @ A @ A @ B @ C )
      = ( k1_enumset1 @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_enumset1) ).

thf(11700,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k6_enumset1 @ A @ A @ A @ A @ A @ A @ B @ C )
      = ( k1_enumset1 @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1905]) ).

thf(946,axiom,
    ! [A: $i,B: $i] :
      ( ( m2_relset_1 @ B @ A @ A )
     => ( ( ( k7_relset_1 @ A @ A @ A @ A @ B @ ( k6_partfun1 @ A ) )
          = B )
        & ( ( k7_relset_1 @ A @ A @ A @ A @ ( k6_partfun1 @ A ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_funct_2) ).

thf(7135,plain,
    ! [A: $i,B: $i] :
      ( ( m2_relset_1 @ B @ A @ A )
     => ( ( ( k7_relset_1 @ A @ A @ A @ A @ B @ ( k6_partfun1 @ A ) )
          = B )
        & ( ( k7_relset_1 @ A @ A @ A @ A @ ( k6_partfun1 @ A ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).

thf(2002,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ ( k10_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relset_1) ).

thf(12298,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ ( k10_relset_1 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2002]) ).

thf(1989,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( r1_tarski @ ( k5_subset_1 @ A @ ( k8_setfam_1 @ A @ B ) @ ( k8_setfam_1 @ A @ C ) ) @ ( k8_setfam_1 @ A @ ( k1_relset_2 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_relset_2) ).

thf(12171,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( r1_tarski @ ( k5_subset_1 @ A @ ( k8_setfam_1 @ A @ B ) @ ( k8_setfam_1 @ A @ C ) ) @ ( k8_setfam_1 @ A @ ( k1_relset_2 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1989]) ).

thf(375,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
       => ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
          & ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_sysrel) ).

thf(4619,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
       => ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
          & ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(739,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ~ ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
             => ( E
                = ( k4_mcart_1 @ ( k8_mcart_1 @ A @ B @ C @ D @ E ) @ ( k9_mcart_1 @ A @ B @ C @ D @ E ) @ ( k10_mcart_1 @ A @ B @ C @ D @ E ) @ ( k11_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_mcart_1) ).

thf(6198,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ~ ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
             => ( E
                = ( k4_mcart_1 @ ( k8_mcart_1 @ A @ B @ C @ D @ E ) @ ( k9_mcart_1 @ A @ B @ C @ D @ E ) @ ( k10_mcart_1 @ A @ B @ C @ D @ E ) @ ( k11_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(1971,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_card_fil @ C @ B )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( r2_hidden @ A @ ( a_3_1_card_fil @ B @ C @ D ) )
      <=> ? [E: $i] :
            ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
            & ( A
              = ( k5_subset_1 @ B @ E @ D ) )
            & ( r2_hidden @ E @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_card_fil) ).

thf(12098,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_card_fil @ C @ B )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( ( r2_hidden @ A @ ( a_3_1_card_fil @ B @ C @ D ) )
         => ? [E: $i] :
              ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
              & ( A
                = ( k5_subset_1 @ B @ E @ D ) )
              & ( r2_hidden @ E @ C ) ) )
        & ( ? [E: $i] :
              ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ B ) )
              & ( A
                = ( k5_subset_1 @ B @ E @ D ) )
              & ( r2_hidden @ E @ C ) )
         => ( r2_hidden @ A @ ( a_3_1_card_fil @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1971]) ).

thf(1435,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ B ) )
     => ! [C: $i] :
          ( ( m1_filter_1 @ C @ A @ B )
         => ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_filter_1) ).

thf(9321,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_relat_1 @ B ) )
     => ! [C: $i] :
          ( ( m1_filter_1 @ C @ A @ B )
         => ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ A )
            & ( m2_relset_1 @ C @ A @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435]) ).

thf(670,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( k1_relat_1 @ C )
          = ( k2_xboole_0 @ A @ ( k1_tarski @ B ) ) )
       => ( C
          = ( k1_funct_4 @ ( k7_relat_1 @ C @ A ) @ ( k3_cqc_lang @ B @ ( k1_funct_1 @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_7) ).

thf(5864,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( k1_relat_1 @ C )
          = ( k2_xboole_0 @ A @ ( k1_tarski @ B ) ) )
       => ( C
          = ( k1_funct_4 @ ( k7_relat_1 @ C @ A ) @ ( k3_cqc_lang @ B @ ( k1_funct_1 @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(1753,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k1_funct_5 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
        = ( k1_tarski @ A ) )
      & ( ( k2_funct_5 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
        = ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_5) ).

thf(10909,plain,
    ! [A: $i,B: $i] :
      ( ( ( k1_funct_5 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
        = ( k1_tarski @ A ) )
      & ( ( k2_funct_5 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) )
        = ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1753]) ).

thf(1745,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ B @ A )
                & ( m2_relset_1 @ C @ B @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ( ( k2_funct_2 @ B @ A @ C @ ( k1_tarski @ D ) )
                    = ( k1_tarski @ ( k8_funct_2 @ B @ A @ C @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_setwiseo) ).

thf(10853,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ B @ A )
                & ( m2_relset_1 @ C @ B @ A ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ( ( k2_funct_2 @ B @ A @ C @ ( k1_tarski @ D ) )
                    = ( k1_tarski @ ( k8_funct_2 @ B @ A @ C @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1745]) ).

thf(934,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k7_subset_1 @ A @ B @ C )
        = ( k5_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_subset_1) ).

thf(7093,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k7_subset_1 @ A @ B @ C )
        = ( k5_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).

thf(1417,axiom,
    ! [A: $i] :
      ( ( k4_xboole_0 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).

thf(9262,plain,
    ! [A: $i] :
      ( ( k4_xboole_0 @ k1_xboole_0 @ A )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417]) ).

thf(153,axiom,
    ( ( k4_relat_1 @ k1_xboole_0 )
    = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_relat_1) ).

thf(3420,plain,
    ( ( k4_relat_1 @ k1_xboole_0 )
    = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(1530,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ( r2_hidden @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_card_fil) ).

thf(9812,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_card_fil @ B @ A )
         => ( r2_hidden @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1530]) ).

thf(2318,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k7_classes2 @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_classes2) ).

thf(13775,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( m1_subset_1 @ ( k7_classes2 @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2318]) ).

thf(1047,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ( ( v2_funct_1 @ B )
       => ! [C: $i,D: $i] :
            ( ( ( r2_hidden @ C @ A )
              & ( r2_hidden @ D @ A )
              & ( ( k1_funct_1 @ B @ C )
                = ( k1_funct_1 @ B @ D ) ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_2) ).

thf(7634,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m2_relset_1 @ B @ A @ A ) )
     => ( ( v2_funct_1 @ B )
       => ! [C: $i,D: $i] :
            ( ( ( r2_hidden @ C @ A )
              & ( r2_hidden @ D @ A )
              & ( ( k1_funct_1 @ B @ C )
                = ( k1_funct_1 @ B @ D ) ) )
           => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).

thf(1669,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( v1_xboole_0 @ C )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
            & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
         => ( ( v1_funct_1 @ ( k2_funct_4 @ D ) )
            & ( v1_funct_2 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C )
            & ( m2_relset_1 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funct_4) ).

thf(10453,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( v1_xboole_0 @ C )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C )
            & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
         => ( ( v1_funct_1 @ ( k2_funct_4 @ D ) )
            & ( v1_funct_2 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C )
            & ( m2_relset_1 @ ( k2_funct_4 @ D ) @ ( k2_zfmisc_1 @ B @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1669]) ).

thf(2300,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ A ) )
     => ( ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G )
        = ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k11_domain_1) ).

thf(13695,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ A ) )
     => ( ( k11_domain_1 @ A @ B @ C @ D @ E @ F @ G )
        = ( k4_enumset1 @ B @ C @ D @ E @ F @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2300]) ).

thf(1219,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k5_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finset_1) ).

thf(8368,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k5_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).

thf(467,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_xboole_0 @ A @ B )
     => ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_xboole_1) ).

thf(5041,plain,
    ! [A: $i,B: $i] :
      ( ( r1_xboole_0 @ A @ B )
     => ( ( k4_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(1915,axiom,
    r1_tarski @ k1_qc_lang1 @ ( k12_mcart_1 @ k1_numbers @ k1_numbers @ k5_numbers @ k5_numbers ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_qc_lang1) ).

thf(11744,plain,
    r1_tarski @ k1_qc_lang1 @ ( k12_mcart_1 @ k1_numbers @ k1_numbers @ k5_numbers @ k5_numbers ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1915]) ).

thf(1801,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ( ( k3_funcsdom @ A @ B @ C )
                = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funcsdom) ).

thf(11167,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ A @ B )
                & ( m2_relset_1 @ C @ A @ B ) )
             => ( ( k3_funcsdom @ A @ B @ C )
                = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1801]) ).

thf(145,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_xboole_0 @ B @ ( k4_relat_1 @ B ) ) )
       => ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
          & ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_sysrel) ).

thf(3379,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_xboole_0 @ B @ ( k4_relat_1 @ B ) ) )
       => ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
          & ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k4_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(899,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ C @ B ) )
        = ( k3_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_xboole_1) ).

thf(6924,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ C @ B ) )
        = ( k3_xboole_0 @ ( k2_xboole_0 @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).

thf(503,axiom,
    ! [A: $i] :
      ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
      = ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_zfmisc_1) ).

thf(5187,plain,
    ! [A: $i] :
      ( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
      = ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(291,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i] :
          ( ( r2_hidden @ B @ ( k4_finseq_1 @ A ) )
         => ( m2_subset_1 @ B @ k1_numbers @ k5_numbers ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finseq_3) ).

thf(4125,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i] :
          ( ( r2_hidden @ B @ ( k4_finseq_1 @ A ) )
         => ( m2_subset_1 @ B @ k1_numbers @ k5_numbers ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(929,axiom,
    ! [A: $i,B: $i] :
      ( ( k5_relat_1 @ ( k6_relat_1 @ B ) @ ( k6_relat_1 @ A ) )
      = ( k6_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funct_1) ).

thf(7081,plain,
    ! [A: $i,B: $i] :
      ( ( k5_relat_1 @ ( k6_relat_1 @ B ) @ ( k6_relat_1 @ A ) )
      = ( k6_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).

thf(1023,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_tarski @ A @ B )
      = ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_enumset1) ).

thf(7542,plain,
    ! [A: $i,B: $i] :
      ( ( k2_tarski @ A @ B )
      = ( k2_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).

thf(1142,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i,E: $i] :
                  ( ( ( v1_relat_1 @ E )
                    & ( v1_funct_1 @ E ) )
                 => ( ( ( k7_relat_1 @ A @ D )
                      = ( k7_relat_1 @ B @ D ) )
                   => ( ( k7_relat_1 @ ( k3_funcop_1 @ E @ C @ A ) @ D )
                      = ( k7_relat_1 @ ( k3_funcop_1 @ E @ C @ B ) @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_funcop_1) ).

thf(8070,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i,E: $i] :
                  ( ( ( v1_relat_1 @ E )
                    & ( v1_funct_1 @ E ) )
                 => ( ( ( k7_relat_1 @ A @ D )
                      = ( k7_relat_1 @ B @ D ) )
                   => ( ( k7_relat_1 @ ( k3_funcop_1 @ E @ C @ A ) @ D )
                      = ( k7_relat_1 @ ( k3_funcop_1 @ E @ C @ B ) @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).

thf(1373,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finset_1) ).

thf(9034,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k2_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373]) ).

thf(943,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( v1_fraenkel @ ( k1_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_fraenkel) ).

thf(7126,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( v1_fraenkel @ ( k1_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(988,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
      = ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_xboole_1) ).

thf(7355,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) )
      = ( k2_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).

thf(1529,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ A @ B )
     => ~ ( ( r2_hidden @ C @ D )
          & ! [E: $i,F: $i] :
              ~ ( ( C
                  = ( k4_tarski @ E @ F ) )
                & ( r2_hidden @ E @ A )
                & ( r2_hidden @ F @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relset_1) ).

thf(9806,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ A @ B )
     => ~ ( ( r2_hidden @ C @ D )
          & ! [E: $i,F: $i] :
              ~ ( ( C
                  = ( k4_tarski @ E @ F ) )
                & ( r2_hidden @ E @ A )
                & ( r2_hidden @ F @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1529]) ).

thf(1947,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ( r2_hidden @ D @ B )
                <=> ~ ( r2_hidden @ D @ C ) ) )
           => ( B
              = ( k3_subset_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_subset_1) ).

thf(11960,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ( ( r2_hidden @ D @ B )
                   => ~ ( r2_hidden @ D @ C ) )
                  & ( ~ ( r2_hidden @ D @ C )
                   => ( r2_hidden @ D @ B ) ) ) )
           => ( B
              = ( k3_subset_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1947]) ).

thf(338,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( B
              = ( k4_relat_1 @ A ) )
          <=> ! [C: $i,D: $i] :
                ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
              <=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).

thf(4378,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( ( ( B
                = ( k4_relat_1 @ A ) )
             => ! [C: $i,D: $i] :
                  ( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
                   => ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
                  & ( ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
                   => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) ) )
            & ( ! [C: $i,D: $i] :
                  ( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
                   => ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
                  & ( ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
                   => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
             => ( B
                = ( k4_relat_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(1985,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_finseq_2 @ B @ A ) )
     => ! [C: $i] :
          ( ( m2_finseq_2 @ C @ A @ B )
         => ( m2_finseq_1 @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_finseq_2) ).

thf(12162,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_finseq_2 @ B @ A ) )
     => ! [C: $i] :
          ( ( m2_finseq_2 @ C @ A @ B )
         => ( m2_finseq_1 @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1985]) ).

thf(2475,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( r2_hidden @ A @ ( a_3_5_domain_1 @ B @ C @ D ) )
      <=> ? [E: $i] :
            ( ( m1_subset_1 @ E @ B )
            & ( A = E )
            & ( ~ ( r2_hidden @ E @ C )
            <=> ( r2_hidden @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_5_domain_1) ).

thf(14386,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( ( r2_hidden @ A @ ( a_3_5_domain_1 @ B @ C @ D ) )
         => ? [E: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( A = E )
              & ( ~ ( r2_hidden @ E @ C )
               => ( r2_hidden @ E @ D ) )
              & ( ( r2_hidden @ E @ D )
               => ~ ( r2_hidden @ E @ C ) ) ) )
        & ( ? [E: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( A = E )
              & ( ~ ( r2_hidden @ E @ C )
               => ( r2_hidden @ E @ D ) )
              & ( ( r2_hidden @ E @ D )
               => ~ ( r2_hidden @ E @ C ) ) )
         => ( r2_hidden @ A @ ( a_3_5_domain_1 @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2475]) ).

thf(1722,axiom,
    m1_subset_1 @ k4_qc_lang1 @ ( k1_zfmisc_1 @ k1_qc_lang1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_qc_lang1) ).

thf(10681,plain,
    m1_subset_1 @ k4_qc_lang1 @ ( k1_zfmisc_1 @ k1_qc_lang1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1722]) ).

thf(854,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m2_relset_1 @ E @ A @ B ) )
     => ! [F: $i] :
          ( ( ( v1_funct_1 @ F )
            & ( v1_funct_2 @ F @ B @ C )
            & ( m2_relset_1 @ F @ B @ C ) )
         => ~ ( ( ( C = k1_xboole_0 )
               => ( B = k1_xboole_0 ) )
              & ( ( B = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ~ ( r1_tarski @ ( k3_funct_2 @ A @ B @ E @ D ) @ ( k3_funct_2 @ A @ C @ ( k1_partfun1 @ A @ B @ B @ C @ E @ F ) @ ( k2_funct_2 @ B @ C @ F @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funct_2) ).

thf(6693,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ B )
        & ( m2_relset_1 @ E @ A @ B ) )
     => ! [F: $i] :
          ( ( ( v1_funct_1 @ F )
            & ( v1_funct_2 @ F @ B @ C )
            & ( m2_relset_1 @ F @ B @ C ) )
         => ~ ( ( ( C = k1_xboole_0 )
               => ( B = k1_xboole_0 ) )
              & ( ( B = k1_xboole_0 )
               => ( A = k1_xboole_0 ) )
              & ~ ( r1_tarski @ ( k3_funct_2 @ A @ B @ E @ D ) @ ( k3_funct_2 @ A @ C @ ( k1_partfun1 @ A @ B @ B @ C @ E @ F ) @ ( k2_funct_2 @ B @ C @ F @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(947,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_fraenkel @ C @ A @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_fraenkel) ).

thf(7140,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_fraenkel @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).

thf(1551,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ! [D: $i,E: $i] :
            ( ( k4_tarski @ D @ E )
           != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_zfmisc_1) ).

thf(9922,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ! [D: $i,E: $i] :
            ( ( k4_tarski @ D @ E )
           != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1551]) ).

thf(122,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k10_finseq_1 @ A @ B )
     != ( k11_finseq_1 @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_finseq_3) ).

thf(3291,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( k10_finseq_1 @ A @ B )
     != ( k11_finseq_1 @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(655,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
     => ( m1_subset_1 @ ( k5_setwiseo @ A @ B @ C ) @ ( k5_finsub_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setwiseo) ).

thf(5796,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
     => ( m1_subset_1 @ ( k5_setwiseo @ A @ B @ C ) @ ( k5_finsub_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(2204,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i,D: $i] :
          ( ( ( r1_tarski @ C @ ( k2_cantor_1 @ A @ B ) )
            & ( r1_tarski @ D @ ( k2_cantor_1 @ A @ B ) ) )
         => ( r1_tarski @ ( k3_setfam_1 @ C @ D ) @ ( k2_cantor_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_cantor_1) ).

thf(13349,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i,D: $i] :
          ( ( ( r1_tarski @ C @ ( k2_cantor_1 @ A @ B ) )
            & ( r1_tarski @ D @ ( k2_cantor_1 @ A @ B ) ) )
         => ( r1_tarski @ ( k3_setfam_1 @ C @ D ) @ ( k2_cantor_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2204]) ).

thf(227,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ ( k1_setwiseo @ A ) )
      & ( m1_subset_1 @ ( k1_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setwiseo) ).

thf(3865,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ ( k1_setwiseo @ A ) )
      & ( m1_subset_1 @ ( k1_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_finseq_2 @ C @ B @ ( k4_finseq_2 @ A @ B ) )
             => ( ( k4_finseq_1 @ C )
                = ( k2_finseq_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_finseq_2) ).

thf(2719,plain,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_finseq_2 @ C @ B @ ( k4_finseq_2 @ A @ B ) )
             => ( ( k4_finseq_1 @ C )
                = ( k2_finseq_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(309,axiom,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ( ( ( k4_finseq_2 @ A @ C )
                  = ( k4_finseq_2 @ B @ C ) )
               => ( A = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_finseq_2) ).

thf(4254,plain,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ( ( ( k4_finseq_2 @ A @ C )
                  = ( k4_finseq_2 @ B @ C ) )
               => ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(1796,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k4_finsub_1 @ A @ B @ C )
        = ( k5_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_finsub_1) ).

thf(11140,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k4_finsub_1 @ A @ B @ C )
        = ( k5_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1796]) ).

thf(962,axiom,
    ! [A: $i] :
      ( ( k2_tarski @ A @ A )
      = ( k1_tarski @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).

thf(7231,plain,
    ! [A: $i] :
      ( ( k2_tarski @ A @ A )
      = ( k1_tarski @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).

thf(1300,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ A @ ( k5_xboole_0 @ B @ C ) )
      = ( k2_xboole_0 @ ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_xboole_1) ).

thf(8754,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ A @ ( k5_xboole_0 @ B @ C ) )
      = ( k2_xboole_0 @ ( k4_xboole_0 @ A @ ( k2_xboole_0 @ B @ C ) ) @ ( k3_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).

thf(184,axiom,
    ! [A: $i,B: $i] :
      ( ( k4_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
      = ( k2_zfmisc_1 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_sysrel) ).

thf(3601,plain,
    ! [A: $i,B: $i] :
      ( ( k4_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
      = ( k2_zfmisc_1 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(2113,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ A @ B )
     => ( ( r1_tarski @ B @ C )
       => ( ( k9_relset_1 @ A @ B @ C @ D )
          = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_relset_1) ).

thf(12876,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m2_relset_1 @ D @ A @ B )
     => ( ( r1_tarski @ B @ C )
       => ( ( k9_relset_1 @ A @ B @ C @ D )
          = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2113]) ).

thf(1055,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( k6_relat_1 @ A )
        = ( k7_relat_1 @ ( k6_relat_1 @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funct_3) ).

thf(7666,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ B )
     => ( ( k6_relat_1 @ A )
        = ( k7_relat_1 @ ( k6_relat_1 @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).

thf(724,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ C )
      = ( k5_xboole_0 @ A @ ( k5_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_xboole_1) ).

thf(6131,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k5_xboole_0 @ ( k5_xboole_0 @ A @ B ) @ C )
      = ( k5_xboole_0 @ A @ ( k5_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(2182,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
     => ( ( r1_tarski @ ( k1_funct_5 @ A ) @ B )
        & ( r1_tarski @ ( k2_funct_5 @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_funct_5) ).

thf(13257,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
     => ( ( r1_tarski @ ( k1_funct_5 @ A ) @ B )
        & ( r1_tarski @ ( k2_funct_5 @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2182]) ).

thf(1336,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( m1_relset_1 @ E @ A @ B )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( ( k7_relset_1 @ A @ B @ C @ D @ E @ F )
        = ( k5_relat_1 @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_relset_1) ).

thf(8908,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( m1_relset_1 @ E @ A @ B )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( ( k7_relset_1 @ A @ B @ C @ D @ E @ F )
        = ( k5_relat_1 @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).

thf(1973,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( r1_tarski @ B @ C )
           => ( r1_tarski @ ( k2_cantor_1 @ A @ B ) @ ( k2_cantor_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_cantor_1) ).

thf(12117,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( ( r1_tarski @ B @ C )
           => ( r1_tarski @ ( k2_cantor_1 @ A @ B ) @ ( k2_cantor_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1973]) ).

thf(76,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
        = ( k2_relat_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).

thf(3100,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
        = ( k2_relat_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(2564,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) )
           => ~ ( v1_xboole_0 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_tex_2) ).

thf(14779,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ( ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) )
           => ~ ( v1_xboole_0 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2564]) ).

thf(2163,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( r1_tarski @ B @ ( k1_cantor_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_cantor_1) ).

thf(13165,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( r1_tarski @ B @ ( k1_cantor_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2163]) ).

thf(2471,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
     => ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_finsub_1) ).

thf(14375,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
     => ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2471]) ).

thf(409,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finset_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finseq_1) ).

thf(4787,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finset_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(420,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( r2_hidden @ D @ ( k1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) ) )
                 => ( ( k1_funct_1 @ ( k3_funcop_1 @ C @ A @ B ) @ D )
                    = ( k1_binop_1 @ C @ ( k1_funct_1 @ A @ D ) @ ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_funcop_1) ).

thf(4841,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ! [D: $i] :
                  ( ( r2_hidden @ D @ ( k1_relat_1 @ ( k3_funcop_1 @ C @ A @ B ) ) )
                 => ( ( k1_funct_1 @ ( k3_funcop_1 @ C @ A @ B ) @ D )
                    = ( k1_binop_1 @ C @ ( k1_funct_1 @ A @ D ) @ ( k1_funct_1 @ B @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(848,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ( ( v2_binop_1 @ C @ B )
                           => ( ( k7_funcop_1 @ B @ A @ C @ ( k8_funcop_1 @ B @ A @ C @ E @ D ) @ F )
                              = ( k8_funcop_1 @ B @ A @ C @ E @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_funcop_1) ).

thf(6671,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ( ( v2_binop_1 @ C @ B )
                           => ( ( k7_funcop_1 @ B @ A @ C @ ( k8_funcop_1 @ B @ A @ C @ E @ D ) @ F )
                              = ( k8_funcop_1 @ B @ A @ C @ E @ ( k7_funcop_1 @ B @ A @ C @ D @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(2402,axiom,
    ! [A: $i] :
      ( ~ ( v2_setfam_1 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ A )
          & ~ ( v1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_setfam_1) ).

thf(14070,plain,
    ! [A: $i] :
      ( ~ ( v2_setfam_1 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ A )
          & ~ ( v1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2402]) ).

thf(87,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k1_relat_1 @ ( k3_cqc_lang @ A @ B ) )
        = ( k1_tarski @ A ) )
      & ( ( k2_relat_1 @ ( k3_cqc_lang @ A @ B ) )
        = ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_cqc_lang) ).

thf(3132,plain,
    ! [A: $i,B: $i] :
      ( ( ( k1_relat_1 @ ( k3_cqc_lang @ A @ B ) )
        = ( k1_tarski @ A ) )
      & ( ( k2_relat_1 @ ( k3_cqc_lang @ A @ B ) )
        = ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(1834,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( ( A != k1_xboole_0 )
         => ( ( m1_eqrel_1 @ B @ A )
          <=> ( ( ( k5_setfam_1 @ A @ B )
                = A )
              & ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                 => ( ( r2_hidden @ C @ B )
                   => ( ( C != k1_xboole_0 )
                      & ! [D: $i] :
                          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                         => ~ ( ( r2_hidden @ D @ B )
                              & ( C != D )
                              & ~ ( r1_xboole_0 @ C @ D ) ) ) ) ) ) ) ) )
        & ( ( A = k1_xboole_0 )
         => ( ( m1_eqrel_1 @ B @ A )
          <=> ( B = k1_xboole_0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_eqrel_1) ).

thf(11341,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( ( A != k1_xboole_0 )
         => ( ( ( m1_eqrel_1 @ B @ A )
             => ( ( ( k5_setfam_1 @ A @ B )
                  = A )
                & ! [C: $i] :
                    ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                   => ( ( r2_hidden @ C @ B )
                     => ( ( C != k1_xboole_0 )
                        & ! [D: $i] :
                            ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                           => ~ ( ( r2_hidden @ D @ B )
                                & ( C != D )
                                & ~ ( r1_xboole_0 @ C @ D ) ) ) ) ) ) ) )
            & ( ( ( ( k5_setfam_1 @ A @ B )
                  = A )
                & ! [C: $i] :
                    ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
                   => ( ( r2_hidden @ C @ B )
                     => ( ( C != k1_xboole_0 )
                        & ! [D: $i] :
                            ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                           => ~ ( ( r2_hidden @ D @ B )
                                & ( C != D )
                                & ~ ( r1_xboole_0 @ C @ D ) ) ) ) ) ) )
             => ( m1_eqrel_1 @ B @ A ) ) ) )
        & ( ( A = k1_xboole_0 )
         => ( ( ( m1_eqrel_1 @ B @ A )
             => ( B = k1_xboole_0 ) )
            & ( ( B = k1_xboole_0 )
             => ( m1_eqrel_1 @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1834]) ).

thf(2179,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ~ ( v1_xboole_0 @ E )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
                     => ( ( A
                          = ( k9_mcart_1 @ B @ C @ D @ E @ F ) )
                      <=> ! [G: $i] :
                            ( ( m1_subset_1 @ G @ B )
                           => ! [H: $i] :
                                ( ( m1_subset_1 @ H @ C )
                               => ! [I: $i] :
                                    ( ( m1_subset_1 @ I @ D )
                                   => ! [J: $i] :
                                        ( ( m1_subset_1 @ J @ E )
                                       => ( ( F
                                            = ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
                                         => ( A = H ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_domain_1) ).

thf(13225,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ! [E: $i] :
                  ( ~ ( v1_xboole_0 @ E )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) )
                     => ( ( ( A
                            = ( k9_mcart_1 @ B @ C @ D @ E @ F ) )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ C )
                                 => ! [I: $i] :
                                      ( ( m1_subset_1 @ I @ D )
                                     => ! [J: $i] :
                                          ( ( m1_subset_1 @ J @ E )
                                         => ( ( F
                                              = ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
                                           => ( A = H ) ) ) ) ) ) )
                        & ( ! [G: $i] :
                              ( ( m1_subset_1 @ G @ B )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ C )
                                 => ! [I: $i] :
                                      ( ( m1_subset_1 @ I @ D )
                                     => ! [J: $i] :
                                          ( ( m1_subset_1 @ J @ E )
                                         => ( ( F
                                              = ( k5_domain_1 @ B @ C @ D @ E @ G @ H @ I @ J ) )
                                           => ( A = H ) ) ) ) ) )
                         => ( A
                            = ( k9_mcart_1 @ B @ C @ D @ E @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2179]) ).

thf(1685,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( ! [B: $i] :
              ( ( m1_subset_1 @ B @ A )
             => ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
          & ( v1_realset1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_realset1) ).

thf(10515,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ~ ( ! [B: $i] :
              ( ( m1_subset_1 @ B @ A )
             => ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
          & ( v1_realset1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1685]) ).

thf(2436,axiom,
    ? [A: $i] :
      ( ( m2_relset_1 @ A @ f1_s1_relset_1 @ f2_s1_relset_1 )
      & ! [B: $i,C: $i] :
          ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
        <=> ( ( r2_hidden @ B @ f1_s1_relset_1 )
            & ( r2_hidden @ C @ f2_s1_relset_1 )
            & ( p1_s1_relset_1 @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_relset_1) ).

thf(14208,plain,
    ? [A: $i] :
      ( ( m2_relset_1 @ A @ f1_s1_relset_1 @ f2_s1_relset_1 )
      & ! [B: $i,C: $i] :
          ( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
           => ( ( r2_hidden @ B @ f1_s1_relset_1 )
              & ( r2_hidden @ C @ f2_s1_relset_1 )
              & ( p1_s1_relset_1 @ B @ C ) ) )
          & ( ( ( r2_hidden @ B @ f1_s1_relset_1 )
              & ( r2_hidden @ C @ f2_s1_relset_1 )
              & ( p1_s1_relset_1 @ B @ C ) )
           => ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2436]) ).

thf(2364,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( m1_subset_1 @ ( a_4_0_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s8_domain_1__e1_22__relset_2) ).

thf(13941,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ( m1_subset_1 @ ( a_4_0_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2364]) ).

thf(613,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( ( r1_xboole_0 @ B @ C )
              & ( r1_xboole_0 @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) )
           => ( B
              = ( k3_subset_1 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_subset_1) ).

thf(5601,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( ( r1_xboole_0 @ B @ C )
              & ( r1_xboole_0 @ ( k3_subset_1 @ A @ B ) @ ( k3_subset_1 @ A @ C ) ) )
           => ( B
              = ( k3_subset_1 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(350,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( k1_funct_2 @ A @ B ) )
    <=> ! [D: $i] :
          ( ( r2_hidden @ D @ C )
        <=> ? [E: $i] :
              ( ( v1_relat_1 @ E )
              & ( v1_funct_1 @ E )
              & ( D = E )
              & ( ( k1_relat_1 @ E )
                = A )
              & ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funct_2) ).

thf(4491,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C
          = ( k1_funct_2 @ A @ B ) )
       => ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ? [E: $i] :
                  ( ( v1_relat_1 @ E )
                  & ( v1_funct_1 @ E )
                  & ( D = E )
                  & ( ( k1_relat_1 @ E )
                    = A )
                  & ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) )
            & ( ? [E: $i] :
                  ( ( v1_relat_1 @ E )
                  & ( v1_funct_1 @ E )
                  & ( D = E )
                  & ( ( k1_relat_1 @ E )
                    = A )
                  & ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) )
             => ( r2_hidden @ D @ C ) ) ) )
      & ( ! [D: $i] :
            ( ( ( r2_hidden @ D @ C )
             => ? [E: $i] :
                  ( ( v1_relat_1 @ E )
                  & ( v1_funct_1 @ E )
                  & ( D = E )
                  & ( ( k1_relat_1 @ E )
                    = A )
                  & ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) ) )
            & ( ? [E: $i] :
                  ( ( v1_relat_1 @ E )
                  & ( v1_funct_1 @ E )
                  & ( D = E )
                  & ( ( k1_relat_1 @ E )
                    = A )
                  & ( r1_tarski @ ( k2_relat_1 @ E ) @ B ) )
             => ( r2_hidden @ D @ C ) ) )
       => ( C
          = ( k1_funct_2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(1770,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m2_relset_1 @ D @ C @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ( ( r2_hidden @ E @ ( k10_relset_1 @ C @ A @ D @ B ) )
                      <=> ? [F: $i] :
                            ( ( m1_subset_1 @ F @ C )
                            & ( r2_hidden @ ( k4_tarski @ F @ E ) @ D )
                            & ( r2_hidden @ F @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_relset_1) ).

thf(10998,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ( m2_relset_1 @ D @ C @ A )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ( ( ( r2_hidden @ E @ ( k10_relset_1 @ C @ A @ D @ B ) )
                         => ? [F: $i] :
                              ( ( m1_subset_1 @ F @ C )
                              & ( r2_hidden @ ( k4_tarski @ F @ E ) @ D )
                              & ( r2_hidden @ F @ B ) ) )
                        & ( ? [F: $i] :
                              ( ( m1_subset_1 @ F @ C )
                              & ( r2_hidden @ ( k4_tarski @ F @ E ) @ D )
                              & ( r2_hidden @ F @ B ) )
                         => ( r2_hidden @ E @ ( k10_relset_1 @ C @ A @ D @ B ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1770]) ).

thf(1397,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_eqrel_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_eqrel_1 @ C @ A )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ B @ C )
                & ( m2_relset_1 @ D @ B @ C ) )
             => ( ! [E: $i] :
                    ( ( r2_hidden @ E @ B )
                   => ( r1_tarski @ E @ ( k1_funct_1 @ D @ E ) ) )
               => ! [E: $i] :
                    ( ( m2_finseq_1 @ E @ B )
                   => ! [F: $i] :
                        ( ( m2_finseq_1 @ F @ C )
                       => ( ( r1_tarski @ ( k4_card_3 @ E ) @ ( k4_card_3 @ F ) )
                        <=> ( ( k1_partfun1 @ k5_numbers @ B @ B @ C @ E @ D )
                            = F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_pua2mss1) ).

thf(9156,plain,
    ! [A: $i,B: $i] :
      ( ( m1_eqrel_1 @ B @ A )
     => ! [C: $i] :
          ( ( m1_eqrel_1 @ C @ A )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ B @ C )
                & ( m2_relset_1 @ D @ B @ C ) )
             => ( ! [E: $i] :
                    ( ( r2_hidden @ E @ B )
                   => ( r1_tarski @ E @ ( k1_funct_1 @ D @ E ) ) )
               => ! [E: $i] :
                    ( ( m2_finseq_1 @ E @ B )
                   => ! [F: $i] :
                        ( ( m2_finseq_1 @ F @ C )
                       => ( ( ( r1_tarski @ ( k4_card_3 @ E ) @ ( k4_card_3 @ F ) )
                           => ( ( k1_partfun1 @ k5_numbers @ B @ B @ C @ E @ D )
                              = F ) )
                          & ( ( ( k1_partfun1 @ k5_numbers @ B @ B @ C @ E @ D )
                              = F )
                           => ( r1_tarski @ ( k4_card_3 @ E ) @ ( k4_card_3 @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397]) ).

thf(428,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ~ ( ( B != k1_xboole_0 )
          & ? [D: $i] :
              ( ( v1_funct_1 @ D )
              & ( v1_funct_2 @ D @ B @ A )
              & ( m2_relset_1 @ D @ B @ A )
              & ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
                = ( k6_partfun1 @ A ) ) )
          & ~ ( v2_funct_1 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_2) ).

thf(4885,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ~ ( ( B != k1_xboole_0 )
          & ? [D: $i] :
              ( ( v1_funct_1 @ D )
              & ( v1_funct_2 @ D @ B @ A )
              & ( m2_relset_1 @ D @ B @ A )
              & ( ( k1_partfun1 @ A @ B @ B @ A @ C @ D )
                = ( k6_partfun1 @ A ) ) )
          & ~ ( v2_funct_1 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(460,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_relset_1 @ C @ B @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ~ ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
                      & ! [E: $i] :
                          ( ( m1_subset_1 @ E @ B )
                         => ~ ( r2_hidden @ E @ ( k4_relset_1 @ B @ A @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_relset_1) ).

thf(5014,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m2_relset_1 @ C @ B @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ~ ( ( r2_hidden @ D @ ( k5_relset_1 @ B @ A @ C ) )
                      & ! [E: $i] :
                          ( ( m1_subset_1 @ E @ B )
                         => ~ ( r2_hidden @ E @ ( k4_relset_1 @ B @ A @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(2098,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ( ( ( E
                                = ( k1_realset1 @ C @ B ) )
                              & ( F
                                = ( k1_realset1 @ D @ B ) )
                              & ( r1_lattice2 @ A @ C @ D ) )
                           => ( r1_lattice2 @ B @ E @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_filter_2) ).

thf(12798,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ( ( ( E
                                = ( k1_realset1 @ C @ B ) )
                              & ( F
                                = ( k1_realset1 @ D @ B ) )
                              & ( r1_lattice2 @ A @ C @ D ) )
                           => ( r1_lattice2 @ B @ E @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2098]) ).

thf(1466,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_tarski @ A @ B )
       => ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_relat_1) ).

thf(9463,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ C )
     => ( ( r1_tarski @ A @ B )
       => ( r1_tarski @ ( k7_relat_1 @ C @ A ) @ ( k7_relat_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466]) ).

thf(1539,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( r1_tarski @ B @ C )
          <=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_subset_1) ).

thf(9844,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ( ( r1_tarski @ B @ C )
             => ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) ) )
            & ( ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ ( k3_subset_1 @ A @ B ) )
             => ( r1_tarski @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1539]) ).

thf(1635,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ F )
                            = ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funcop_1) ).

thf(10280,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ B @ A )
                    & ( m2_relset_1 @ D @ B @ A ) )
                 => ! [E: $i] :
                      ( ( m1_subset_1 @ E @ A )
                     => ! [F: $i] :
                          ( ( m1_subset_1 @ F @ B )
                         => ( ( k8_funct_2 @ B @ A @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ F )
                            = ( k2_binop_1 @ A @ A @ A @ C @ ( k8_funct_2 @ B @ A @ D @ F ) @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1635]) ).

thf(336,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( ( k1_relat_1 @ B )
          = ( k1_tarski @ A ) )
       => ( ( k2_relat_1 @ B )
          = ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_1) ).

thf(4367,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( ( k1_relat_1 @ B )
          = ( k1_tarski @ A ) )
       => ( ( k2_relat_1 @ B )
          = ( k1_tarski @ ( k1_funct_1 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(2148,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) )
     => ( ( r2_hidden @ A @ ( a_2_0_cantor_1 @ B @ C ) )
      <=> ? [D: $i] :
            ( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) @ C )
            & ( A
              = ( k8_setfam_1 @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_cantor_1) ).

thf(13096,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) )
     => ( ( ( r2_hidden @ A @ ( a_2_0_cantor_1 @ B @ C ) )
         => ? [D: $i] :
              ( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) @ C )
              & ( A
                = ( k8_setfam_1 @ B @ D ) ) ) )
        & ( ? [D: $i] :
              ( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) @ C )
              & ( A
                = ( k8_setfam_1 @ B @ D ) ) )
         => ( r2_hidden @ A @ ( a_2_0_cantor_1 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2148]) ).

thf(645,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( v2_funct_2 @ C @ A @ B )
       => ( r1_tarski @ ( k6_partfun1 @ B ) @ ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ A ) @ ( k2_zfmisc_1 @ B @ B ) @ ( k16_funct_3 @ A @ A @ B @ B @ C @ C ) @ ( k6_partfun1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_functor0) ).

thf(5760,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( v2_funct_2 @ C @ A @ B )
       => ( r1_tarski @ ( k6_partfun1 @ B ) @ ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ A ) @ ( k2_zfmisc_1 @ B @ B ) @ ( k16_funct_3 @ A @ A @ B @ B @ C @ C ) @ ( k6_partfun1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(1562,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).

thf(9976,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( r2_hidden @ B @ C )
        & ( r2_hidden @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562]) ).

thf(360,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k4_relat_1 @ ( k4_relat_1 @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).

thf(4565,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k4_relat_1 @ ( k4_relat_1 @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(692,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ B @ C )
                    & ( m2_relset_1 @ E @ B @ C ) )
                 => ! [F: $i] :
                      ( ( m1_pboole @ F @ A )
                     => ! [G: $i] :
                          ( ( m1_pboole @ G @ B )
                         => ! [H: $i] :
                              ( ( m1_pboole @ H @ C )
                             => ! [I: $i] :
                                  ( ( m1_functor0 @ I @ A @ B @ D @ F @ G )
                                 => ! [J: $i] :
                                      ( ( m1_functor0 @ J @ A @ C @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ ( k7_pboole @ A @ B @ D @ G ) @ H )
                                     => ( ! [K: $i] :
                                            ~ ( ( r2_hidden @ K @ A )
                                              & ( ( k1_funct_1 @ ( k7_pboole @ A @ B @ D @ G ) @ K )
                                                = k1_xboole_0 )
                                              & ( ( k1_funct_1 @ F @ K )
                                               != k1_xboole_0 )
                                              & ( ( k1_funct_1 @ ( k7_pboole @ A @ C @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ H ) @ K )
                                               != k1_xboole_0 ) )
                                       => ( m1_functor0 @ ( k13_pboole @ I @ J ) @ A @ C @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ F @ H ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_functor0) ).

thf(5990,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ B @ C )
                    & ( m2_relset_1 @ E @ B @ C ) )
                 => ! [F: $i] :
                      ( ( m1_pboole @ F @ A )
                     => ! [G: $i] :
                          ( ( m1_pboole @ G @ B )
                         => ! [H: $i] :
                              ( ( m1_pboole @ H @ C )
                             => ! [I: $i] :
                                  ( ( m1_functor0 @ I @ A @ B @ D @ F @ G )
                                 => ! [J: $i] :
                                      ( ( m1_functor0 @ J @ A @ C @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ ( k7_pboole @ A @ B @ D @ G ) @ H )
                                     => ( ! [K: $i] :
                                            ~ ( ( r2_hidden @ K @ A )
                                              & ( ( k1_funct_1 @ ( k7_pboole @ A @ B @ D @ G ) @ K )
                                                = k1_xboole_0 )
                                              & ( ( k1_funct_1 @ F @ K )
                                               != k1_xboole_0 )
                                              & ( ( k1_funct_1 @ ( k7_pboole @ A @ C @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ H ) @ K )
                                               != k1_xboole_0 ) )
                                       => ( m1_functor0 @ ( k13_pboole @ I @ J ) @ A @ C @ ( k7_funct_2 @ A @ B @ C @ D @ E ) @ F @ H ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(1488,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( k1_funct_5 @ A ) )
    <=> ! [C: $i] :
          ( ( r2_hidden @ C @ B )
        <=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_5) ).

thf(9541,plain,
    ! [A: $i,B: $i] :
      ( ( ( B
          = ( k1_funct_5 @ A ) )
       => ! [C: $i] :
            ( ( ( r2_hidden @ C @ B )
             => ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
            & ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
             => ( r2_hidden @ C @ B ) ) ) )
      & ( ! [C: $i] :
            ( ( ( r2_hidden @ C @ B )
             => ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
            & ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
             => ( r2_hidden @ C @ B ) ) )
       => ( B
          = ( k1_funct_5 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1488]) ).

thf(128,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ! [C: $i] :
            ~ ( ( r2_hidden @ C @ A )
              & ! [D: $i] :
                  ~ ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
                    & ( C
                      = ( k1_funct_1 @ B @ D ) ) ) )
       => ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_1) ).

thf(3323,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ! [C: $i] :
            ~ ( ( r2_hidden @ C @ A )
              & ! [D: $i] :
                  ~ ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
                    & ( C
                      = ( k1_funct_1 @ B @ D ) ) ) )
       => ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(538,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ( r1_tarski @ ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ A ) @ ( k2_zfmisc_1 @ B @ B ) @ ( k16_funct_3 @ A @ A @ B @ B @ C @ C ) @ ( k6_partfun1 @ A ) ) @ ( k6_partfun1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_functor0) ).

thf(5322,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ( r1_tarski @ ( k2_funct_2 @ ( k2_zfmisc_1 @ A @ A ) @ ( k2_zfmisc_1 @ B @ B ) @ ( k16_funct_3 @ A @ A @ B @ B @ C @ C ) @ ( k6_partfun1 @ A ) ) @ ( k6_partfun1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(2035,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( m2_cantor_1 @ B @ ( g1_pre_topc @ A @ ( k1_cantor_1 @ A @ ( k2_cantor_1 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_cantor_1) ).

thf(12444,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
         => ( m2_cantor_1 @ B @ ( g1_pre_topc @ A @ ( k1_cantor_1 @ A @ ( k2_cantor_1 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2035]) ).

thf(600,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k5_xboole_0 @ ( k1_funct_5 @ A ) @ ( k1_funct_5 @ B ) ) @ ( k1_funct_5 @ ( k5_xboole_0 @ A @ B ) ) )
      & ( r1_tarski @ ( k5_xboole_0 @ ( k2_funct_5 @ A ) @ ( k2_funct_5 @ B ) ) @ ( k2_funct_5 @ ( k5_xboole_0 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_5) ).

thf(5559,plain,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ ( k5_xboole_0 @ ( k1_funct_5 @ A ) @ ( k1_funct_5 @ B ) ) @ ( k1_funct_5 @ ( k5_xboole_0 @ A @ B ) ) )
      & ( r1_tarski @ ( k5_xboole_0 @ ( k2_funct_5 @ A ) @ ( k2_funct_5 @ B ) ) @ ( k2_funct_5 @ ( k5_xboole_0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(253,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_partfun1 @ A @ B )
          <=> ! [C: $i] :
                ( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
               => ( ( k1_funct_1 @ A @ C )
                  = ( k1_funct_1 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_partfun1) ).

thf(3982,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( r1_partfun1 @ A @ B )
             => ! [C: $i] :
                  ( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                 => ( ( k1_funct_1 @ A @ C )
                    = ( k1_funct_1 @ B @ C ) ) ) )
            & ( ! [C: $i] :
                  ( ( r2_hidden @ C @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
                 => ( ( k1_funct_1 @ A @ C )
                    = ( k1_funct_1 @ B @ C ) ) )
             => ( r1_partfun1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(1271,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ( ~ ( ( ( k4_ens_1 @ A @ B )
                  = k1_xboole_0 )
                & ( ( k3_ens_1 @ A @ B )
                 != k1_xboole_0 ) )
            & ( v1_funct_1 @ ( k2_mcart_1 @ B ) )
            & ( v1_funct_2 @ ( k2_mcart_1 @ B ) @ ( k3_ens_1 @ A @ B ) @ ( k4_ens_1 @ A @ B ) )
            & ( m2_relset_1 @ ( k2_mcart_1 @ B ) @ ( k3_ens_1 @ A @ B ) @ ( k4_ens_1 @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_ens_1) ).

thf(8616,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ( ~ ( ( ( k4_ens_1 @ A @ B )
                  = k1_xboole_0 )
                & ( ( k3_ens_1 @ A @ B )
                 != k1_xboole_0 ) )
            & ( v1_funct_1 @ ( k2_mcart_1 @ B ) )
            & ( v1_funct_2 @ ( k2_mcart_1 @ B ) @ ( k3_ens_1 @ A @ B ) @ ( k4_ens_1 @ A @ B ) )
            & ( m2_relset_1 @ ( k2_mcart_1 @ B ) @ ( k3_ens_1 @ A @ B ) @ ( k4_ens_1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).

thf(785,axiom,
    ! [A: $i,B: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_relat_1) ).

thf(6411,plain,
    ! [A: $i,B: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(980,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ C @ D ) )
      = ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ A @ D ) ) @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_zfmisc_1) ).

thf(7323,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_zfmisc_1 @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ C @ D ) )
      = ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ A @ D ) ) @ ( k2_zfmisc_1 @ B @ C ) ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).

thf(1719,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ B @ k1_xboole_0 ) )
         => ( C = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_partfun1) ).

thf(10649,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ B @ k1_xboole_0 ) )
         => ( C = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1719]) ).

thf(1071,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ C )
        & ( v1_classes2 @ C ) )
     => ( ( ( r2_hidden @ A @ C )
          & ( r2_hidden @ B @ C ) )
       => ( ( r2_hidden @ ( k2_xboole_0 @ A @ B ) @ C )
          & ( r2_hidden @ ( k3_xboole_0 @ A @ B ) @ C )
          & ( r2_hidden @ ( k4_xboole_0 @ A @ B ) @ C )
          & ( r2_hidden @ ( k5_xboole_0 @ A @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_classes2) ).

thf(7727,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ C )
        & ( v1_classes2 @ C ) )
     => ( ( ( r2_hidden @ A @ C )
          & ( r2_hidden @ B @ C ) )
       => ( ( r2_hidden @ ( k2_xboole_0 @ A @ B ) @ C )
          & ( r2_hidden @ ( k3_xboole_0 @ A @ B ) @ C )
          & ( r2_hidden @ ( k4_xboole_0 @ A @ B ) @ C )
          & ( r2_hidden @ ( k5_xboole_0 @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).

thf(2449,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
     => ~ ( v1_xboole_0 @ ( k1_funct_5 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_yellow_3) ).

thf(14266,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
     => ~ ( v1_xboole_0 @ ( k1_funct_5 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2449]) ).

thf(1604,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( r2_hidden @ A @ B )
       => ! [C: $i] :
            ( ( r2_hidden @ C @ ( k2_cantor_1 @ A @ B ) )
          <=> ? [D: $i] :
                ( ~ ( v1_xboole_0 @ D )
                & ( v1_finset_1 @ D )
                & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
                & ( r1_tarski @ D @ B )
                & ( C
                  = ( k8_setfam_1 @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_yellow_9) ).

thf(10141,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( r2_hidden @ A @ B )
       => ! [C: $i] :
            ( ( ( r2_hidden @ C @ ( k2_cantor_1 @ A @ B ) )
             => ? [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                  & ( v1_finset_1 @ D )
                  & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
                  & ( r1_tarski @ D @ B )
                  & ( C
                    = ( k8_setfam_1 @ A @ D ) ) ) )
            & ( ? [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                  & ( v1_finset_1 @ D )
                  & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
                  & ( r1_tarski @ D @ B )
                  & ( C
                    = ( k8_setfam_1 @ A @ D ) ) )
             => ( r2_hidden @ C @ ( k2_cantor_1 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1604]) ).

thf(1785,axiom,
    ! [A: $i,B: $i] :
      ( ( r1_tarski @ A @ ( k1_tarski @ B ) )
    <=> ( ( A = k1_xboole_0 )
        | ( A
          = ( k1_tarski @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).

thf(11082,plain,
    ! [A: $i,B: $i] :
      ( ( ( r1_tarski @ A @ ( k1_tarski @ B ) )
       => ( ( A = k1_xboole_0 )
          | ( A
            = ( k1_tarski @ B ) ) ) )
      & ( ( ( A = k1_xboole_0 )
          | ( A
            = ( k1_tarski @ B ) ) )
       => ( r1_tarski @ A @ ( k1_tarski @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1785]) ).

thf(129,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) )
        & ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_funct_2) ).

thf(3328,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) )
        & ( m2_relset_1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(1028,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_pboole @ D @ B )
        & ( m1_pboole @ E @ C )
        & ( m1_subset_1 @ F @ C )
        & ( m1_subset_1 @ G @ ( k1_funct_1 @ E @ F ) ) )
     => ( ( r2_hidden @ A @ ( a_6_0_functor0 @ B @ C @ D @ E @ F @ G ) )
      <=> ? [H: $i] :
            ( ( m1_subset_1 @ H @ B )
            & ( A
              = ( k4_tarski @ H @ ( k10_pboole @ ( k1_funct_1 @ D @ H ) @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_6_0_functor0) ).

thf(7557,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_pboole @ D @ B )
        & ( m1_pboole @ E @ C )
        & ( m1_subset_1 @ F @ C )
        & ( m1_subset_1 @ G @ ( k1_funct_1 @ E @ F ) ) )
     => ( ( ( r2_hidden @ A @ ( a_6_0_functor0 @ B @ C @ D @ E @ F @ G ) )
         => ? [H: $i] :
              ( ( m1_subset_1 @ H @ B )
              & ( A
                = ( k4_tarski @ H @ ( k10_pboole @ ( k1_funct_1 @ D @ H ) @ G ) ) ) ) )
        & ( ? [H: $i] :
              ( ( m1_subset_1 @ H @ B )
              & ( A
                = ( k4_tarski @ H @ ( k10_pboole @ ( k1_funct_1 @ D @ H ) @ G ) ) ) )
         => ( r2_hidden @ A @ ( a_6_0_functor0 @ B @ C @ D @ E @ F @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(331,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( ( k2_relat_1 @ A )
                = ( k1_relat_1 @ B ) )
              & ( ( k5_relat_1 @ A @ B )
                = ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
           => ( B
              = ( k2_funct_1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funct_1) ).

thf(4350,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( v2_funct_1 @ A )
              & ( ( k2_relat_1 @ A )
                = ( k1_relat_1 @ B ) )
              & ( ( k5_relat_1 @ A @ B )
                = ( k6_relat_1 @ ( k1_relat_1 @ A ) ) ) )
           => ( B
              = ( k2_funct_1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(1181,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( ( k4_card_3 @ A )
          = k1_xboole_0 )
      <=> ( r2_hidden @ k1_xboole_0 @ ( k2_relat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_card_3) ).

thf(8207,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( ( ( k4_card_3 @ A )
            = k1_xboole_0 )
         => ( r2_hidden @ k1_xboole_0 @ ( k2_relat_1 @ A ) ) )
        & ( ( r2_hidden @ k1_xboole_0 @ ( k2_relat_1 @ A ) )
         => ( ( k4_card_3 @ A )
            = k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).

thf(172,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k3_xboole_0 @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relat_1) ).

thf(3560,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k3_xboole_0 @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(633,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
             => ( ( ( k3_ens_1 @ A @ B )
                  = ( k4_ens_1 @ A @ C ) )
               => ( ( ( k2_mcart_1 @ ( k6_ens_1 @ A @ C @ B ) )
                    = ( k5_relat_1 @ ( k2_mcart_1 @ C ) @ ( k2_mcart_1 @ B ) ) )
                  & ( ( k3_ens_1 @ A @ ( k6_ens_1 @ A @ C @ B ) )
                    = ( k3_ens_1 @ A @ C ) )
                  & ( ( k4_ens_1 @ A @ ( k6_ens_1 @ A @ C @ B ) )
                    = ( k4_ens_1 @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_ens_1) ).

thf(5709,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k2_ens_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k2_ens_1 @ A ) )
             => ( ( ( k3_ens_1 @ A @ B )
                  = ( k4_ens_1 @ A @ C ) )
               => ( ( ( k2_mcart_1 @ ( k6_ens_1 @ A @ C @ B ) )
                    = ( k5_relat_1 @ ( k2_mcart_1 @ C ) @ ( k2_mcart_1 @ B ) ) )
                  & ( ( k3_ens_1 @ A @ ( k6_ens_1 @ A @ C @ B ) )
                    = ( k3_ens_1 @ A @ C ) )
                  & ( ( k4_ens_1 @ A @ ( k6_ens_1 @ A @ C @ B ) )
                    = ( k4_ens_1 @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(431,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ! [D: $i] :
              ( ( ( v1_relat_1 @ D )
                & ( v1_funct_1 @ D ) )
             => ( ( r2_hidden @ C @ ( k4_card_3 @ B ) )
               => ( r2_hidden @ ( k5_relat_1 @ D @ C ) @ ( k4_card_3 @ ( k5_relat_1 @ D @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_pre_circ) ).

thf(4895,plain,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ! [D: $i] :
              ( ( ( v1_relat_1 @ D )
                & ( v1_funct_1 @ D ) )
             => ( ( r2_hidden @ C @ ( k4_card_3 @ B ) )
               => ( r2_hidden @ ( k5_relat_1 @ D @ C ) @ ( k4_card_3 @ ( k5_relat_1 @ D @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(2277,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k1_cantor_1 @ A @ ( k2_cantor_1 @ A @ ( k1_cantor_1 @ A @ B ) ) )
        = ( k1_cantor_1 @ A @ ( k2_cantor_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_yellow_9) ).

thf(13614,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k1_cantor_1 @ A @ ( k2_cantor_1 @ A @ ( k1_cantor_1 @ A @ B ) ) )
        = ( k1_cantor_1 @ A @ ( k2_cantor_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2277]) ).

thf(2456,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( m1_subset_1 @ ( k2_cat_5 @ A @ B @ C @ D ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_cat_5) ).

thf(14315,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) )
     => ( m1_subset_1 @ ( k2_cat_5 @ A @ B @ C @ D ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2456]) ).

thf(134,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ~ ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
           => ( ( k1_funct_1 @ ( k1_funct_4 @ C @ B ) @ A )
              = ( k1_funct_1 @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_4) ).

thf(3347,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ~ ( r2_hidden @ A @ ( k1_relat_1 @ B ) )
           => ( ( k1_funct_1 @ ( k1_funct_4 @ C @ B ) @ A )
              = ( k1_funct_1 @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(721,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
          ( ( ( v1_funct_1 @ F )
            & ( v1_funct_2 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) @ A )
            & ( m2_relset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) @ A ) )
         => ! [G: $i] :
              ( ( ( v1_funct_1 @ G )
                & ( v1_funct_2 @ G @ ( k4_zfmisc_1 @ B @ C @ D @ E ) @ A )
                & ( m2_relset_1 @ G @ ( k4_zfmisc_1 @ B @ C @ D @ E ) @ A ) )
             => ( ! [H: $i,I: $i,J: $i,K: $i] :
                    ( ( ( r2_hidden @ H @ B )
                      & ( r2_hidden @ I @ C )
                      & ( r2_hidden @ J @ D )
                      & ( r2_hidden @ K @ E ) )
                   => ( ( k1_funct_1 @ F @ ( k4_mcart_1 @ H @ I @ J @ K ) )
                      = ( k1_funct_1 @ G @ ( k4_mcart_1 @ H @ I @ J @ K ) ) ) )
               => ( F = G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_multop_1) ).

thf(6114,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
          ( ( ( v1_funct_1 @ F )
            & ( v1_funct_2 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) @ A )
            & ( m2_relset_1 @ F @ ( k4_zfmisc_1 @ B @ C @ D @ E ) @ A ) )
         => ! [G: $i] :
              ( ( ( v1_funct_1 @ G )
                & ( v1_funct_2 @ G @ ( k4_zfmisc_1 @ B @ C @ D @ E ) @ A )
                & ( m2_relset_1 @ G @ ( k4_zfmisc_1 @ B @ C @ D @ E ) @ A ) )
             => ( ! [H: $i,I: $i,J: $i,K: $i] :
                    ( ( ( r2_hidden @ H @ B )
                      & ( r2_hidden @ I @ C )
                      & ( r2_hidden @ J @ D )
                      & ( r2_hidden @ K @ E ) )
                   => ( ( k1_funct_1 @ F @ ( k4_mcart_1 @ H @ I @ J @ K ) )
                      = ( k1_funct_1 @ G @ ( k4_mcart_1 @ H @ I @ J @ K ) ) ) )
               => ( F = G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(1609,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( v1_finset_1 @ ( k3_enumset1 @ A @ B @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_finset_1) ).

thf(10168,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( v1_finset_1 @ ( k3_enumset1 @ A @ B @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1609]) ).

thf(118,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ ( k2_funct_4 @ C ) ) )
       => ( ( k1_funct_1 @ ( k2_funct_4 @ C ) @ ( k4_tarski @ A @ B ) )
          = ( k1_funct_1 @ C @ ( k4_tarski @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_4) ).

thf(3277,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ ( k2_funct_4 @ C ) ) )
       => ( ( k1_funct_1 @ ( k2_funct_4 @ C ) @ ( k4_tarski @ A @ B ) )
          = ( k1_funct_1 @ C @ ( k4_tarski @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(1294,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_finset_1 @ A )
     => ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finset_1) ).

thf(8737,plain,
    ! [A: $i,B: $i] :
      ( ( v1_finset_1 @ A )
     => ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).

thf(316,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ ( k11_finseq_1 @ A @ B @ C ) )
      & ( v1_funct_1 @ ( k11_finseq_1 @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_finseq_1) ).

thf(4286,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_relat_1 @ ( k11_finseq_1 @ A @ B @ C ) )
      & ( v1_funct_1 @ ( k11_finseq_1 @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(2587,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ C ) ) )
     => ( ( r2_hidden @ A @ ( a_4_1_domain_1 @ B @ C @ D @ E ) )
      <=> ? [F: $i,G: $i] :
            ( ( m1_subset_1 @ F @ B )
            & ( m1_subset_1 @ G @ C )
            & ( A
              = ( k1_domain_1 @ B @ C @ F @ G ) )
            & ( r2_hidden @ F @ D )
            & ( r2_hidden @ G @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_1_domain_1) ).

thf(14903,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ C ) ) )
     => ( ( ( r2_hidden @ A @ ( a_4_1_domain_1 @ B @ C @ D @ E ) )
         => ? [F: $i,G: $i] :
              ( ( m1_subset_1 @ F @ B )
              & ( m1_subset_1 @ G @ C )
              & ( A
                = ( k1_domain_1 @ B @ C @ F @ G ) )
              & ( r2_hidden @ F @ D )
              & ( r2_hidden @ G @ E ) ) )
        & ( ? [F: $i,G: $i] :
              ( ( m1_subset_1 @ F @ B )
              & ( m1_subset_1 @ G @ C )
              & ( A
                = ( k1_domain_1 @ B @ C @ F @ G ) )
              & ( r2_hidden @ F @ D )
              & ( r2_hidden @ G @ E ) )
         => ( r2_hidden @ A @ ( a_4_1_domain_1 @ B @ C @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2587]) ).

thf(1937,axiom,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_setfam_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_setfam_1) ).

thf(11903,plain,
    ? [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
      & ( v1_setfam_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1937]) ).

thf(450,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ~ ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
             => ! [F: $i] :
                  ( ( m1_subset_1 @ F @ A )
                 => ( ( F
                      = ( k8_mcart_1 @ A @ B @ C @ D @ E ) )
                  <=> ! [G: $i,H: $i,I: $i,J: $i] :
                        ( ( E
                          = ( k4_mcart_1 @ G @ H @ I @ J ) )
                       => ( F = G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_mcart_1) ).

thf(4968,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ~ ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
             => ! [F: $i] :
                  ( ( m1_subset_1 @ F @ A )
                 => ( ( ( F
                        = ( k8_mcart_1 @ A @ B @ C @ D @ E ) )
                     => ! [G: $i,H: $i,I: $i,J: $i] :
                          ( ( E
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( F = G ) ) )
                    & ( ! [G: $i,H: $i,I: $i,J: $i] :
                          ( ( E
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( F = G ) )
                     => ( F
                        = ( k8_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(1190,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ C @ D )
                            & ( m2_relset_1 @ F @ C @ D ) )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ A )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ C )
                                 => ( ( k1_funct_1 @ ( k16_funct_3 @ A @ C @ B @ D @ E @ F ) @ ( k4_tarski @ G @ H ) )
                                    = ( k4_tarski @ ( k8_funct_2 @ A @ B @ E @ G ) @ ( k8_funct_2 @ C @ D @ F @ H ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_funct_3) ).

thf(8241,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ C @ D )
                            & ( m2_relset_1 @ F @ C @ D ) )
                         => ! [G: $i] :
                              ( ( m1_subset_1 @ G @ A )
                             => ! [H: $i] :
                                  ( ( m1_subset_1 @ H @ C )
                                 => ( ( k1_funct_1 @ ( k16_funct_3 @ A @ C @ B @ D @ E @ F ) @ ( k4_tarski @ G @ H ) )
                                    = ( k4_tarski @ ( k8_funct_2 @ A @ B @ E @ G ) @ ( k8_funct_2 @ C @ D @ F @ H ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).

thf(1257,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( v1_partfun1 @ C @ A @ B )
      <=> ( ( k4_relset_1 @ A @ B @ C )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_partfun1) ).

thf(8557,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( ( v1_partfun1 @ C @ A @ B )
         => ( ( k4_relset_1 @ A @ B @ C )
            = A ) )
        & ( ( ( k4_relset_1 @ A @ B @ C )
            = A )
         => ( v1_partfun1 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).

thf(2423,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A ) )
     => ( ( k8_domain_1 @ A @ B @ C @ D )
        = ( k1_enumset1 @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_domain_1) ).

thf(14159,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A ) )
     => ( ( k8_domain_1 @ A @ B @ C @ D )
        = ( k1_enumset1 @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2423]) ).

thf(841,axiom,
    ! [A: $i] :
      ( ( k20_mcart_1 @ A )
      = ( k2_mcart_1 @ ( k2_mcart_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_mcart_1) ).

thf(6644,plain,
    ! [A: $i] :
      ( ( k20_mcart_1 @ A )
      = ( k2_mcart_1 @ ( k2_mcart_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(923,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_finseq_2 @ B @ A ) )
     => ? [C: $i] : ( m2_finseq_2 @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_finseq_2) ).

thf(7050,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_finseq_2 @ B @ A ) )
     => ? [C: $i] : ( m2_finseq_2 @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).

thf(1339,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_relat_1 @ B ) )
     => ( v1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).

thf(8921,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_relat_1 @ B ) )
     => ( v1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339]) ).

thf(1231,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( r2_hidden @ C @ A )
         => ( r1_xboole_0 @ C @ B ) )
     => ( r1_xboole_0 @ ( k3_tarski @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_zfmisc_1) ).

thf(8424,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( r2_hidden @ C @ A )
         => ( r1_xboole_0 @ C @ B ) )
     => ( r1_xboole_0 @ ( k3_tarski @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).

thf(1418,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
     => ( m1_subset_1 @ ( k7_mcart_1 @ A @ B @ C @ D ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_mcart_1) ).

thf(9265,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
     => ( m1_subset_1 @ ( k7_mcart_1 @ A @ B @ C @ D ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418]) ).

thf(279,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relat_1) ).

thf(4083,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ! [B: $i] :
          ( ( v1_relat_1 @ B )
         => ( r1_tarski @ ( k1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(2482,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( r2_hidden @ A @ ( a_3_4_domain_1 @ B @ C @ D ) )
      <=> ? [E: $i] :
            ( ( m1_subset_1 @ E @ B )
            & ( A = E )
            & ( ( ( r2_hidden @ E @ C )
                & ~ ( r2_hidden @ E @ D ) )
              | ( ~ ( r2_hidden @ E @ C )
                & ( r2_hidden @ E @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_4_domain_1) ).

thf(14422,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
     => ( ( ( r2_hidden @ A @ ( a_3_4_domain_1 @ B @ C @ D ) )
         => ? [E: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( A = E )
              & ( ( ( r2_hidden @ E @ C )
                  & ~ ( r2_hidden @ E @ D ) )
                | ( ~ ( r2_hidden @ E @ C )
                  & ( r2_hidden @ E @ D ) ) ) ) )
        & ( ? [E: $i] :
              ( ( m1_subset_1 @ E @ B )
              & ( A = E )
              & ( ( ( r2_hidden @ E @ C )
                  & ~ ( r2_hidden @ E @ D ) )
                | ( ~ ( r2_hidden @ E @ C )
                  & ( r2_hidden @ E @ D ) ) ) )
         => ( r2_hidden @ A @ ( a_3_4_domain_1 @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2482]) ).

thf(21,axiom,
    ! [A: $i,B: $i] :
      ( ( m2_pua2mss1 @ B @ A )
     => ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_pua2mss1) ).

thf(2704,plain,
    ! [A: $i,B: $i] :
      ( ( m2_pua2mss1 @ B @ A )
     => ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(601,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( ! [E: $i] :
                  ( B
                 != ( k1_tarski @ E ) )
              & ( ( k5_partfun1 @ A @ B @ C )
                = ( k5_partfun1 @ A @ B @ D ) ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t168_funct_2) ).

thf(5564,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( ! [E: $i] :
                  ( B
                 != ( k1_tarski @ E ) )
              & ( ( k5_partfun1 @ A @ B @ C )
                = ( k5_partfun1 @ A @ B @ D ) ) )
           => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(2015,axiom,
    ! [A: $i] :
      ( ( A = k1_xboole_0 )
    <=> ! [B: $i] :
          ~ ( r2_hidden @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).

thf(12352,plain,
    ! [A: $i] :
      ( ( ( A = k1_xboole_0 )
       => ! [B: $i] :
            ~ ( r2_hidden @ B @ A ) )
      & ( ! [B: $i] :
            ~ ( r2_hidden @ B @ A )
       => ( A = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2015]) ).

thf(1546,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ~ ( v1_xboole_0 @ E )
                     => ( ( A
                          = ( k4_zfmisc_1 @ B @ C @ D @ E ) )
                      <=> ! [F: $i] :
                            ( ( r2_hidden @ F @ A )
                          <=> ? [G: $i] :
                                ( ( m1_subset_1 @ G @ B )
                                & ? [H: $i] :
                                    ( ( m1_subset_1 @ H @ C )
                                    & ? [I: $i] :
                                        ( ( m1_subset_1 @ I @ D )
                                        & ? [J: $i] :
                                            ( ( m1_subset_1 @ J @ E )
                                            & ( F
                                              = ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_domain_1) ).

thf(9874,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ~ ( v1_xboole_0 @ C )
             => ! [D: $i] :
                  ( ~ ( v1_xboole_0 @ D )
                 => ! [E: $i] :
                      ( ~ ( v1_xboole_0 @ E )
                     => ( ( ( A
                            = ( k4_zfmisc_1 @ B @ C @ D @ E ) )
                         => ! [F: $i] :
                              ( ( ( r2_hidden @ F @ A )
                               => ? [G: $i] :
                                    ( ( m1_subset_1 @ G @ B )
                                    & ? [H: $i] :
                                        ( ( m1_subset_1 @ H @ C )
                                        & ? [I: $i] :
                                            ( ( m1_subset_1 @ I @ D )
                                            & ? [J: $i] :
                                                ( ( m1_subset_1 @ J @ E )
                                                & ( F
                                                  = ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) ) )
                              & ( ? [G: $i] :
                                    ( ( m1_subset_1 @ G @ B )
                                    & ? [H: $i] :
                                        ( ( m1_subset_1 @ H @ C )
                                        & ? [I: $i] :
                                            ( ( m1_subset_1 @ I @ D )
                                            & ? [J: $i] :
                                                ( ( m1_subset_1 @ J @ E )
                                                & ( F
                                                  = ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) )
                               => ( r2_hidden @ F @ A ) ) ) )
                        & ( ! [F: $i] :
                              ( ( ( r2_hidden @ F @ A )
                               => ? [G: $i] :
                                    ( ( m1_subset_1 @ G @ B )
                                    & ? [H: $i] :
                                        ( ( m1_subset_1 @ H @ C )
                                        & ? [I: $i] :
                                            ( ( m1_subset_1 @ I @ D )
                                            & ? [J: $i] :
                                                ( ( m1_subset_1 @ J @ E )
                                                & ( F
                                                  = ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) ) )
                              & ( ? [G: $i] :
                                    ( ( m1_subset_1 @ G @ B )
                                    & ? [H: $i] :
                                        ( ( m1_subset_1 @ H @ C )
                                        & ? [I: $i] :
                                            ( ( m1_subset_1 @ I @ D )
                                            & ? [J: $i] :
                                                ( ( m1_subset_1 @ J @ E )
                                                & ( F
                                                  = ( k4_mcart_1 @ G @ H @ I @ J ) ) ) ) ) )
                               => ( r2_hidden @ F @ A ) ) )
                         => ( A
                            = ( k4_zfmisc_1 @ B @ C @ D @ E ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1546]) ).

thf(2045,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ A )
                     => ( ( k10_setwiseo @ A @ B @ ( k4_setwiseo @ A @ D @ E @ F ) @ C )
                        = ( k5_setwiseo @ B @ ( k5_setwiseo @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ E ) ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_setwiseo) ).

thf(12503,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ ( k5_finsub_1 @ B ) )
            & ( m2_relset_1 @ C @ A @ ( k5_finsub_1 @ B ) ) )
         => ! [D: $i] :
              ( ( m1_subset_1 @ D @ A )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ A )
                 => ! [F: $i] :
                      ( ( m1_subset_1 @ F @ A )
                     => ( ( k10_setwiseo @ A @ B @ ( k4_setwiseo @ A @ D @ E @ F ) @ C )
                        = ( k5_setwiseo @ B @ ( k5_setwiseo @ B @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ D ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ E ) ) @ ( k8_funct_2 @ A @ ( k5_finsub_1 @ B ) @ C @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2045]) ).

thf(859,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != B )
        & ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_funct_4 @ ( k6_partfun1 @ C ) @ ( k3_cqc_lang @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_7) ).

thf(6729,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != B )
        & ( r2_hidden @ A @ ( k2_relat_1 @ ( k1_funct_4 @ ( k6_partfun1 @ C ) @ ( k3_cqc_lang @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(541,axiom,
    ! [A: $i,B: $i] :
      ( ( m2_relset_1 @ B @ A @ A )
     => ( ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
          = B )
        & ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relset_1) ).

thf(5339,plain,
    ! [A: $i,B: $i] :
      ( ( m2_relset_1 @ B @ A @ A )
     => ( ( ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) )
          = B )
        & ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ B )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(2378,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
     => ( m1_subset_1 @ ( k16_domain_1 @ A @ B @ C @ D ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_domain_1) ).

thf(14001,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
     => ( m1_subset_1 @ ( k16_domain_1 @ A @ B @ C @ D ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2378]) ).

thf(2292,axiom,
    ! [A: $i] :
      ( ( r2_hidden @ A @ a_0_0_altcat_2 )
    <=> ? [B: $i] :
          ( ( m1_subset_1 @ B @ f1_s1_altcat_2 )
          & ( A
            = ( k4_tarski @ B @ ( f2_s1_altcat_2 @ B ) ) )
          & ( p1_s1_altcat_2 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_0_altcat_2) ).

thf(13663,plain,
    ! [A: $i] :
      ( ( ( r2_hidden @ A @ a_0_0_altcat_2 )
       => ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s1_altcat_2 )
            & ( A
              = ( k4_tarski @ B @ ( f2_s1_altcat_2 @ B ) ) )
            & ( p1_s1_altcat_2 @ B ) ) )
      & ( ? [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s1_altcat_2 )
            & ( A
              = ( k4_tarski @ B @ ( f2_s1_altcat_2 @ B ) ) )
            & ( p1_s1_altcat_2 @ B ) )
       => ( r2_hidden @ A @ a_0_0_altcat_2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2292]) ).

thf(753,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k7_relat_1 @ A @ k1_xboole_0 )
        = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_relat_1) ).

thf(6258,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k7_relat_1 @ A @ k1_xboole_0 )
        = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(2041,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [E: $i,F: $i,G: $i,H: $i] :
          ( ( ( g1_quantal1 @ A @ B @ C @ D )
            = ( g1_quantal1 @ E @ F @ G @ H ) )
         => ( ( A = E )
            & ( B = F )
            & ( C = G )
            & ( D = H ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_quantal1) ).

thf(12476,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ! [E: $i,F: $i,G: $i,H: $i] :
          ( ( ( g1_quantal1 @ A @ B @ C @ D )
            = ( g1_quantal1 @ E @ F @ G @ H ) )
         => ( ( A = E )
            & ( B = F )
            & ( C = G )
            & ( D = H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2041]) ).

thf(466,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ? [C: $i] :
          ( ( m1_relset_1 @ C @ A @ B )
          & ~ ( v1_xboole_0 @ C )
          & ( v1_relat_1 @ C )
          & ( v1_funct_1 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_pua2mss1) ).

thf(5036,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ? [C: $i] :
          ( ( m1_relset_1 @ C @ A @ B )
          & ~ ( v1_xboole_0 @ C )
          & ( v1_relat_1 @ C )
          & ( v1_funct_1 @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(671,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_eqrel_1 @ D @ B ) )
     => ( ( r2_hidden @ A @ ( a_3_1_pua2mss1 @ B @ C @ D ) )
      <=> ? [E: $i] :
            ( ( m2_subset_1 @ E @ ( k1_zfmisc_1 @ B ) @ D )
            & ( A
              = ( k3_xboole_0 @ E @ C ) )
            & ~ ( r1_xboole_0 @ E @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_pua2mss1) ).

thf(5867,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_eqrel_1 @ D @ B ) )
     => ( ( ( r2_hidden @ A @ ( a_3_1_pua2mss1 @ B @ C @ D ) )
         => ? [E: $i] :
              ( ( m2_subset_1 @ E @ ( k1_zfmisc_1 @ B ) @ D )
              & ( A
                = ( k3_xboole_0 @ E @ C ) )
              & ~ ( r1_xboole_0 @ E @ C ) ) )
        & ( ? [E: $i] :
              ( ( m2_subset_1 @ E @ ( k1_zfmisc_1 @ B ) @ D )
              & ( A
                = ( k3_xboole_0 @ E @ C ) )
              & ~ ( r1_xboole_0 @ E @ C ) )
         => ( r2_hidden @ A @ ( a_3_1_pua2mss1 @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(2544,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_tex_2) ).

thf(14704,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2544]) ).

thf(1894,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m2_card_fil @ B @ A )
         => ( r2_hidden @ k1_xboole_0 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_card_fil) ).

thf(11668,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m2_card_fil @ B @ A )
         => ( r2_hidden @ k1_xboole_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1894]) ).

thf(2583,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_setfam_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_triang_1) ).

thf(14888,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_setfam_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2583]) ).

thf(1200,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r1_tarski @ B @ A )
              & ( v6_ordinal1 @ B )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ! [D: $i] :
                        ( ( r2_hidden @ D @ B )
                       => ( r1_tarski @ C @ D ) ) ) )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ( C != B )
                    & ( r1_tarski @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t176_orders_1) ).

thf(8268,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r1_tarski @ B @ A )
              & ( v6_ordinal1 @ B )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ! [D: $i] :
                        ( ( r2_hidden @ D @ B )
                       => ( r1_tarski @ C @ D ) ) ) )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i] :
                  ~ ( ( r2_hidden @ C @ A )
                    & ( C != B )
                    & ( r1_tarski @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( ( k1_relat_1 @ ( k6_relat_1 @ A ) )
        = A )
      & ( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).

thf(2795,plain,
    ! [A: $i] :
      ( ( ( k1_relat_1 @ ( k6_relat_1 @ A ) )
        = A )
      & ( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(1744,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ B @ A )
        & ( m1_relset_1 @ D @ B @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( ( v1_funct_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) )
        & ( v1_funct_2 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
        & ( m2_relset_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funcop_1) ).

thf(10849,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ B @ A )
        & ( m1_relset_1 @ D @ B @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( ( v1_funct_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) )
        & ( v1_funct_2 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A )
        & ( m2_relset_1 @ ( k7_funcop_1 @ A @ B @ C @ D @ E ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1744]) ).

thf(2371,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ~ ( v1_xboole_0 @ ( k4_card_fil @ A ) )
        & ( m1_subset_1 @ ( k4_card_fil @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_card_fil) ).

thf(13966,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ~ ( v1_xboole_0 @ ( k4_card_fil @ A ) )
        & ( m1_subset_1 @ ( k4_card_fil @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2371]) ).

thf(2250,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k2_finsub_1 @ A @ B @ C )
        = ( k4_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).

thf(13517,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v4_finsub_1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k2_finsub_1 @ A @ B @ C )
        = ( k4_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2250]) ).

thf(1809,axiom,
    ! [A: $i] :
      ( ( k1_subset_1 @ A )
      = ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_subset_1) ).

thf(11204,plain,
    ! [A: $i] :
      ( ( k1_subset_1 @ A )
      = ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1809]) ).

thf(1787,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ( r2_hidden @ D @ B )
                 => ( r2_hidden @ D @ C ) ) )
           => ( r1_tarski @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_subset_1) ).

thf(11099,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ! [C: $i] :
          ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
         => ( ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ( r2_hidden @ D @ B )
                 => ( r2_hidden @ D @ C ) ) )
           => ( r1_tarski @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1787]) ).

thf(1862,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( r1_tarski @ B @ A )
         => ! [C: $i] :
              ( ( m1_eqrel_1 @ C @ A )
             => ( m1_eqrel_1 @ ( a_3_1_pua2mss1 @ A @ B @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_pua2mss1) ).

thf(11509,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( r1_tarski @ B @ A )
         => ! [C: $i] :
              ( ( m1_eqrel_1 @ C @ A )
             => ( m1_eqrel_1 @ ( a_3_1_pua2mss1 @ A @ B @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1862]) ).

thf(1713,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_funct_1 @ ( k9_funct_2 @ A @ B @ C ) )
      & ( v1_funct_2 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
      & ( m2_relset_1 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_funct_2) ).

thf(10622,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( v1_funct_1 @ ( k9_funct_2 @ A @ B @ C ) )
      & ( v1_funct_2 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
      & ( m2_relset_1 @ ( k9_funct_2 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1713]) ).

thf(1954,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
     => ( ( k17_domain_1 @ A @ B @ C @ D )
        = ( k20_mcart_1 @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k17_domain_1) ).

thf(12022,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ D @ ( k2_zfmisc_1 @ A @ ( k2_zfmisc_1 @ B @ C ) ) ) )
     => ( ( k17_domain_1 @ A @ B @ C @ D )
        = ( k20_mcart_1 @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1954]) ).

thf(2484,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k5_ens_1 @ A @ B ) @ ( k2_ens_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_ens_1) ).

thf(14439,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k5_ens_1 @ A @ B ) @ ( k2_ens_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2484]) ).

thf(1675,axiom,
    ( ( ( k1_funct_5 @ k1_xboole_0 )
      = k1_xboole_0 )
    & ( ( k2_funct_5 @ k1_xboole_0 )
      = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_funct_5) ).

thf(10485,plain,
    ( ( ( k1_funct_5 @ k1_xboole_0 )
      = k1_xboole_0 )
    & ( ( k2_funct_5 @ k1_xboole_0 )
      = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1675]) ).

thf(40,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( r1_binop_1 @ A @ B @ C )
          <=> ! [D: $i] :
                ( ( m1_subset_1 @ D @ A )
               => ( ( k1_binop_1 @ C @ B @ D )
                  = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_binop_1) ).

thf(2783,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ A )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ( ( ( r1_binop_1 @ A @ B @ C )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( k1_binop_1 @ C @ B @ D )
                    = D ) ) )
            & ( ! [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                 => ( ( k1_binop_1 @ C @ B @ D )
                    = D ) )
             => ( r1_binop_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(1061,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k1_funct_2 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_fraenkel) ).

thf(7684,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_finset_1 @ A )
        & ( v1_finset_1 @ B ) )
     => ( v1_finset_1 @ ( k1_funct_2 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).

thf(1734,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( r2_hidden @ k1_xboole_0 @ B )
       => ( ( k8_setfam_1 @ A @ B )
          = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_mssubfam) ).

thf(10781,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( r2_hidden @ k1_xboole_0 @ B )
       => ( ( k8_setfam_1 @ A @ B )
          = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734]) ).

thf(539,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i,E: $i,F: $i] :
                  ( ( ( r2_hidden @ C @ D )
                    & ( r2_hidden @ D @ E )
                    & ( r2_hidden @ E @ F )
                    & ( r2_hidden @ F @ B ) )
                 => ( r1_xboole_0 @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_mcart_1) ).

thf(5324,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i,E: $i,F: $i] :
                  ( ( ( r2_hidden @ C @ D )
                    & ( r2_hidden @ D @ E )
                    & ( r2_hidden @ E @ F )
                    & ( r2_hidden @ F @ B ) )
                 => ( r1_xboole_0 @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(1019,axiom,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i,E: $i] :
                  ~ ( ( ( r2_hidden @ C @ A )
                      | ( r2_hidden @ D @ A ) )
                    & ( B
                      = ( k3_mcart_1 @ C @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_mcart_1) ).

thf(7525,plain,
    ! [A: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i,E: $i] :
                  ~ ( ( ( r2_hidden @ C @ A )
                      | ( r2_hidden @ D @ A ) )
                    & ( B
                      = ( k3_mcart_1 @ C @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(1823,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k12_classes2 @ A @ B @ C )
        = ( k1_funct_2 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k12_classes2) ).

thf(11290,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A ) )
     => ( ( k12_classes2 @ A @ B @ C )
        = ( k1_funct_2 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1823]) ).

thf(756,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ C )
    <=> ( ( r2_hidden @ A @ C )
        & ( r2_hidden @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).

thf(6269,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r1_tarski @ ( k2_tarski @ A @ B ) @ C )
       => ( ( r2_hidden @ A @ C )
          & ( r2_hidden @ B @ C ) ) )
      & ( ( ( r2_hidden @ A @ C )
          & ( r2_hidden @ B @ C ) )
       => ( r1_tarski @ ( k2_tarski @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(809,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D ) )
     => ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_xboole_1) ).

thf(6503,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( r1_tarski @ A @ B )
        & ( r1_tarski @ C @ D ) )
     => ( r1_tarski @ ( k2_xboole_0 @ A @ C ) @ ( k2_xboole_0 @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(2286,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( ( r2_hidden @ B @ C )
            & ( r2_hidden @ C @ A ) )
         => ( r2_hidden @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_grcat_1) ).

thf(13646,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A ) )
     => ! [B: $i,C: $i] :
          ( ( ( r2_hidden @ B @ C )
            & ( r2_hidden @ C @ A ) )
         => ( r2_hidden @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2286]) ).

thf(1752,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A ) )
     => ! [G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
          ( ( ( g3_quantal1 @ A @ B @ C @ D @ E @ F )
            = ( g3_quantal1 @ G @ H @ I @ J @ K @ L ) )
         => ( ( A = G )
            & ( B = H )
            & ( C = I )
            & ( D = J )
            & ( E = K )
            & ( F = L ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_quantal1) ).

thf(10896,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A ) )
     => ! [G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
          ( ( ( g3_quantal1 @ A @ B @ C @ D @ E @ F )
            = ( g3_quantal1 @ G @ H @ I @ J @ K @ L ) )
         => ( ( A = G )
            & ( B = H )
            & ( C = I )
            & ( D = J )
            & ( E = K )
            & ( F = L ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1752]) ).

thf(1141,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ( ( ( r1_lattice2 @ A @ C @ D )
                              & ( r1_lattice2 @ B @ E @ F ) )
                          <=> ( r1_lattice2 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_filter_1) ).

thf(8066,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A )
                    & ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ( ( ( ( r1_lattice2 @ A @ C @ D )
                                & ( r1_lattice2 @ B @ E @ F ) )
                             => ( r1_lattice2 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) )
                            & ( ( r1_lattice2 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) )
                             => ( ( r1_lattice2 @ A @ C @ D )
                                & ( r1_lattice2 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).

thf(2066,axiom,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s12_funct_2 )
       => ( r2_hidden @ ( f3_s12_funct_2 @ A ) @ f2_s12_funct_2 ) )
   => ? [A: $i] :
        ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
        & ( m2_relset_1 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s12_funct_2 )
           => ( ( k8_funct_2 @ f1_s12_funct_2 @ f2_s12_funct_2 @ A @ B )
              = ( f3_s12_funct_2 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s12_funct_2) ).

thf(12626,plain,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s12_funct_2 )
       => ( r2_hidden @ ( f3_s12_funct_2 @ A ) @ f2_s12_funct_2 ) )
   => ? [A: $i] :
        ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
        & ( m2_relset_1 @ A @ f1_s12_funct_2 @ f2_s12_funct_2 )
        & ! [B: $i] :
            ( ( m1_subset_1 @ B @ f1_s12_funct_2 )
           => ( ( k8_funct_2 @ f1_s12_funct_2 @ f2_s12_funct_2 @ A @ B )
              = ( f3_s12_funct_2 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2066]) ).

thf(412,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ( ( A = k1_xboole_0 )
      <=> ( ( k4_finseq_1 @ A )
          = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finseq_1) ).

thf(4799,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ( ( ( A = k1_xboole_0 )
         => ( ( k4_finseq_1 @ A )
            = k1_xboole_0 ) )
        & ( ( ( k4_finseq_1 @ A )
            = k1_xboole_0 )
         => ( A = k1_xboole_0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(1470,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ( E != k1_xboole_0 )
        & ( F != k1_xboole_0 )
        & ( G != k1_xboole_0 )
        & ( H != k1_xboole_0 )
        & ? [I: $i] :
            ( ( m1_subset_1 @ I @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
            & ? [J: $i] :
                ( ( m1_subset_1 @ J @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
                & ( I = J )
                & ~ ( ( ( k8_mcart_1 @ A @ B @ C @ D @ I )
                      = ( k8_mcart_1 @ E @ F @ G @ H @ J ) )
                    & ( ( k9_mcart_1 @ A @ B @ C @ D @ I )
                      = ( k9_mcart_1 @ E @ F @ G @ H @ J ) )
                    & ( ( k10_mcart_1 @ A @ B @ C @ D @ I )
                      = ( k10_mcart_1 @ E @ F @ G @ H @ J ) )
                    & ( ( k11_mcart_1 @ A @ B @ C @ D @ I )
                      = ( k11_mcart_1 @ E @ F @ G @ H @ J ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_mcart_1) ).

thf(9474,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ( E != k1_xboole_0 )
        & ( F != k1_xboole_0 )
        & ( G != k1_xboole_0 )
        & ( H != k1_xboole_0 )
        & ? [I: $i] :
            ( ( m1_subset_1 @ I @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
            & ? [J: $i] :
                ( ( m1_subset_1 @ J @ ( k4_zfmisc_1 @ E @ F @ G @ H ) )
                & ( I = J )
                & ~ ( ( ( k8_mcart_1 @ A @ B @ C @ D @ I )
                      = ( k8_mcart_1 @ E @ F @ G @ H @ J ) )
                    & ( ( k9_mcart_1 @ A @ B @ C @ D @ I )
                      = ( k9_mcart_1 @ E @ F @ G @ H @ J ) )
                    & ( ( k10_mcart_1 @ A @ B @ C @ D @ I )
                      = ( k10_mcart_1 @ E @ F @ G @ H @ J ) )
                    & ( ( k11_mcart_1 @ A @ B @ C @ D @ I )
                      = ( k11_mcart_1 @ E @ F @ G @ H @ J ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470]) ).

thf(1476,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_xboole_1) ).

thf(9504,plain,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1476]) ).

thf(1393,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ? [E: $i] :
            ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
            & ? [F: $i,G: $i,H: $i,I: $i] :
                ( ( E
                  = ( k4_mcart_1 @ F @ G @ H @ I ) )
                & ~ ( ( ( k8_mcart_1 @ A @ B @ C @ D @ E )
                      = F )
                    & ( ( k9_mcart_1 @ A @ B @ C @ D @ E )
                      = G )
                    & ( ( k10_mcart_1 @ A @ B @ C @ D @ E )
                      = H )
                    & ( ( k11_mcart_1 @ A @ B @ C @ D @ E )
                      = I ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_mcart_1) ).

thf(9110,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ? [E: $i] :
            ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
            & ? [F: $i,G: $i,H: $i,I: $i] :
                ( ( E
                  = ( k4_mcart_1 @ F @ G @ H @ I ) )
                & ~ ( ( ( k8_mcart_1 @ A @ B @ C @ D @ E )
                      = F )
                    & ( ( k9_mcart_1 @ A @ B @ C @ D @ E )
                      = G )
                    & ( ( k10_mcart_1 @ A @ B @ C @ D @ E )
                      = H )
                    & ( ( k11_mcart_1 @ A @ B @ C @ D @ E )
                      = I ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393]) ).

thf(445,axiom,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ! [B: $i] :
          ( ( m4_realset1 @ B @ A )
         => ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_realset1) ).

thf(4955,plain,
    ! [A: $i] :
      ( ~ ( v1_realset1 @ A )
     => ! [B: $i] :
          ( ( m4_realset1 @ B @ A )
         => ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(1436,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
             => ( ( ( k1_funct_5 @ ( k9_relat_1 @ ( k15_funct_3 @ A @ B ) @ C ) )
                  = ( k9_relat_1 @ A @ ( k1_funct_5 @ C ) ) )
                & ( ( k2_funct_5 @ ( k9_relat_1 @ ( k15_funct_3 @ A @ B ) @ C ) )
                  = ( k9_relat_1 @ B @ ( k2_funct_5 @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_waybel20) ).

thf(9325,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) )
             => ( ( ( k1_funct_5 @ ( k9_relat_1 @ ( k15_funct_3 @ A @ B ) @ C ) )
                  = ( k9_relat_1 @ A @ ( k1_funct_5 @ C ) ) )
                & ( ( k2_funct_5 @ ( k9_relat_1 @ ( k15_funct_3 @ A @ B ) @ C ) )
                  = ( k9_relat_1 @ B @ ( k2_funct_5 @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436]) ).

thf(1287,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
      = ( k2_enumset1 @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ A @ D ) @ ( k4_tarski @ B @ C ) @ ( k4_tarski @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_mcart_1) ).

thf(8692,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_zfmisc_1 @ ( k2_tarski @ A @ B ) @ ( k2_tarski @ C @ D ) )
      = ( k2_enumset1 @ ( k4_tarski @ A @ C ) @ ( k4_tarski @ A @ D ) @ ( k4_tarski @ B @ C ) @ ( k4_tarski @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).

thf(726,axiom,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k1_numbers )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ k1_numbers )
         => ( ( k1_metric_1 @ k1_numbers @ k1_numbers @ k7_metric_1 @ A @ B )
            = ( k1_metric_1 @ k1_numbers @ k1_numbers @ k7_metric_1 @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_metric_1) ).

thf(6136,plain,
    ! [A: $i] :
      ( ( m1_subset_1 @ A @ k1_numbers )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ k1_numbers )
         => ( ( k1_metric_1 @ k1_numbers @ k1_numbers @ k7_metric_1 @ A @ B )
            = ( k1_metric_1 @ k1_numbers @ k1_numbers @ k7_metric_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(1532,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k13_ens_1 @ A @ B ) @ ( u1_cat_1 @ ( k12_ens_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_ens_1) ).

thf(9816,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k13_ens_1 @ A @ B ) @ ( u1_cat_1 @ ( k12_ens_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1532]) ).

thf(1444,axiom,
    ? [A: $i] :
      ( ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A )
      & ( v1_finset_1 @ A )
      & ( v1_fraenkel @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_closure2) ).

thf(9367,plain,
    ? [A: $i] :
      ( ( v1_xboole_0 @ A )
      & ( v1_relat_1 @ A )
      & ( v1_funct_1 @ A )
      & ( v2_funct_1 @ A )
      & ( v1_finset_1 @ A )
      & ( v1_fraenkel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444]) ).

thf(2522,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k7_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_subset_1) ).

thf(14640,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k7_subset_1 @ A @ B @ C ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2522]) ).

thf(2569,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_domain_1) ).

thf(14797,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( m1_subset_1 @ ( k6_domain_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2569]) ).

thf(68,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( C
                  = ( k3_funct_4 @ A @ B ) )
              <=> ( ! [D: $i] :
                      ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
                    <=> ? [E: $i,F: $i,G: $i,H: $i] :
                          ( ( D
                            = ( k4_tarski @ ( k4_tarski @ E @ G ) @ ( k4_tarski @ F @ H ) ) )
                          & ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k1_relat_1 @ A ) )
                          & ( r2_hidden @ ( k4_tarski @ G @ H ) @ ( k1_relat_1 @ B ) ) ) )
                  & ! [D: $i,E: $i,F: $i,G: $i] :
                      ( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ ( k1_relat_1 @ A ) )
                        & ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k1_relat_1 @ B ) ) )
                     => ( ( k1_funct_1 @ C @ ( k4_tarski @ ( k4_tarski @ D @ F ) @ ( k4_tarski @ E @ G ) ) )
                        = ( k4_tarski @ ( k1_funct_1 @ A @ ( k4_tarski @ D @ E ) ) @ ( k1_funct_1 @ B @ ( k4_tarski @ F @ G ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_funct_4) ).

thf(3025,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( ( C
                    = ( k3_funct_4 @ A @ B ) )
                 => ( ! [D: $i] :
                        ( ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
                         => ? [E: $i,F: $i,G: $i,H: $i] :
                              ( ( D
                                = ( k4_tarski @ ( k4_tarski @ E @ G ) @ ( k4_tarski @ F @ H ) ) )
                              & ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k1_relat_1 @ A ) )
                              & ( r2_hidden @ ( k4_tarski @ G @ H ) @ ( k1_relat_1 @ B ) ) ) )
                        & ( ? [E: $i,F: $i,G: $i,H: $i] :
                              ( ( D
                                = ( k4_tarski @ ( k4_tarski @ E @ G ) @ ( k4_tarski @ F @ H ) ) )
                              & ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k1_relat_1 @ A ) )
                              & ( r2_hidden @ ( k4_tarski @ G @ H ) @ ( k1_relat_1 @ B ) ) )
                         => ( r2_hidden @ D @ ( k1_relat_1 @ C ) ) ) )
                    & ! [D: $i,E: $i,F: $i,G: $i] :
                        ( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ ( k1_relat_1 @ A ) )
                          & ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k1_relat_1 @ B ) ) )
                       => ( ( k1_funct_1 @ C @ ( k4_tarski @ ( k4_tarski @ D @ F ) @ ( k4_tarski @ E @ G ) ) )
                          = ( k4_tarski @ ( k1_funct_1 @ A @ ( k4_tarski @ D @ E ) ) @ ( k1_funct_1 @ B @ ( k4_tarski @ F @ G ) ) ) ) ) ) )
                & ( ( ! [D: $i] :
                        ( ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
                         => ? [E: $i,F: $i,G: $i,H: $i] :
                              ( ( D
                                = ( k4_tarski @ ( k4_tarski @ E @ G ) @ ( k4_tarski @ F @ H ) ) )
                              & ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k1_relat_1 @ A ) )
                              & ( r2_hidden @ ( k4_tarski @ G @ H ) @ ( k1_relat_1 @ B ) ) ) )
                        & ( ? [E: $i,F: $i,G: $i,H: $i] :
                              ( ( D
                                = ( k4_tarski @ ( k4_tarski @ E @ G ) @ ( k4_tarski @ F @ H ) ) )
                              & ( r2_hidden @ ( k4_tarski @ E @ F ) @ ( k1_relat_1 @ A ) )
                              & ( r2_hidden @ ( k4_tarski @ G @ H ) @ ( k1_relat_1 @ B ) ) )
                         => ( r2_hidden @ D @ ( k1_relat_1 @ C ) ) ) )
                    & ! [D: $i,E: $i,F: $i,G: $i] :
                        ( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ ( k1_relat_1 @ A ) )
                          & ( r2_hidden @ ( k4_tarski @ F @ G ) @ ( k1_relat_1 @ B ) ) )
                       => ( ( k1_funct_1 @ C @ ( k4_tarski @ ( k4_tarski @ D @ F ) @ ( k4_tarski @ E @ G ) ) )
                          = ( k4_tarski @ ( k1_funct_1 @ A @ ( k4_tarski @ D @ E ) ) @ ( k1_funct_1 @ B @ ( k4_tarski @ F @ G ) ) ) ) ) )
                 => ( C
                    = ( k3_funct_4 @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(1658,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k3_enumset1 @ A @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_enumset1) ).

thf(10421,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k3_enumset1 @ A @ A @ B @ C @ D )
      = ( k2_enumset1 @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1658]) ).

thf(766,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( B != k1_xboole_0 )
       => ( ( ( k2_relat_1 @ C )
            = B )
        <=> ! [D: $i] :
              ( ( D != k1_xboole_0 )
             => ! [E: $i] :
                  ( ( ( v1_funct_1 @ E )
                    & ( v1_funct_2 @ E @ B @ D )
                    & ( m2_relset_1 @ E @ B @ D ) )
                 => ! [F: $i] :
                      ( ( ( v1_funct_1 @ F )
                        & ( v1_funct_2 @ F @ B @ D )
                        & ( m2_relset_1 @ F @ B @ D ) )
                     => ( ( ( k1_partfun1 @ A @ B @ B @ D @ C @ E )
                          = ( k1_partfun1 @ A @ B @ B @ D @ C @ F ) )
                       => ( E = F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_2) ).

thf(6316,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( B != k1_xboole_0 )
       => ( ( ( ( k2_relat_1 @ C )
              = B )
           => ! [D: $i] :
                ( ( D != k1_xboole_0 )
               => ! [E: $i] :
                    ( ( ( v1_funct_1 @ E )
                      & ( v1_funct_2 @ E @ B @ D )
                      & ( m2_relset_1 @ E @ B @ D ) )
                   => ! [F: $i] :
                        ( ( ( v1_funct_1 @ F )
                          & ( v1_funct_2 @ F @ B @ D )
                          & ( m2_relset_1 @ F @ B @ D ) )
                       => ( ( ( k1_partfun1 @ A @ B @ B @ D @ C @ E )
                            = ( k1_partfun1 @ A @ B @ B @ D @ C @ F ) )
                         => ( E = F ) ) ) ) ) )
          & ( ! [D: $i] :
                ( ( D != k1_xboole_0 )
               => ! [E: $i] :
                    ( ( ( v1_funct_1 @ E )
                      & ( v1_funct_2 @ E @ B @ D )
                      & ( m2_relset_1 @ E @ B @ D ) )
                   => ! [F: $i] :
                        ( ( ( v1_funct_1 @ F )
                          & ( v1_funct_2 @ F @ B @ D )
                          & ( m2_relset_1 @ F @ B @ D ) )
                       => ( ( ( k1_partfun1 @ A @ B @ B @ D @ C @ E )
                            = ( k1_partfun1 @ A @ B @ B @ D @ C @ F ) )
                         => ( E = F ) ) ) ) )
           => ( ( k2_relat_1 @ C )
              = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(2032,axiom,
    ( ( k6_relat_1 @ k1_xboole_0 )
    = k1_xboole_0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_relat_1) ).

thf(12435,plain,
    ( ( k6_relat_1 @ k1_xboole_0 )
    = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2032]) ).

thf(865,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ( ( r2_subset_1 @ A @ B )
      <=> ( r1_xboole_0 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r2_subset_1) ).

thf(6750,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ( ( ( r2_subset_1 @ A @ B )
         => ( r1_xboole_0 @ A @ B ) )
        & ( ( r1_xboole_0 @ A @ B )
         => ( r2_subset_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(2415,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m2_card_fil @ B @ A )
         => ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_card_fil) ).

thf(14127,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m2_card_fil @ B @ A )
         => ( ~ ( v1_xboole_0 @ B )
            & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2415]) ).

thf(2333,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ( ( r2_zfrefle1 @ A @ B )
       => ( r2_zfrefle1 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r2_zfrefle1) ).

thf(13807,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B ) )
     => ( ( r2_zfrefle1 @ A @ B )
       => ( r2_zfrefle1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2333]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
     => ( ( k6_setwiseo @ A @ B @ C )
        = ( k4_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setwiseo) ).

thf(2600,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k5_finsub_1 @ A ) ) )
     => ( ( k6_setwiseo @ A @ B @ C )
        = ( k4_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(2527,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k4_subset_1 @ A @ B @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).

thf(14651,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k4_subset_1 @ A @ B @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2527]) ).

thf(2560,axiom,
    ~ ( v1_xboole_0 @ k4_qc_lang1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_qc_lang1) ).

thf(14764,plain,
    ~ ( v1_xboole_0 @ k4_qc_lang1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2560]) ).

thf(1276,axiom,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ A @ B )
      = ( k2_xboole_0 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

thf(8643,plain,
    ! [A: $i,B: $i] :
      ( ( k2_xboole_0 @ A @ B )
      = ( k2_xboole_0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).

thf(1908,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k4_subset_1 @ A @ B @ ( k3_subset_1 @ A @ B ) )
        = ( k2_subset_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_subset_1) ).

thf(11707,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k4_subset_1 @ A @ B @ ( k3_subset_1 @ A @ B ) )
        = ( k2_subset_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1908]) ).

thf(621,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( v1_xboole_0 @ C )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ C )
            & ( m2_relset_1 @ D @ A @ C ) )
         => ( ( r1_tarski @ B @ ( k1_zfmisc_1 @ A ) )
           => ( ( k2_funct_2 @ A @ C @ D @ ( k3_tarski @ B ) )
              = ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ D ) @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_3) ).

thf(5637,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( v1_xboole_0 @ C )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( v1_funct_2 @ D @ A @ C )
            & ( m2_relset_1 @ D @ A @ C ) )
         => ( ( r1_tarski @ B @ ( k1_zfmisc_1 @ A ) )
           => ( ( k2_funct_2 @ A @ C @ D @ ( k3_tarski @ B ) )
              = ( k3_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ D ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(2440,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k7_subset_1 @ A @ B @ C )
                = ( a_3_4_domain_1 @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_domain_1) ).

thf(14225,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
             => ( ( k7_subset_1 @ A @ B @ C )
                = ( a_3_4_domain_1 @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2440]) ).

thf(1629,axiom,
    ! [A: $i] :
      ~ ( ( v6_ordinal1 @ A )
        & ! [B: $i] :
            ~ ( ( r1_tarski @ B @ A )
              & ( ( k3_tarski @ B )
                = ( k3_tarski @ A ) )
              & ! [C: $i] :
                  ~ ( ( r1_tarski @ C @ B )
                    & ( C != k1_xboole_0 )
                    & ! [D: $i] :
                        ~ ( ( r2_hidden @ D @ C )
                          & ! [E: $i] :
                              ( ( r2_hidden @ E @ C )
                             => ( r1_tarski @ D @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_card_3) ).

thf(10255,plain,
    ! [A: $i] :
      ~ ( ( v6_ordinal1 @ A )
        & ! [B: $i] :
            ~ ( ( r1_tarski @ B @ A )
              & ( ( k3_tarski @ B )
                = ( k3_tarski @ A ) )
              & ! [C: $i] :
                  ~ ( ( r1_tarski @ C @ B )
                    & ( C != k1_xboole_0 )
                    & ! [D: $i] :
                        ~ ( ( r2_hidden @ D @ C )
                          & ! [E: $i] :
                              ( ( r2_hidden @ E @ C )
                             => ( r1_tarski @ D @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1629]) ).

thf(2353,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( r1_filter_2 @ A @ B @ C )
       => ( r1_filter_2 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_filter_2) ).

thf(13894,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( r1_filter_2 @ A @ B @ C )
       => ( r1_filter_2 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2353]) ).

thf(1433,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k1_tarski @ A ) )
     => ! [E: $i] :
          ( ( m1_subset_1 @ E @ ( k1_tarski @ B ) )
         => ( ( k1_funct_1 @ ( k1_cat_1 @ A @ B @ C ) @ ( k4_tarski @ D @ E ) )
            = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_cat_1) ).

thf(9314,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( m1_subset_1 @ D @ ( k1_tarski @ A ) )
     => ! [E: $i] :
          ( ( m1_subset_1 @ E @ ( k1_tarski @ B ) )
         => ( ( k1_funct_1 @ ( k1_cat_1 @ A @ B @ C ) @ ( k4_tarski @ D @ E ) )
            = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1433]) ).

thf(2130,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ~ ( v1_xboole_0 @ E )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
        & ( m1_relset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
        & ( m1_subset_1 @ G @ A )
        & ( m1_subset_1 @ H @ B )
        & ( m1_subset_1 @ I @ C )
        & ( m1_subset_1 @ J @ D ) )
     => ( ( k4_multop_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J )
        = ( k3_multop_1 @ F @ G @ H @ I @ J ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_multop_1) ).

thf(12984,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ~ ( v1_xboole_0 @ E )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
        & ( m1_relset_1 @ F @ ( k4_zfmisc_1 @ A @ B @ C @ D ) @ E )
        & ( m1_subset_1 @ G @ A )
        & ( m1_subset_1 @ H @ B )
        & ( m1_subset_1 @ I @ C )
        & ( m1_subset_1 @ J @ D ) )
     => ( ( k4_multop_1 @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J )
        = ( k3_multop_1 @ F @ G @ H @ I @ J ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2130]) ).

thf(274,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_relat_1) ).

thf(4066,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(1394,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ( k8_funct_2 @ A @ A @ ( k8_funcop_1 @ A @ A @ B @ C @ ( k6_partfun1 @ A ) ) @ C )
                = ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funcop_1) ).

thf(9124,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ( v1_funct_1 @ B )
            & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
            & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ( k8_funct_2 @ A @ A @ ( k8_funcop_1 @ A @ A @ B @ C @ ( k6_partfun1 @ A ) ) @ C )
                = ( k2_binop_1 @ A @ A @ A @ B @ C @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394]) ).

thf(112,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ( v3_binop_1 @ B @ A )
      <=> ! [C: $i] :
            ( ( m1_subset_1 @ C @ A )
           => ( ( k1_binop_1 @ B @ C @ C )
              = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_binop_1) ).

thf(3245,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m2_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
     => ( ( ( v3_binop_1 @ B @ A )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ( k1_binop_1 @ B @ C @ C )
                = C ) ) )
        & ( ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ( k1_binop_1 @ B @ C @ C )
                = C ) )
         => ( v3_binop_1 @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(1743,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ( ( ( r1_binop_1 @ A @ C @ E )
                              & ( r1_binop_1 @ B @ D @ F ) )
                          <=> ( r1_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_filter_1) ).

thf(10845,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ( ( ( ( r1_binop_1 @ A @ C @ E )
                                & ( r1_binop_1 @ B @ D @ F ) )
                             => ( r1_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) )
                            & ( ( r1_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) )
                             => ( ( r1_binop_1 @ A @ C @ E )
                                & ( r1_binop_1 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1743]) ).

thf(920,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( r2_hidden @ A @ ( a_1_0_ens_1 @ B ) )
      <=> ? [C: $i,D: $i] :
            ( ( m1_subset_1 @ C @ B )
            & ( m1_subset_1 @ D @ B )
            & ( A
              = ( k1_funct_2 @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_ens_1) ).

thf(7025,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( ( r2_hidden @ A @ ( a_1_0_ens_1 @ B ) )
         => ? [C: $i,D: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( m1_subset_1 @ D @ B )
              & ( A
                = ( k1_funct_2 @ C @ D ) ) ) )
        & ( ? [C: $i,D: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( m1_subset_1 @ D @ B )
              & ( A
                = ( k1_funct_2 @ C @ D ) ) )
         => ( r2_hidden @ A @ ( a_1_0_ens_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).

thf(620,axiom,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i] :
                  ( ( k4_tarski @ C @ D )
                 != B ) )
        & ! [B: $i,C: $i,D: $i] :
            ( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
              & ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
           => ( C = D ) ) )
     => ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funct_1) ).

thf(5623,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ~ ( ( r2_hidden @ B @ A )
              & ! [C: $i,D: $i] :
                  ( ( k4_tarski @ C @ D )
                 != B ) )
        & ! [B: $i,C: $i,D: $i] :
            ( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
              & ( r2_hidden @ ( k4_tarski @ B @ D ) @ A ) )
           => ( C = D ) ) )
     => ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(469,axiom,
    ! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relat_1) ).

thf(5046,plain,
    ! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(1076,axiom,
    ! [A: $i,B: $i] :
      ( ( k3_xboole_0 @ A @ ( k3_tarski @ B ) )
      = ( k3_tarski @ ( k3_setfam_1 @ ( k1_tarski @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_setfam_1) ).

thf(7755,plain,
    ! [A: $i,B: $i] :
      ( ( k3_xboole_0 @ A @ ( k3_tarski @ B ) )
      = ( k3_tarski @ ( k3_setfam_1 @ ( k1_tarski @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).

thf(649,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B )
            & ( v1_finseq_1 @ B ) )
         => ( ( ( ( k4_finseq_1 @ A )
                = ( k4_finseq_1 @ B ) )
              & ! [C: $i] :
                  ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
                 => ( ( r2_hidden @ C @ ( k4_finseq_1 @ A ) )
                   => ( ( k1_funct_1 @ A @ C )
                      = ( k1_funct_1 @ B @ C ) ) ) ) )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finseq_1) ).

thf(5774,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_finseq_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B )
            & ( v1_finseq_1 @ B ) )
         => ( ( ( ( k4_finseq_1 @ A )
                = ( k4_finseq_1 @ B ) )
              & ! [C: $i] :
                  ( ( m2_subset_1 @ C @ k1_numbers @ k5_numbers )
                 => ( ( r2_hidden @ C @ ( k4_finseq_1 @ A ) )
                   => ( ( k1_funct_1 @ A @ C )
                      = ( k1_funct_1 @ B @ C ) ) ) ) )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(383,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k1_relat_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_relat_1) ).

thf(4659,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ ( k1_relat_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(394,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( ( r1_tarski @ ( k1_relat_1 @ A ) @ C )
                & ( r1_tarski @ ( k1_relat_1 @ B ) @ D )
                & ( r1_xboole_0 @ C @ D ) )
             => ( ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ C )
                  = A )
                & ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ D )
                  = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_funct_4) ).

thf(4713,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i,D: $i] :
              ( ( ( r1_tarski @ ( k1_relat_1 @ A ) @ C )
                & ( r1_tarski @ ( k1_relat_1 @ B ) @ D )
                & ( r1_xboole_0 @ C @ D ) )
             => ( ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ C )
                  = A )
                & ( ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ D )
                  = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(2515,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( r2_hidden @ A @ ( a_1_0_card_fil @ B ) )
      <=> ? [C: $i] :
            ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
            & ( A = C )
            & ( m1_card_fil @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_card_fil) ).

thf(14610,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( ( r2_hidden @ A @ ( a_1_0_card_fil @ B ) )
         => ? [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
              & ( A = C )
              & ( m1_card_fil @ C @ B ) ) )
        & ( ? [C: $i] :
              ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
              & ( A = C )
              & ( m1_card_fil @ C @ B ) )
         => ( r2_hidden @ A @ ( a_1_0_card_fil @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2515]) ).

thf(1566,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
        & ~ ( v1_xboole_0 @ D )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
        & ( v1_funct_1 @ E )
        & ( m1_relset_1 @ E @ ( k12_mcart_1 @ A @ A @ C @ C ) @ C )
        & ( v1_funct_1 @ F )
        & ( m1_relset_1 @ F @ ( k12_mcart_1 @ B @ B @ D @ D ) @ D ) )
     => ( ( k2_nattra_1 @ A @ B @ C @ D @ E @ F )
        = ( k3_funct_4 @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_nattra_1) ).

thf(9992,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
        & ~ ( v1_xboole_0 @ D )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) )
        & ( v1_funct_1 @ E )
        & ( m1_relset_1 @ E @ ( k12_mcart_1 @ A @ A @ C @ C ) @ C )
        & ( v1_funct_1 @ F )
        & ( m1_relset_1 @ F @ ( k12_mcart_1 @ B @ B @ D @ D ) @ D ) )
     => ( ( k2_nattra_1 @ A @ B @ C @ D @ E @ F )
        = ( k3_funct_4 @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1566]) ).

thf(513,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ~ ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
             => ( ( D
                 != ( k5_mcart_1 @ A @ B @ C @ D ) )
                & ( D
                 != ( k6_mcart_1 @ A @ B @ C @ D ) )
                & ( D
                 != ( k7_mcart_1 @ A @ B @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_mcart_1) ).

thf(5236,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ~ ! [D: $i] :
              ( ( m1_subset_1 @ D @ ( k3_zfmisc_1 @ A @ B @ C ) )
             => ( ( D
                 != ( k5_mcart_1 @ A @ B @ C @ D ) )
                & ( D
                 != ( k6_mcart_1 @ A @ B @ C @ D ) )
                & ( D
                 != ( k7_mcart_1 @ A @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(2500,axiom,
    ( ( ! [A: $i] :
          ( ( m1_subset_1 @ A @ f1_s4_subset_1 )
         => ( ( r2_hidden @ A @ f2_s4_subset_1 )
          <=> ( p1_s4_subset_1 @ A ) ) )
      & ! [A: $i] :
          ( ( m1_subset_1 @ A @ f1_s4_subset_1 )
         => ( ( r2_hidden @ A @ f3_s4_subset_1 )
          <=> ( p1_s4_subset_1 @ A ) ) ) )
   => ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_subset_1) ).

thf(14528,plain,
    ( ( ! [A: $i] :
          ( ( m1_subset_1 @ A @ f1_s4_subset_1 )
         => ( ( ( r2_hidden @ A @ f2_s4_subset_1 )
             => ( p1_s4_subset_1 @ A ) )
            & ( ( p1_s4_subset_1 @ A )
             => ( r2_hidden @ A @ f2_s4_subset_1 ) ) ) )
      & ! [A: $i] :
          ( ( m1_subset_1 @ A @ f1_s4_subset_1 )
         => ( ( ( r2_hidden @ A @ f3_s4_subset_1 )
             => ( p1_s4_subset_1 @ A ) )
            & ( ( p1_s4_subset_1 @ A )
             => ( r2_hidden @ A @ f3_s4_subset_1 ) ) ) ) )
   => ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2500]) ).

thf(1832,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ( ( ( r2_binop_1 @ A @ C @ E )
                              & ( r2_binop_1 @ B @ D @ F ) )
                          <=> ( r2_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_filter_1) ).

thf(11330,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ B )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( v1_funct_2 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ( ( ( ( r2_binop_1 @ A @ C @ E )
                                & ( r2_binop_1 @ B @ D @ F ) )
                             => ( r2_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) ) )
                            & ( ( r2_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k1_domain_1 @ A @ B @ C @ D ) @ ( k7_filter_1 @ A @ B @ E @ F ) )
                             => ( ( r2_binop_1 @ A @ C @ E )
                                & ( r2_binop_1 @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1832]) ).

thf(1691,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ B @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_enumset1) ).

thf(10535,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ B @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1691]) ).

thf(717,axiom,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i,C: $i] :
          ( ( m2_finseq_1 @ C @ B )
         => ( ( r2_hidden @ A @ ( k4_finseq_1 @ C ) )
           => ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finseq_2) ).

thf(6104,plain,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i,C: $i] :
          ( ( m2_finseq_1 @ C @ B )
         => ( ( r2_hidden @ A @ ( k4_finseq_1 @ C ) )
           => ( r2_hidden @ ( k1_funct_1 @ C @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(1665,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_relset_1 @ C @ A @ B )
    <=> ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).

thf(10440,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m1_relset_1 @ C @ A @ B )
       => ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
      & ( ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) )
       => ( m1_relset_1 @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1665]) ).

thf(932,axiom,
    ! [A: $i,B: $i] :
      ( ( k4_enumset1 @ A @ A @ A @ A @ A @ B )
      = ( k2_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_enumset1) ).

thf(7088,plain,
    ! [A: $i,B: $i] :
      ( ( k4_enumset1 @ A @ A @ A @ A @ A @ B )
      = ( k2_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).

thf(2190,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ k1_xboole_0 @ B ) )
         => ( C = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_partfun1) ).

thf(13279,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ k1_xboole_0 @ B ) )
         => ( C = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2190]) ).

thf(2228,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
        & ( m1_relset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ B )
        & ( m1_subset_1 @ H @ C ) )
     => ( ( k2_multop_1 @ A @ B @ C @ D @ E @ F @ G @ H )
        = ( k1_multop_1 @ E @ F @ G @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_multop_1) ).

thf(13449,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ~ ( v1_xboole_0 @ D )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
        & ( m1_relset_1 @ E @ ( k3_zfmisc_1 @ A @ B @ C ) @ D )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ B )
        & ( m1_subset_1 @ H @ C ) )
     => ( ( k2_multop_1 @ A @ B @ C @ D @ E @ F @ G @ H )
        = ( k1_multop_1 @ E @ F @ G @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2228]) ).

thf(1717,axiom,
    ! [A: $i] :
      ( ( k3_tarski @ ( k1_tarski @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).

thf(10642,plain,
    ! [A: $i] :
      ( ( k3_tarski @ ( k1_tarski @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1717]) ).

thf(1284,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D )
      = ( k2_xboole_0 @ A @ ( k2_xboole_0 @ ( k2_xboole_0 @ B @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_xboole_1) ).

thf(8680,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_xboole_0 @ ( k2_xboole_0 @ ( k2_xboole_0 @ A @ B ) @ C ) @ D )
      = ( k2_xboole_0 @ A @ ( k2_xboole_0 @ ( k2_xboole_0 @ B @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).

thf(1563,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ C @ ( k4_partfun1 @ A @ B ) )
     => ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_partfun1) ).

thf(9979,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r2_hidden @ C @ ( k4_partfun1 @ A @ B ) )
     => ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1563]) ).

thf(1164,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( m1_pboole @ C @ A )
         => ( ! [D: $i] :
                ( ( r2_hidden @ D @ A )
               => ( ( k1_funct_1 @ B @ D )
                  = ( k1_funct_1 @ C @ D ) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_pboole) ).

thf(8147,plain,
    ! [A: $i,B: $i] :
      ( ( m1_pboole @ B @ A )
     => ! [C: $i] :
          ( ( m1_pboole @ C @ A )
         => ( ! [D: $i] :
                ( ( r2_hidden @ D @ A )
               => ( ( k1_funct_1 @ B @ D )
                  = ( k1_funct_1 @ C @ D ) ) )
           => ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).

thf(80,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( ( k1_funct_4 @ A @ B )
              = ( k1_funct_4 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_funct_4) ).

thf(3113,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) )
           => ( ( k1_funct_4 @ A @ B )
              = ( k1_funct_4 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(894,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ B @ ( k1_zfmisc_1 @ C ) )
        & ( m1_relset_1 @ D @ B @ ( k1_zfmisc_1 @ C ) ) )
     => ( ( k3_cantor_1 @ A @ B @ C @ D @ E )
        = ( k1_funct_1 @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_cantor_1) ).

thf(6911,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ B @ ( k1_zfmisc_1 @ C ) )
        & ( m1_relset_1 @ D @ B @ ( k1_zfmisc_1 @ C ) ) )
     => ( ( k3_cantor_1 @ A @ B @ C @ D @ E )
        = ( k1_funct_1 @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).

thf(1940,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ C @ D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_enumset1) ).

thf(11910,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k2_enumset1 @ A @ B @ C @ D )
      = ( k2_enumset1 @ C @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1940]) ).

thf(745,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_funct_4 @ ( k2_funcop_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
      = ( k2_funcop_1 @ ( k2_zfmisc_1 @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_6) ).

thf(6222,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k2_funct_4 @ ( k2_funcop_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
      = ( k2_funcop_1 @ ( k2_zfmisc_1 @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(1538,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_fraenkel @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_closure2) ).

thf(9842,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( v1_fraenkel @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538]) ).

thf(2297,axiom,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(13689,plain,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2297]) ).

thf(1930,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_eqrel_1 @ B @ A )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_setfam_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_borsuk_1) ).

thf(11875,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_eqrel_1 @ B @ A )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_setfam_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1930]) ).

thf(1232,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ ( k6_partfun1 @ B ) ) )
                    = ( k6_funcop_1 @ B @ A @ C @ D @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funcop_1) ).

thf(8427,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ( ( k7_funct_2 @ A @ B @ B @ D @ ( k6_funcop_1 @ B @ B @ C @ ( k6_partfun1 @ B ) @ ( k6_partfun1 @ B ) ) )
                    = ( k6_funcop_1 @ B @ A @ C @ D @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).

thf(330,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( ( k1_relat_1 @ A )
                = ( k1_relat_1 @ B ) )
              & ! [C: $i] :
                  ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
                 => ( ( k1_funct_1 @ A @ C )
                    = ( k1_funct_1 @ B @ C ) ) ) )
           => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).

thf(4345,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( ( ( k1_relat_1 @ A )
                = ( k1_relat_1 @ B ) )
              & ! [C: $i] :
                  ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
                 => ( ( k1_funct_1 @ A @ C )
                    = ( k1_funct_1 @ B @ C ) ) ) )
           => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(1206,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
        & ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_zfmisc_1) ).

thf(8305,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
        & ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).

thf(2412,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( r2_zfrefle1 @ A @ B )
          <=> ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ k9_zf_lang ) )
               => ( ( r1_zfrefle1 @ A @ C )
                <=> ( r1_zfrefle1 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfrefle1) ).

thf(14114,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( ( ( r2_zfrefle1 @ A @ B )
             => ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ k9_zf_lang ) )
                 => ( ( ( r1_zfrefle1 @ A @ C )
                     => ( r1_zfrefle1 @ B @ C ) )
                    & ( ( r1_zfrefle1 @ B @ C )
                     => ( r1_zfrefle1 @ A @ C ) ) ) ) )
            & ( ! [C: $i] :
                  ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ k9_zf_lang ) )
                 => ( ( ( r1_zfrefle1 @ A @ C )
                     => ( r1_zfrefle1 @ B @ C ) )
                    & ( ( r1_zfrefle1 @ B @ C )
                     => ( r1_zfrefle1 @ A @ C ) ) ) )
             => ( r2_zfrefle1 @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2412]) ).

thf(1338,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_realset1 @ C @ A @ B ) )
     => ( ( k2_realset1 @ A @ B @ C )
        = ( k1_realset1 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_realset1) ).

thf(8918,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_relset_1 @ B @ ( k2_zfmisc_1 @ A @ A ) @ A )
        & ( m1_realset1 @ C @ A @ B ) )
     => ( ( k2_realset1 @ A @ B @ C )
        = ( k1_realset1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).

thf(2477,axiom,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s1_filter_1 )
       => ( p1_s1_filter_1 @ ( k2_filter_1 @ f1_s1_filter_1 @ f2_s1_filter_1 @ A ) ) )
   => ! [A: $i] :
        ( ( m2_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s1_filter_1 ) @ ( k8_eqrel_1 @ f1_s1_filter_1 @ f2_s1_filter_1 ) )
       => ( p1_s1_filter_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_filter_1) ).

thf(14407,plain,
    ( ! [A: $i] :
        ( ( m1_subset_1 @ A @ f1_s1_filter_1 )
       => ( p1_s1_filter_1 @ ( k2_filter_1 @ f1_s1_filter_1 @ f2_s1_filter_1 @ A ) ) )
   => ! [A: $i] :
        ( ( m2_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s1_filter_1 ) @ ( k8_eqrel_1 @ f1_s1_filter_1 @ f2_s1_filter_1 ) )
       => ( p1_s1_filter_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2477]) ).

thf(966,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ~ ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
             => ! [F: $i] :
                  ( ( m1_subset_1 @ F @ C )
                 => ( ( F
                      = ( k10_mcart_1 @ A @ B @ C @ D @ E ) )
                  <=> ! [G: $i,H: $i,I: $i,J: $i] :
                        ( ( E
                          = ( k4_mcart_1 @ G @ H @ I @ J ) )
                       => ( F = I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_mcart_1) ).

thf(7246,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ~ ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
             => ! [F: $i] :
                  ( ( m1_subset_1 @ F @ C )
                 => ( ( ( F
                        = ( k10_mcart_1 @ A @ B @ C @ D @ E ) )
                     => ! [G: $i,H: $i,I: $i,J: $i] :
                          ( ( E
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( F = I ) ) )
                    & ( ! [G: $i,H: $i,I: $i,J: $i] :
                          ( ( E
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( F = I ) )
                     => ( F
                        = ( k10_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).

thf(302,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ( ( ( ( k1_relat_1 @ C )
                = ( k2_zfmisc_1 @ A @ B ) )
              & ( ( k1_relat_1 @ D )
                = ( k2_zfmisc_1 @ A @ B ) )
              & ! [E: $i,F: $i] :
                  ( ( ( r2_hidden @ E @ A )
                    & ( r2_hidden @ F @ B ) )
                 => ( ( k1_funct_1 @ C @ ( k4_tarski @ E @ F ) )
                    = ( k1_funct_1 @ D @ ( k4_tarski @ E @ F ) ) ) ) )
           => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_3) ).

thf(4221,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ! [D: $i] :
          ( ( ( v1_relat_1 @ D )
            & ( v1_funct_1 @ D ) )
         => ( ( ( ( k1_relat_1 @ C )
                = ( k2_zfmisc_1 @ A @ B ) )
              & ( ( k1_relat_1 @ D )
                = ( k2_zfmisc_1 @ A @ B ) )
              & ! [E: $i,F: $i] :
                  ( ( ( r2_hidden @ E @ A )
                    & ( r2_hidden @ F @ B ) )
                 => ( ( k1_funct_1 @ C @ ( k4_tarski @ E @ F ) )
                    = ( k1_funct_1 @ D @ ( k4_tarski @ E @ F ) ) ) ) )
           => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(2550,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k8_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_setfam_1) ).

thf(14727,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k8_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2550]) ).

thf(573,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
        = k1_xboole_0 )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_zfmisc_1) ).

thf(5473,plain,
    ! [A: $i,B: $i] :
      ( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
        = k1_xboole_0 )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(666,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ~ ( ( r2_hidden @ C @ ( k2_relat_1 @ D ) )
          & ! [E: $i] :
              ( ( m1_subset_1 @ E @ A )
             => ~ ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ D ) )
                  & ( C
                    = ( k1_funct_1 @ D @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_partfun1) ).

thf(5845,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( v1_funct_1 @ D )
        & ( m2_relset_1 @ D @ A @ B ) )
     => ~ ( ( r2_hidden @ C @ ( k2_relat_1 @ D ) )
          & ! [E: $i] :
              ( ( m1_subset_1 @ E @ A )
             => ~ ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ D ) )
                  & ( C
                    = ( k1_funct_1 @ D @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(1848,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ! [C: $i] :
            ( ( r2_hidden @ C @ A )
           => ( r2_hidden @ ( k4_tarski @ C @ C ) @ B ) )
       => ( r1_tarski @ ( k6_relat_1 @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_relat_1) ).

thf(11430,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ B )
     => ( ! [C: $i] :
            ( ( r2_hidden @ C @ A )
           => ( r2_hidden @ ( k4_tarski @ C @ C ) @ B ) )
       => ( r1_tarski @ ( k6_relat_1 @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1848]) ).

thf(542,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( v2_funct_1 @ ( k6_pralg_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_pralg_1) ).

thf(5344,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ( v2_funct_1 @ ( k6_pralg_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(132,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B )
        & ( v1_finseq_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ C ) )
           => ( ( v1_relat_1 @ ( k5_funcop_1 @ C @ A @ B ) )
              & ( v1_funct_1 @ ( k5_funcop_1 @ C @ A @ B ) )
              & ( v1_finseq_1 @ ( k5_funcop_1 @ C @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_finseq_2) ).

thf(3341,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B )
        & ( v1_finseq_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ C ) )
           => ( ( v1_relat_1 @ ( k5_funcop_1 @ C @ A @ B ) )
              & ( v1_funct_1 @ ( k5_funcop_1 @ C @ A @ B ) )
              & ( v1_finseq_1 @ ( k5_funcop_1 @ C @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(2252,axiom,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ~ ( r2_hidden @ C @ B )
               => ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).

thf(13524,plain,
    ! [A: $i] :
      ( ( A != k1_xboole_0 )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ A )
             => ( ~ ( r2_hidden @ C @ B )
               => ( r2_hidden @ C @ ( k3_subset_1 @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2252]) ).

thf(2360,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A ) )
     => ( m1_subset_1 @ ( k10_domain_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_domain_1) ).

thf(13922,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A ) )
     => ( m1_subset_1 @ ( k10_domain_1 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2360]) ).

thf(595,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( r1_xboole_0 @ A @ B )
        & ( r1_xboole_0 @ A @ C )
        & ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_xboole_1) ).

thf(5542,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ~ ( r1_xboole_0 @ A @ B )
        & ( r1_xboole_0 @ A @ C )
        & ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(2062,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C ) )
     => ( ( r2_hidden @ A @ ( a_2_0_lattice5 @ B @ C ) )
      <=> ? [D: $i,E: $i] :
            ( ( m1_subset_1 @ D @ B )
            & ( m1_subset_1 @ E @ C )
            & ( A
              = ( k2_zfmisc_1 @ D @ E ) )
            & ( r2_hidden @ D @ B )
            & ( r2_hidden @ E @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice5) ).

thf(12579,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C ) )
     => ( ( ( r2_hidden @ A @ ( a_2_0_lattice5 @ B @ C ) )
         => ? [D: $i,E: $i] :
              ( ( m1_subset_1 @ D @ B )
              & ( m1_subset_1 @ E @ C )
              & ( A
                = ( k2_zfmisc_1 @ D @ E ) )
              & ( r2_hidden @ D @ B )
              & ( r2_hidden @ E @ C ) ) )
        & ( ? [D: $i,E: $i] :
              ( ( m1_subset_1 @ D @ B )
              & ( m1_subset_1 @ E @ C )
              & ( A
                = ( k2_zfmisc_1 @ D @ E ) )
              & ( r2_hidden @ D @ B )
              & ( r2_hidden @ E @ C ) )
         => ( r2_hidden @ A @ ( a_2_0_lattice5 @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2062]) ).

thf(752,axiom,
    ! [A: $i,B: $i] :
      ( ( ( k4_xboole_0 @ A @ B )
        = ( k4_xboole_0 @ B @ A ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_xboole_1) ).

thf(6254,plain,
    ! [A: $i,B: $i] :
      ( ( ( k4_xboole_0 @ A @ B )
        = ( k4_xboole_0 @ B @ A ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(783,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ~ ( v1_xboole_0 @ C )
                & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
             => ! [D: $i] :
                  ( ( ~ ( v1_xboole_0 @ D )
                    & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ! [G: $i] :
                              ( ( ( v1_funct_1 @ G )
                                & ( m2_relset_1 @ G @ ( k12_mcart_1 @ A @ A @ C @ C ) @ C ) )
                             => ( ( G
                                  = ( k1_realset1 @ E @ C ) )
                               => ! [H: $i] :
                                    ( ( ( v1_funct_1 @ H )
                                      & ( m2_relset_1 @ H @ ( k12_mcart_1 @ B @ B @ D @ D ) @ D ) )
                                   => ( ( H
                                        = ( k1_realset1 @ F @ D ) )
                                     => ( ( k2_nattra_1 @ A @ B @ C @ D @ G @ H )
                                        = ( k1_realset1 @ ( k10_cat_2 @ A @ B @ E @ F ) @ ( k12_mcart_1 @ A @ B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_nattra_1) ).

thf(6404,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ~ ( v1_xboole_0 @ C )
                & ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) )
             => ! [D: $i] :
                  ( ( ~ ( v1_xboole_0 @ D )
                    & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ B ) ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( m2_relset_1 @ E @ ( k2_zfmisc_1 @ A @ A ) @ A ) )
                     => ! [F: $i] :
                          ( ( ( v1_funct_1 @ F )
                            & ( m2_relset_1 @ F @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
                         => ! [G: $i] :
                              ( ( ( v1_funct_1 @ G )
                                & ( m2_relset_1 @ G @ ( k12_mcart_1 @ A @ A @ C @ C ) @ C ) )
                             => ( ( G
                                  = ( k1_realset1 @ E @ C ) )
                               => ! [H: $i] :
                                    ( ( ( v1_funct_1 @ H )
                                      & ( m2_relset_1 @ H @ ( k12_mcart_1 @ B @ B @ D @ D ) @ D ) )
                                   => ( ( H
                                        = ( k1_realset1 @ F @ D ) )
                                     => ( ( k2_nattra_1 @ A @ B @ C @ D @ G @ H )
                                        = ( k1_realset1 @ ( k10_cat_2 @ A @ B @ E @ F ) @ ( k12_mcart_1 @ A @ B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(400,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( k1_relat_1 @ C )
          = k1_xboole_0 )
       => ( ( v1_funct_1 @ C )
          & ( m2_relset_1 @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_partfun1) ).

thf(4734,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_relat_1 @ C )
        & ( v1_funct_1 @ C ) )
     => ( ( ( k1_relat_1 @ C )
          = k1_xboole_0 )
       => ( ( v1_funct_1 @ C )
          & ( m2_relset_1 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(2517,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( r2_hidden @ A @ ( a_1_6_domain_1 @ B ) )
      <=> ? [C: $i] :
            ( ( m1_subset_1 @ C @ B )
            & ( A = C )
            & ( p2_s6_domain_1 @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_6_domain_1) ).

thf(14621,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ( ( ( r2_hidden @ A @ ( a_1_6_domain_1 @ B ) )
         => ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A = C )
              & ( p2_s6_domain_1 @ C ) ) )
        & ( ? [C: $i] :
              ( ( m1_subset_1 @ C @ B )
              & ( A = C )
              & ( p2_s6_domain_1 @ C ) )
         => ( r2_hidden @ A @ ( a_1_6_domain_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2517]) ).

thf(1730,axiom,
    ! [A: $i,B: $i] :
      ~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).

thf(10706,plain,
    ! [A: $i,B: $i] :
      ~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1730]) ).

thf(500,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ~ ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
             => ! [F: $i] :
                  ( ( m1_subset_1 @ F @ B )
                 => ( ( F
                      = ( k9_mcart_1 @ A @ B @ C @ D @ E ) )
                  <=> ! [G: $i,H: $i,I: $i,J: $i] :
                        ( ( E
                          = ( k4_mcart_1 @ G @ H @ I @ J ) )
                       => ( F = H ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_mcart_1) ).

thf(5172,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ~ ( ( A != k1_xboole_0 )
        & ( B != k1_xboole_0 )
        & ( C != k1_xboole_0 )
        & ( D != k1_xboole_0 )
        & ~ ! [E: $i] :
              ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
             => ! [F: $i] :
                  ( ( m1_subset_1 @ F @ B )
                 => ( ( ( F
                        = ( k9_mcart_1 @ A @ B @ C @ D @ E ) )
                     => ! [G: $i,H: $i,I: $i,J: $i] :
                          ( ( E
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( F = H ) ) )
                    & ( ! [G: $i,H: $i,I: $i,J: $i] :
                          ( ( E
                            = ( k4_mcart_1 @ G @ H @ I @ J ) )
                         => ( F = H ) )
                     => ( F
                        = ( k9_mcart_1 @ A @ B @ C @ D @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(2486,axiom,
    m1_subset_1 @ a_0_0_group_5 @ ( k1_zfmisc_1 @ f2_s1_group_5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_group_5) ).

thf(14443,plain,
    m1_subset_1 @ a_0_0_group_5 @ ( k1_zfmisc_1 @ f2_s1_group_5 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2486]) ).

thf(2326,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k5_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).

thf(13792,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( m1_subset_1 @ ( k5_setfam_1 @ A @ B ) @ ( k1_zfmisc_1 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2326]) ).

thf(1348,axiom,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ ( k3_cqc_lang @ A @ B ) )
      & ( v1_funct_1 @ ( k3_cqc_lang @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_cqc_lang) ).

thf(8950,plain,
    ! [A: $i,B: $i] :
      ( ( v1_relat_1 @ ( k3_cqc_lang @ A @ B ) )
      & ( v1_funct_1 @ ( k3_cqc_lang @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).

thf(1559,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_eqrel_1 @ B @ A )
     => ( v1_setfam_1 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_eqrel_1) ).

thf(9954,plain,
    ! [A: $i,B: $i] :
      ( ( m1_eqrel_1 @ B @ A )
     => ( v1_setfam_1 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1559]) ).

thf(681,axiom,
    ! [A: $i,B: $i] :
      ( ( k10_pboole @ A @ B )
      = ( k2_funcop_1 @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_pboole) ).

thf(5943,plain,
    ! [A: $i,B: $i] :
      ( ( k10_pboole @ A @ B )
      = ( k2_funcop_1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(1981,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
     => ( m2_relset_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_funcop_1) ).

thf(12149,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ~ ( v1_xboole_0 @ B )
        & ~ ( v1_xboole_0 @ C )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( m1_relset_1 @ D @ A @ ( k2_zfmisc_1 @ B @ C ) ) )
     => ( m2_relset_1 @ ( k9_funcop_1 @ A @ B @ C @ D ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1981]) ).

thf(494,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( k5_relat_1 @ C @ ( k6_relat_1 @ B ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_partfun1) ).

thf(5155,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( k5_relat_1 @ C @ ( k6_relat_1 @ B ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(1027,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ~ ( v1_realset1 @ A )
      <=> ! [B: $i] :
            ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_realset1) ).

thf(7553,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( ~ ( v1_realset1 @ A )
         => ! [B: $i] :
              ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) )
        & ( ! [B: $i] :
              ~ ( v1_xboole_0 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
         => ~ ( v1_realset1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).

thf(2577,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ! [B: $i] :
            ( ( m1_subset_1 @ B @ A )
           => ( ( p1_s5_domain_1 @ B )
             => ( p2_s5_domain_1 @ B ) ) )
       => ( r1_tarski @ ( a_1_3_domain_1 @ A ) @ ( a_1_4_domain_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s5_domain_1) ).

thf(14858,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ! [B: $i] :
            ( ( m1_subset_1 @ B @ A )
           => ( ( p1_s5_domain_1 @ B )
             => ( p2_s5_domain_1 @ B ) ) )
       => ( r1_tarski @ ( a_1_3_domain_1 @ A ) @ ( a_1_4_domain_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2577]) ).

thf(1082,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_funct_4 @ A @ B @ C @ C )
      = ( k2_funcop_1 @ ( k2_tarski @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_4) ).

thf(7776,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_funct_4 @ A @ B @ C @ C )
      = ( k2_funcop_1 @ ( k2_tarski @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).

thf(1732,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( H
        = ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G ) )
    <=> ! [I: $i] :
          ( ( r2_hidden @ I @ H )
        <=> ~ ( ( I != A )
              & ( I != B )
              & ( I != C )
              & ( I != D )
              & ( I != E )
              & ( I != F )
              & ( I != G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_enumset1) ).

thf(10723,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ( H
          = ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G ) )
       => ! [I: $i] :
            ( ( ( r2_hidden @ I @ H )
             => ~ ( ( I != A )
                  & ( I != B )
                  & ( I != C )
                  & ( I != D )
                  & ( I != E )
                  & ( I != F )
                  & ( I != G ) ) )
            & ( ~ ( ( I != A )
                  & ( I != B )
                  & ( I != C )
                  & ( I != D )
                  & ( I != E )
                  & ( I != F )
                  & ( I != G ) )
             => ( r2_hidden @ I @ H ) ) ) )
      & ( ! [I: $i] :
            ( ( ( r2_hidden @ I @ H )
             => ~ ( ( I != A )
                  & ( I != B )
                  & ( I != C )
                  & ( I != D )
                  & ( I != E )
                  & ( I != F )
                  & ( I != G ) ) )
            & ( ~ ( ( I != A )
                  & ( I != B )
                  & ( I != C )
                  & ( I != D )
                  & ( I != E )
                  & ( I != F )
                  & ( I != G ) )
             => ( r2_hidden @ I @ H ) ) )
       => ( H
          = ( k5_enumset1 @ A @ B @ C @ D @ E @ F @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1732]) ).

thf(1365,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
           => ( v1_partfun1 @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t169_partfun1) ).

thf(9006,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ! [D: $i] :
          ( ( ( v1_funct_1 @ D )
            & ( m2_relset_1 @ D @ A @ B ) )
         => ( ( r2_hidden @ D @ ( k5_partfun1 @ A @ B @ C ) )
           => ( v1_partfun1 @ D @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).

thf(2350,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( ( k5_funct_4 @ A @ B @ C @ D @ E )
        = ( k4_funct_4 @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_funct_4) ).

thf(13881,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A ) )
     => ( ( k5_funct_4 @ A @ B @ C @ D @ E )
        = ( k4_funct_4 @ B @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2350]) ).

thf(2124,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m1_relset_1 @ D @ A @ B )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ B @ C )
        & ( m1_relset_1 @ E @ B @ C ) )
     => ( ( k7_funct_2 @ A @ B @ C @ D @ E )
        = ( k5_relat_1 @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).

thf(12965,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ D )
        & ( v1_funct_2 @ D @ A @ B )
        & ( m1_relset_1 @ D @ A @ B )
        & ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ B @ C )
        & ( m1_relset_1 @ E @ B @ C ) )
     => ( ( k7_funct_2 @ A @ B @ C @ D @ E )
        = ( k5_relat_1 @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2124]) ).

thf(1614,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_funct_4 @ A @ B @ C @ D )
      = ( k1_funct_4 @ ( k2_funcop_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_funcop_1 @ ( k1_tarski @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_4) ).

thf(10187,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_funct_4 @ A @ B @ C @ D )
      = ( k1_funct_4 @ ( k2_funcop_1 @ ( k1_tarski @ A ) @ C ) @ ( k2_funcop_1 @ ( k1_tarski @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1614]) ).

thf(2177,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
      & ( v1_realset1 @ ( k1_tarski @ A ) )
      & ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_tex_2) ).

thf(13215,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
      & ( v1_realset1 @ ( k1_tarski @ A ) )
      & ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2177]) ).

thf(241,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( ( v2_funct_1 @ B )
          & ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
       => ( ( A
            = ( k1_funct_1 @ ( k2_funct_1 @ B ) @ ( k1_funct_1 @ B @ A ) ) )
          & ( A
            = ( k1_funct_1 @ ( k5_relat_1 @ B @ ( k2_funct_1 @ B ) ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funct_1) ).

thf(3924,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( ( v2_funct_1 @ B )
          & ( r2_hidden @ A @ ( k1_relat_1 @ B ) ) )
       => ( ( A
            = ( k1_funct_1 @ ( k2_funct_1 @ B ) @ ( k1_funct_1 @ B @ A ) ) )
          & ( A
            = ( k1_funct_1 @ ( k5_relat_1 @ B @ ( k2_funct_1 @ B ) ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(1953,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_card_fil @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                 => ( ( r2_hidden @ D @ ( k3_card_fil @ A @ C @ B ) )
                  <=> ? [E: $i] :
                        ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
                        & ( r2_hidden @ E @ C )
                        & ( r1_tarski @ ( k5_subset_1 @ A @ E @ B ) @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_card_fil) ).

thf(12017,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
         => ! [C: $i] :
              ( ( m1_card_fil @ C @ A )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) )
                 => ( ( ( r2_hidden @ D @ ( k3_card_fil @ A @ C @ B ) )
                     => ? [E: $i] :
                          ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
                          & ( r2_hidden @ E @ C )
                          & ( r1_tarski @ ( k5_subset_1 @ A @ E @ B ) @ D ) ) )
                    & ( ? [E: $i] :
                          ( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ A ) )
                          & ( r2_hidden @ E @ C )
                          & ( r1_tarski @ ( k5_subset_1 @ A @ E @ B ) @ D ) )
                     => ( r2_hidden @ D @ ( k3_card_fil @ A @ C @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1953]) ).

thf(632,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_tarski @ A @ B )
           => ( r1_partfun1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t135_partfun1) ).

thf(5707,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( ( r1_tarski @ A @ B )
           => ( r1_partfun1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(2283,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( v1_funct_1 @ ( k9_ens_1 @ A ) )
        & ( v1_funct_2 @ ( k9_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ A )
        & ( m2_relset_1 @ ( k9_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_ens_1) ).

thf(13631,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ( ( v1_funct_1 @ ( k9_ens_1 @ A ) )
        & ( v1_funct_2 @ ( k9_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ A )
        & ( m2_relset_1 @ ( k9_ens_1 @ A ) @ ( k2_ens_1 @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2283]) ).

thf(2590,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ A )
        & ( m1_subset_1 @ H @ A ) )
     => ( ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H )
        = ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k12_domain_1) ).

thf(14920,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m1_subset_1 @ C @ A )
        & ( m1_subset_1 @ D @ A )
        & ( m1_subset_1 @ E @ A )
        & ( m1_subset_1 @ F @ A )
        & ( m1_subset_1 @ G @ A )
        & ( m1_subset_1 @ H @ A ) )
     => ( ( k12_domain_1 @ A @ B @ C @ D @ E @ F @ G @ H )
        = ( k5_enumset1 @ B @ C @ D @ E @ F @ G @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2590]) ).

thf(2214,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ( k1_classes2 @ A @ B )
        = ( k1_tarski @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_classes2) ).

thf(13400,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_classes2 @ A )
        & ( m1_subset_1 @ B @ A ) )
     => ( ( k1_classes2 @ A @ B )
        = ( k1_tarski @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2214]) ).

thf(224,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( r1_tarski @ ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_funct_4) ).

thf(3854,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( r1_tarski @ ( k7_relat_1 @ ( k1_funct_4 @ A @ B ) @ ( k4_xboole_0 @ ( k1_relat_1 @ A ) @ ( k1_relat_1 @ B ) ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(860,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( r2_hidden @ A @ ( k3_xboole_0 @ ( k2_zfmisc_1 @ B @ C ) @ ( k2_zfmisc_1 @ D @ E ) ) )
        & ! [F: $i,G: $i] :
            ~ ( ( A
                = ( k4_tarski @ F @ G ) )
              & ( r2_hidden @ F @ ( k3_xboole_0 @ B @ D ) )
              & ( r2_hidden @ G @ ( k3_xboole_0 @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_zfmisc_1) ).

thf(6733,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( r2_hidden @ A @ ( k3_xboole_0 @ ( k2_zfmisc_1 @ B @ C ) @ ( k2_zfmisc_1 @ D @ E ) ) )
        & ! [F: $i,G: $i] :
            ~ ( ( A
                = ( k4_tarski @ F @ G ) )
              & ( r2_hidden @ F @ ( k3_xboole_0 @ B @ D ) )
              & ( r2_hidden @ G @ ( k3_xboole_0 @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(408,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( v2_funct_2 @ C @ A @ B )
      <=> ( v2_funct_2 @ ( k16_funct_3 @ A @ A @ B @ B @ C @ C ) @ ( k2_zfmisc_1 @ A @ A ) @ ( k2_zfmisc_1 @ B @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_functor0) ).

thf(4784,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( v2_funct_2 @ C @ A @ B )
         => ( v2_funct_2 @ ( k16_funct_3 @ A @ A @ B @ B @ C @ C ) @ ( k2_zfmisc_1 @ A @ A ) @ ( k2_zfmisc_1 @ B @ B ) ) )
        & ( ( v2_funct_2 @ ( k16_funct_3 @ A @ A @ B @ B @ C @ C ) @ ( k2_zfmisc_1 @ A @ A ) @ ( k2_zfmisc_1 @ B @ B ) )
         => ( v2_funct_2 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(404,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( ( k1_relat_1 @ B )
                = A )
              & ( ( k1_relat_1 @ C )
                = A ) )
           => ( ( k13_funct_3 @ B @ C )
              = ( k5_relat_1 @ ( k12_funct_3 @ A ) @ ( k15_funct_3 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_funct_3) ).

thf(4767,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( ( ( k1_relat_1 @ B )
                = A )
              & ( ( k1_relat_1 @ C )
                = A ) )
           => ( ( k13_funct_3 @ B @ C )
              = ( k5_relat_1 @ ( k12_funct_3 @ A ) @ ( k15_funct_3 @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(2255,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( r1_tarski @ B @ ( k2_cantor_1 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_cantor_1) ).

thf(13534,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
     => ( r1_tarski @ B @ ( k2_cantor_1 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2255]) ).

thf(1419,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( m1_subset_1 @ ( k11_mcart_1 @ A @ B @ C @ D @ E ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_mcart_1) ).

thf(9267,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( m1_subset_1 @ E @ ( k4_zfmisc_1 @ A @ B @ C @ D ) )
     => ( m1_subset_1 @ ( k11_mcart_1 @ A @ B @ C @ D @ E ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419]) ).

thf(1524,axiom,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) )
        & ( m2_relset_1 @ A @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) )
     => ( A = k7_vectsp_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_vectsp_2) ).

thf(9784,plain,
    ! [A: $i] :
      ( ( ( v1_funct_1 @ A )
        & ( v1_funct_2 @ A @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) )
        & ( m2_relset_1 @ A @ ( k1_tarski @ k1_xboole_0 ) @ ( k1_tarski @ k1_xboole_0 ) ) )
     => ( A = k7_vectsp_2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1524]) ).

thf(979,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_fraenkel @ C @ A @ B )
     => ( ~ ( v1_xboole_0 @ C )
        & ( v1_fraenkel @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_fraenkel) ).

thf(7320,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_fraenkel @ C @ A @ B )
     => ( ~ ( v1_xboole_0 @ C )
        & ( v1_fraenkel @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(858,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ~ ( ( ( B = k1_xboole_0 )
           => ( A = k1_xboole_0 ) )
          & ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ? [E: $i] :
                  ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
                  & ( ( k1_funct_1 @ D @ E )
                   != ( k1_funct_1 @ C @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_funct_2) ).

thf(6718,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ~ ( ( ( B = k1_xboole_0 )
           => ( A = k1_xboole_0 ) )
          & ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ? [E: $i] :
                  ( ( r2_hidden @ E @ ( k4_relset_1 @ A @ B @ C ) )
                  & ( ( k1_funct_1 @ D @ E )
                   != ( k1_funct_1 @ C @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(2322,axiom,
    m1_subset_1 @ a_0_2_domain_1 @ ( k1_zfmisc_1 @ f3_s9_domain_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s9_domain_1) ).

thf(13785,plain,
    m1_subset_1 @ a_0_2_domain_1 @ ( k1_zfmisc_1 @ f3_s9_domain_1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2322]) ).

thf(2380,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_trees_3 @ A ) )
         => ( v1_finset_1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_pre_circ) ).

thf(14006,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( k5_trees_3 @ A ) )
         => ( v1_finset_1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2380]) ).

thf(2242,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_eqrel_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ A ) @ B )
             => ? [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                  & ( ( k8_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ D )
                    = C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_borsuk_1) ).

thf(13493,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ( ~ ( v1_xboole_0 @ B )
            & ( m1_eqrel_1 @ B @ A ) )
         => ! [C: $i] :
              ( ( m2_subset_1 @ C @ ( k1_zfmisc_1 @ A ) @ B )
             => ? [D: $i] :
                  ( ( m1_subset_1 @ D @ A )
                  & ( ( k8_funct_2 @ A @ B @ ( k2_borsuk_1 @ A @ B ) @ D )
                    = C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2242]) ).

thf(1432,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( v1_relat_1 @ D )
     => ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ ( k6_relat_1 @ C ) @ D ) )
      <=> ( ( r2_hidden @ A @ C )
          & ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).

thf(9310,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( v1_relat_1 @ D )
     => ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ ( k6_relat_1 @ C ) @ D ) )
         => ( ( r2_hidden @ A @ C )
            & ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) ) )
        & ( ( ( r2_hidden @ A @ C )
            & ( r2_hidden @ ( k4_tarski @ A @ B ) @ D ) )
         => ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k5_relat_1 @ ( k6_relat_1 @ C ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432]) ).

thf(294,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ! [C: $i] :
              ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
             => ( ( k1_funct_1 @ A @ C )
                = B ) )
         => ( A
            = ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funcop_1) ).

thf(4161,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ! [C: $i] :
              ( ( r2_hidden @ C @ ( k1_relat_1 @ A ) )
             => ( ( k1_funct_1 @ A @ C )
                = B ) )
         => ( A
            = ( k2_funcop_1 @ ( k1_relat_1 @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(910,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( r2_hidden @ A @ ( k4_card_3 @ B ) )
             => ( r2_hidden @ ( k7_relat_1 @ A @ C ) @ ( k4_card_3 @ ( k7_relat_1 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_pralg_3) ).

thf(6984,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( r2_hidden @ A @ ( k4_card_3 @ B ) )
             => ( r2_hidden @ ( k7_relat_1 @ A @ C ) @ ( k4_card_3 @ ( k7_relat_1 @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).

thf(1173,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( k4_relset_1 @ A @ B @ C )
          = A )
       => ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ A @ B )
          & ( m2_relset_1 @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_funct_2) ).

thf(8179,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ C )
        & ( m2_relset_1 @ C @ A @ B ) )
     => ( ( ( k4_relset_1 @ A @ B @ C )
          = A )
       => ( ( v1_funct_1 @ C )
          & ( v1_funct_2 @ C @ A @ B )
          & ( m2_relset_1 @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).

thf(564,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
      = ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_xboole_1) ).

thf(5436,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
      = ( k2_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(354,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( v2_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).

thf(4547,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( v2_funct_1 @ ( k2_funct_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(2136,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( k2_funct_5 @ A ) )
    <=> ! [C: $i] :
          ( ( r2_hidden @ C @ B )
        <=> ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funct_5) ).

thf(13011,plain,
    ! [A: $i,B: $i] :
      ( ( ( B
          = ( k2_funct_5 @ A ) )
       => ! [C: $i] :
            ( ( ( r2_hidden @ C @ B )
             => ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
            & ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
             => ( r2_hidden @ C @ B ) ) ) )
      & ( ! [C: $i] :
            ( ( ( r2_hidden @ C @ B )
             => ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
            & ( ? [D: $i] : ( r2_hidden @ ( k4_tarski @ D @ C ) @ A )
             => ( r2_hidden @ C @ B ) ) )
       => ( B
          = ( k2_funct_5 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2136]) ).

thf(1269,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_pboole @ C @ A )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ C ) ) )
         => ( m1_subset_1 @ ( k4_xboole_0 @ D @ B ) @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_closure2) ).

thf(8611,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_pboole @ C @ A )
     => ! [D: $i] :
          ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ C ) ) )
         => ( m1_subset_1 @ ( k4_xboole_0 @ D @ B ) @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).

thf(1038,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r1_partfun1 @ A @ B )
       => ( r1_partfun1 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_partfun1) ).

thf(7602,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A )
        & ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ( ( r1_partfun1 @ A @ B )
       => ( r1_partfun1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).

thf(1754,axiom,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ~ ( ( r2_hidden @ C @ A )
              & ! [D: $i,E: $i] :
                  ( C
                 != ( k4_tarski @ D @ E ) ) )
        & ! [C: $i] :
            ~ ( ( r2_hidden @ C @ B )
              & ! [D: $i,E: $i] :
                  ( C
                 != ( k4_tarski @ D @ E ) ) )
        & ! [C: $i,D: $i] :
            ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
          <=> ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_zfmisc_1) ).

thf(10916,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ~ ( ( r2_hidden @ C @ A )
              & ! [D: $i,E: $i] :
                  ( C
                 != ( k4_tarski @ D @ E ) ) )
        & ! [C: $i] :
            ~ ( ( r2_hidden @ C @ B )
              & ! [D: $i,E: $i] :
                  ( C
                 != ( k4_tarski @ D @ E ) ) )
        & ! [C: $i,D: $i] :
            ( ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
             => ( r2_hidden @ ( k4_tarski @ C @ D ) @ B ) )
            & ( ( r2_hidden @ ( k4_tarski @ C @ D ) @ B )
             => ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1754]) ).

thf(880,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ A @ ( k2_xboole_0 @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_xboole_1) ).

thf(6857,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ A @ ( k2_xboole_0 @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(1431,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
                 => ( ! [F: $i] :
                        ( ( m1_subset_1 @ F @ A )
                       => ( ( r2_hidden @ F @ E )
                         => ( ( k1_funct_1 @ C @ F )
                            = ( k1_funct_1 @ D @ F ) ) ) )
                   => ( ( k1_funct_4 @ D @ ( k2_partfun1 @ A @ B @ C @ E ) )
                      = D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_lattice2) ).

thf(9303,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ( ( v1_funct_1 @ C )
            & ( v1_funct_2 @ C @ A @ B )
            & ( m2_relset_1 @ C @ A @ B ) )
         => ! [D: $i] :
              ( ( ( v1_funct_1 @ D )
                & ( v1_funct_2 @ D @ A @ B )
                & ( m2_relset_1 @ D @ A @ B ) )
             => ! [E: $i] :
                  ( ( m1_subset_1 @ E @ ( k5_finsub_1 @ A ) )
                 => ( ! [F: $i] :
                        ( ( m1_subset_1 @ F @ A )
                       => ( ( r2_hidden @ F @ E )
                         => ( ( k1_funct_1 @ C @ F )
                            = ( k1_funct_1 @ D @ F ) ) ) )
                   => ( ( k1_funct_4 @ D @ ( k2_partfun1 @ A @ B @ C @ E ) )
                      = D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431]) ).

thf(2411,axiom,
    ? [A: $i] : ( v1_xboole_0 @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(14112,plain,
    ? [A: $i] : ( v1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2411]) ).

thf(1429,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
      = ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_xboole_1) ).

thf(9297,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( k3_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) )
      = ( k4_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429]) ).

thf(1006,axiom,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ k5_numbers @ B )
                & ( m2_relset_1 @ C @ k5_numbers @ B ) )
             => ( m2_finseq_1 @ ( k2_partfun1 @ k5_numbers @ B @ C @ ( k2_finseq_1 @ A ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_finseq_2) ).

thf(7478,plain,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ k5_numbers @ B )
                & ( m2_relset_1 @ C @ k5_numbers @ B ) )
             => ( m2_finseq_1 @ ( k2_partfun1 @ k5_numbers @ B @ C @ ( k2_finseq_1 @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).

thf(2206,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_classes2 @ B ) )
     => ( ( r2_hidden @ A @ B )
       => ( ( r2_hidden @ ( k1_zfmisc_1 @ A ) @ B )
          & ( r2_hidden @ ( k3_tarski @ A ) @ B )
          & ( r2_hidden @ ( k1_setfam_1 @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_classes2) ).

thf(13353,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_classes2 @ B ) )
     => ( ( r2_hidden @ A @ B )
       => ( ( r2_hidden @ ( k1_zfmisc_1 @ A ) @ B )
          & ( r2_hidden @ ( k3_tarski @ A ) @ B )
          & ( r2_hidden @ ( k1_setfam_1 @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2206]) ).

thf(1776,axiom,
    ! [A: $i] :
      ( ( k4_enumset1 @ A @ A @ A @ A @ A @ A )
      = ( k1_tarski @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_enumset1) ).

thf(11048,plain,
    ! [A: $i] :
      ( ( k4_enumset1 @ A @ A @ A @ A @ A @ A )
      = ( k1_tarski @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1776]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
           => ( ( k1_funct_1 @ ( k5_relat_1 @ C @ B ) @ A )
              = ( k1_funct_1 @ B @ ( k1_funct_1 @ C @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).

thf(2615,plain,
    ! [A: $i,B: $i] :
      ( ( ( v1_relat_1 @ B )
        & ( v1_funct_1 @ B ) )
     => ! [C: $i] :
          ( ( ( v1_relat_1 @ C )
            & ( v1_funct_1 @ C ) )
         => ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relat_1 @ C @ B ) ) )
           => ( ( k1_funct_1 @ ( k5_relat_1 @ C @ B ) @ A )
              = ( k1_funct_1 @ B @ ( k1_funct_1 @ C @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(1264,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( r1_tarski @ A @ B )
               => ( r1_tarski @ ( k1_funct_4 @ A @ C ) @ ( k1_funct_4 @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_pre_circ) ).

thf(8596,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ! [C: $i] :
              ( ( ( v1_relat_1 @ C )
                & ( v1_funct_1 @ C ) )
             => ( ( r1_tarski @ A @ B )
               => ( r1_tarski @ ( k1_funct_4 @ A @ C ) @ ( k1_funct_4 @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).

thf(451,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i,D: $i,E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) @ A )
            & ( m2_relset_1 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) @ A ) )
         => ! [F: $i] :
              ( ( ( v1_funct_1 @ F )
                & ( v1_funct_2 @ F @ ( k3_zfmisc_1 @ B @ C @ D ) @ A )
                & ( m2_relset_1 @ F @ ( k3_zfmisc_1 @ B @ C @ D ) @ A ) )
             => ( ! [G: $i,H: $i,I: $i] :
                    ( ( ( r2_hidden @ G @ B )
                      & ( r2_hidden @ H @ C )
                      & ( r2_hidden @ I @ D ) )
                   => ( ( k1_funct_1 @ E @ ( k3_mcart_1 @ G @ H @ I ) )
                      = ( k1_funct_1 @ F @ ( k3_mcart_1 @ G @ H @ I ) ) ) )
               => ( E = F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_multop_1) ).

thf(4977,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i,C: $i,D: $i,E: $i] :
          ( ( ( v1_funct_1 @ E )
            & ( v1_funct_2 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) @ A )
            & ( m2_relset_1 @ E @ ( k3_zfmisc_1 @ B @ C @ D ) @ A ) )
         => ! [F: $i] :
              ( ( ( v1_funct_1 @ F )
                & ( v1_funct_2 @ F @ ( k3_zfmisc_1 @ B @ C @ D ) @ A )
                & ( m2_relset_1 @ F @ ( k3_zfmisc_1 @ B @ C @ D ) @ A ) )
             => ( ! [G: $i,H: $i,I: $i] :
                    ( ( ( r2_hidden @ G @ B )
                      & ( r2_hidden @ H @ C )
                      & ( r2_hidden @ I @ D ) )
                   => ( ( k1_funct_1 @ E @ ( k3_mcart_1 @ G @ H @ I ) )
                      = ( k1_funct_1 @ F @ ( k3_mcart_1 @ G @ H @ I ) ) ) )
               => ( E = F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(2014,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ C )
        & ( m1_relset_1 @ E @ A @ C )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ B @ D )
        & ( m1_relset_1 @ F @ B @ D ) )
     => ( ( v1_funct_1 @ ( k16_funct_3 @ A @ B @ C @ D @ E @ F ) )
        & ( v1_funct_2 @ ( k16_funct_3 @ A @ B @ C @ D @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
        & ( m2_relset_1 @ ( k16_funct_3 @ A @ B @ C @ D @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_funct_3) ).

thf(12348,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( v1_funct_1 @ E )
        & ( v1_funct_2 @ E @ A @ C )
        & ( m1_relset_1 @ E @ A @ C )
        & ( v1_funct_1 @ F )
        & ( v1_funct_2 @ F @ B @ D )
        & ( m1_relset_1 @ F @ B @ D ) )
     => ( ( v1_funct_1 @ ( k16_funct_3 @ A @ B @ C @ D @ E @ F ) )
        & ( v1_funct_2 @ ( k16_funct_3 @ A @ B @ C @ D @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) )
        & ( m2_relset_1 @ ( k16_funct_3 @ A @ B @ C @ D @ E @ F ) @ ( k2_zfmisc_1 @ A @ B ) @ ( k2_zfmisc_1 @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2014]) ).

thf(127,axiom,
    ( ( ( k1_binop_1 @ k2_midsp_1 @ k1_xboole_0 @ k1_xboole_0 )
      = k1_xboole_0 )
    & ( ( k1_funct_1 @ k7_vectsp_2 @ k1_xboole_0 )
      = k1_xboole_0 )
    & ( k8_vectsp_2 = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_grcat_1) ).

thf(3316,plain,
    ( ( ( k1_binop_1 @ k2_midsp_1 @ k1_xboole_0 @ k1_xboole_0 )
      = k1_xboole_0 )
    & ( ( k1_funct_1 @ k7_vectsp_2 @ k1_xboole_0 )
      = k1_xboole_0 )
    & ( k8_vectsp_2 = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(728,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( k2_xboole_0 @ A @ B )
          = ( k2_xboole_0 @ C @ B ) )
        & ( r1_xboole_0 @ A @ B )
        & ( r1_xboole_0 @ C @ B ) )
     => ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_xboole_1) ).

thf(6141,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( k2_xboole_0 @ A @ B )
          = ( k2_xboole_0 @ C @ B ) )
        & ( r1_xboole_0 @ A @ B )
        & ( r1_xboole_0 @ C @ B ) )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(2582,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_realset1 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_tex_2) ).

thf(14884,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ? [B: $i] :
          ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
          & ~ ( v1_xboole_0 @ B )
          & ( v1_realset1 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2582]) ).

thf(1222,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ ( k1_funct_4 @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_4) ).

thf(8380,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ! [B: $i] :
          ( ( ( v1_relat_1 @ B )
            & ( v1_funct_1 @ B ) )
         => ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k2_relat_1 @ ( k1_funct_4 @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).

thf(59,axiom,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k1_numbers )
        & ( m1_subset_1 @ B @ k1_numbers ) )
     => ( m1_subset_1 @ ( k10_binop_2 @ A @ B ) @ k1_numbers ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_binop_2) ).

thf(2993,plain,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k1_numbers )
        & ( m1_subset_1 @ B @ k1_numbers ) )
     => ( m1_subset_1 @ ( k10_binop_2 @ A @ B ) @ k1_numbers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(1569,axiom,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v2_cat_5 @ A ) )
     => ? [B: $i] : ( m1_cat_5 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_cat_5) ).

thf(10002,plain,
    ! [A: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v2_cat_5 @ A ) )
     => ? [B: $i] : ( m1_cat_5 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1569]) ).

thf(2458,axiom,
    ? [A: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s1_subset_1 ) )
      & ! [B: $i] :
          ( ( r2_hidden @ B @ A )
        <=> ( ( r2_hidden @ B @ f1_s1_subset_1 )
            & ( p1_s1_subset_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_subset_1) ).

thf(14320,plain,
    ? [A: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ f1_s1_subset_1 ) )
      & ! [B: $i] :
          ( ( ( r2_hidden @ B @ A )
           => ( ( r2_hidden @ B @ f1_s1_subset_1 )
              & ( p1_s1_subset_1 @ B ) ) )
          & ( ( ( r2_hidden @ B @ f1_s1_subset_1 )
              & ( p1_s1_subset_1 @ B ) )
           => ( r2_hidden @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2458]) ).

thf(1414,axiom,
    ! [A: $i,B: $i] :
      ~ ( ~ ( r1_xboole_0 @ A @ B )
        & ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_xboole_1) ).

thf(9254,plain,
    ! [A: $i,B: $i] :
      ~ ( ~ ( r1_xboole_0 @ A @ B )
        & ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414]) ).

thf(1107,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).

thf(7893,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( r1_tarski @ A @ B )
     => ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ ( k4_xboole_0 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).

thf(1863,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ A ) )
     => ( m1_subset_1 @ ( k8_funct_2 @ A @ B @ C @ D ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_funct_2) ).

thf(11511,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ A ) )
     => ( m1_subset_1 @ ( k8_funct_2 @ A @ B @ C @ D ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1863]) ).

thf(861,axiom,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( v2_funct_1 @ ( k2_funct_4 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_functor0) ).

thf(6739,plain,
    ! [A: $i] :
      ( ( ( v1_relat_1 @ A )
        & ( v1_funct_1 @ A ) )
     => ( ( v2_funct_1 @ A )
       => ( v2_funct_1 @ ( k2_funct_4 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(243,axiom,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ( ( v1_binop_1 @ C @ B )
                       => ( ( k6_funcop_1 @ B @ A @ C @ D @ E )
                          = ( k6_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_funcop_1) ).

thf(3933,plain,
    ! [A: $i] :
      ( ~ ( v1_xboole_0 @ A )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B )
                & ( m2_relset_1 @ C @ ( k2_zfmisc_1 @ B @ B ) @ B ) )
             => ! [D: $i] :
                  ( ( ( v1_funct_1 @ D )
                    & ( v1_funct_2 @ D @ A @ B )
                    & ( m2_relset_1 @ D @ A @ B ) )
                 => ! [E: $i] :
                      ( ( ( v1_funct_1 @ E )
                        & ( v1_funct_2 @ E @ A @ B )
                        & ( m2_relset_1 @ E @ A @ B ) )
                     => ( ( v1_binop_1 @ C @ B )
                       => ( ( k6_funcop_1 @ B @ A @ C @ D @ E )
                          = ( k6_funcop_1 @ B @ A @ C @ E @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(1788,axiom,
    ! [A: $i] :
      ( ( v1_setfam_1 @ A )
     => ( v4_orders_3 @ ( k2_yellow21 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_yellow21) ).

thf(11103,plain,
    ! [A: $i] :
      ( ( v1_setfam_1 @ A )
     => ( v4_orders_3 @ ( k2_yellow21 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1788]) ).

thf(2200,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( k1_tarski @ A ) )
    <=> ! [C: $i] :
          ( ( r2_hidden @ C @ B )
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

thf(13311,plain,
    ! [A: $i,B: $i] :
      ( ( ( B
          = ( k1_tarski @ A ) )
       => ! [C: $i] :
            ( ( ( r2_hidden @ C @ B )
             => ( C = A ) )
            & ( ( C = A )
             => ( r2_hidden @ C @ B ) ) ) )
      & ( ! [C: $i] :
            ( ( ( r2_hidden @ C @ B )
             => ( C = A ) )
            & ( ( C = A )
             => ( r2_hidden @ C @ B ) ) )
       => ( B
          = ( k1_tarski @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2200]) ).

thf(2237,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_realset1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m3_realset1 @ C @ A @ B ) )
     => ( ( v1_funct_1 @ ( k4_realset1 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k4_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
        & ( m2_relset_1 @ ( k4_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_realset1) ).

thf(13478,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( v1_realset1 @ A )
        & ( m1_subset_1 @ B @ A )
        & ( m3_realset1 @ C @ A @ B ) )
     => ( ( v1_funct_1 @ ( k4_realset1 @ A @ B @ C ) )
        & ( v1_funct_2 @ ( k4_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) )
        & ( m2_relset_1 @ ( k4_realset1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) @ ( k4_xboole_0 @ A @ ( k1_tarski @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2237]) ).

thf(207,axiom,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( ( k1_funct_5 @ A )
          = ( k1_relat_1 @ A ) )
        & ( ( k2_funct_5 @ A )
          = ( k2_relat_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_5) ).

thf(3721,plain,
    ! [A: $i] :
      ( ( v1_relat_1 @ A )
     => ( ( ( k1_funct_5 @ A )
          = ( k1_relat_1 @ A ) )
        & ( ( k2_funct_5 @ A )
          = ( k2_relat_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(2407,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) ) )
     => ! [C: $i] :
          ( ( m1_triang_1 @ C @ A @ B )
         => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_triang_1) ).

thf(14102,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) ) )
     => ! [C: $i] :
          ( ( m1_triang_1 @ C @ A @ B )
         => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2407]) ).

thf(1229,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( ( ( B = k1_xboole_0 )
           => ( A = k1_xboole_0 ) )
         => ( ( v1_funct_2 @ C @ A @ B )
          <=> ( A
              = ( k4_relset_1 @ A @ B @ C ) ) ) )
        & ( ( B = k1_xboole_0 )
         => ( ( A = k1_xboole_0 )
            | ( ( v1_funct_2 @ C @ A @ B )
            <=> ( C = k1_xboole_0 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).

thf(8405,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( ( ( ( B = k1_xboole_0 )
           => ( A = k1_xboole_0 ) )
         => ( ( ( v1_funct_2 @ C @ A @ B )
             => ( A
                = ( k4_relset_1 @ A @ B @ C ) ) )
            & ( ( A
                = ( k4_relset_1 @ A @ B @ C ) )
             => ( v1_funct_2 @ C @ A @ B ) ) ) )
        & ( ( B = k1_xboole_0 )
         => ( ( A = k1_xboole_0 )
            | ( ( ( v1_funct_2 @ C @ A @ B )
               => ( C = k1_xboole_0 ) )
              & ( ( C = k1_xboole_0 )
               => ( v1_funct_2 @ C @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).

thf(904,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( ( k1_tarski @ A )
          = ( k2_xboole_0 @ B @ C ) )
        & ~ ( ( B
              = ( k1_tarski @ A ) )
            & ( C
              = ( k1_tarski @ A ) ) )
        & ~ ( ( B = k1_xboole_0 )
            & ( C
              = ( k1_tarski @ A ) ) )
        & ~ ( ( B
              = ( k1_tarski @ A ) )
            & ( C = k1_xboole_0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).

thf(6948,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( ( k1_tarski @ A )
          = ( k2_xboole_0 @ B @ C ) )
        & ~ ( ( B
              = ( k1_tarski @ A ) )
            & ( C
              = ( k1_tarski @ A ) ) )
        & ~ ( ( B = k1_xboole_0 )
            & ( C
              = ( k1_tarski @ A ) ) )
        & ~ ( ( B
              = ( k1_tarski @ A ) )
            & ( C = k1_xboole_0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).

thf(1825,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ( ( r2_hidden @ A @ ( k3_zfmisc_1 @ B @ C @ D ) )
              <=> ? [E: $i] :
                    ( ( m1_subset_1 @ E @ B )
                    & ? [F: $i] :
                        ( ( m1_subset_1 @ F @ C )
                        & ? [G: $i] :
                            ( ( m1_subset_1 @ G @ D )
                            & ( A
                              = ( k3_mcart_1 @ E @ F @ G ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_domain_1) ).

thf(11294,plain,
    ! [A: $i,B: $i] :
      ( ~ ( v1_xboole_0 @ B )
     => ! [C: $i] :
          ( ~ ( v1_xboole_0 @ C )
         => ! [D: $i] :
              ( ~ ( v1_xboole_0 @ D )
             => ( ( ( r2_hidden @ A @ ( k3_zfmisc_1 @ B @ C @ D ) )
                 => ? [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                      & ? [F: $i] :
                          ( ( m1_subset_1 @ F @ C )
                          & ? [G: $i] :
                              ( ( m1_subset_1 @ G @ D )
                              & ( A
                                = ( k3_mcart_1 @ E @ F @ G ) ) ) ) ) )
                & ( ? [E: $i] :
                      ( ( m1_subset_1 @ E @ B )
                      & ? [F: $i] :
                          ( ( m1_subset_1 @ F @ C )
                          & ? [G: $i] :
                              ( ( m1_subset_1 @ G @ D )
                              & ( A
                                = ( k3_mcart_1 @ E @ F @ G ) ) ) ) )
                 => ( r2_hidden @ A @ ( k3_zfmisc_1 @ B @ C @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1825]) ).

thf(1888,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( m1_relset_1 @ E @ A @ B )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( m2_relset_1 @ ( k2_yellow_3 @ A @ B @ C @ D @ E @ F ) @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yellow_3) ).

thf(11648,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( m1_relset_1 @ E @ A @ B )
        & ( m1_relset_1 @ F @ C @ D ) )
     => ( m2_relset_1 @ ( k2_yellow_3 @ A @ B @ C @ D @ E @ F ) @ ( k2_zfmisc_1 @ A @ C ) @ ( k2_zfmisc_1 @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1888]) ).

thf(1536,axiom,
    ! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).

thf(9831,plain,
    ! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1536]) ).

thf(1187,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k1_nattra_1 @ A @ B @ C @ D )
        = ( k7_relat_1 @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_nattra_1) ).

thf(8232,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ~ ( v1_xboole_0 @ B )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ B )
        & ( m1_relset_1 @ C @ A @ B )
        & ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ A ) ) )
     => ( ( k1_nattra_1 @ A @ B @ C @ D )
        = ( k7_relat_1 @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).

thf(1674,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) )
        & ! [G: $i,H: $i] :
            ( ( r2_hidden @ ( k4_tarski @ G @ H ) @ A )
          <=> ( r2_hidden @ ( k4_tarski @ G @ H ) @ D ) ) )
     => ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_zfmisc_1) ).

thf(10475,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) )
        & ! [G: $i,H: $i] :
            ( ( ( r2_hidden @ ( k4_tarski @ G @ H ) @ A )
             => ( r2_hidden @ ( k4_tarski @ G @ H ) @ D ) )
            & ( ( r2_hidden @ ( k4_tarski @ G @ H ) @ D )
             => ( r2_hidden @ ( k4_tarski @ G @ H ) @ A ) ) ) )
     => ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1674]) ).

thf(2313,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k3_subset_1 @ A @ ( k3_subset_1 @ A @ B ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).

thf(13743,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
     => ( ( k3_subset_1 @ A @ ( k3_subset_1 @ A @ B ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2313]) ).

thf(715,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) ) )
     => ( r1_tarski @ ( k2_xboole_0 @ A @ D ) @ ( k2_zfmisc_1 @ ( k2_xboole_0 @ B @ E ) @ ( k2_xboole_0 @ C @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_partfun1) ).

thf(6094,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( r1_tarski @ A @ ( k2_zfmisc_1 @ B @ C ) )
        & ( r1_tarski @ D @ ( k2_zfmisc_1 @ E @ F ) ) )
     => ( r1_tarski @ ( k2_xboole_0 @ A @ D ) @ ( k2_zfmisc_1 @ ( k2_xboole_0 @ B @ E ) @ ( k2_xboole_0 @ C @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(604,axiom,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_finseq_1 @ A ) @ B )
                & ( m2_relset_1 @ C @ ( k2_finseq_1 @ A ) @ B ) )
             => ( m2_finseq_1 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finseq_2) ).

thf(5574,plain,
    ! [A: $i] :
      ( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
     => ! [B: $i] :
          ( ~ ( v1_xboole_0 @ B )
         => ! [C: $i] :
              ( ( ( v1_funct_1 @ C )
                & ( v1_funct_2 @ C @ ( k2_finseq_1 @ A ) @ B )
                & ( m2_relset_1 @ C @ ( k2_finseq_1 @ A ) @ B ) )
             => ( m2_finseq_1 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(890,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m1_relset_1 @ B @ A @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ A )
        & ( m1_relset_1 @ C @ A @ A ) )
     => ( ( k2_monoid_0 @ A @ B @ C )
        = ( k5_relat_1 @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_monoid_0) ).

thf(6896,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( v1_funct_1 @ B )
        & ( v1_funct_2 @ B @ A @ A )
        & ( m1_relset_1 @ B @ A @ A )
        & ( v1_funct_1 @ C )
        & ( v1_funct_2 @ C @ A @ A )
        & ( m1_relset_1 @ C @ A @ A ) )
     => ( ( k2_monoid_0 @ A @ B @ C )
        = ( k5_relat_1 @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(56,axiom,
    ( ( ( k1_relat_1 @ k1_xboole_0 )
      = k1_xboole_0 )
    & ( ( k2_relat_1 @ k1_xboole_0 )
      = k1_xboole_0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).

thf(2980,plain,
    ( ( ( k1_relat_1 @ k1_xboole_0 )
      = k1_xboole_0 )
    & ( ( k2_relat_1 @ k1_xboole_0 )
      = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(175,axiom,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k1_numbers )
        & ( m1_subset_1 @ B @ k1_numbers ) )
     => ( ( k11_binop_2 @ A @ B )
        = ( k11_binop_2 @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k11_binop_2) ).

thf(3575,plain,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ k1_numbers )
        & ( m1_subset_1 @ B @ k1_numbers ) )
     => ( ( k11_binop_2 @ A @ B )
        = ( k11_binop_2 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(356,axiom,
    ! [A: $i] : ( v2_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_setwiseo) ).

thf(4552,plain,
    ! [A: $i] : ( v2_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(2211,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_zfmisc_1 @ A @ B @ C @ D )
      = ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_mcart_1) ).

thf(13381,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( k4_zfmisc_1 @ A @ B @ C @ D )
      = ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2211]) ).

thf(1590,axiom,
    ! [A: $i] :
      ( ~ ( v2_setfam_1 @ A )
     => ~ ( v1_xboole_0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_setfam_1) ).

thf(10096,plain,
    ! [A: $i] :
      ( ~ ( v2_setfam_1 @ A )
     => ~ ( v1_xboole_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1590]) ).

thf(15004,plain,
    $false,
    inference(cvc4,[status(thm)],[8960,6836,11313,3581,5999,6690,14221,8607,10822,5810,5659,9929,8536,5509,9982,7304,10007,13266,8186,9458,4094,7272,12055,6355,3345,4571,4101,5857,4464,4824,7854,11211,7569,6231,5260,14801,6976,4899,10267,4022,12975,14574,5950,14404,13783,8114,7673,9833,7100,8283,12753,12731,6431,5654,3969,9076,6845,8646,3566,11394,6566,7285,9091,7396,6014,12699,5582,6374,11659,12738,4904,8200,9437,12549,4166,6808,4043,5842,13062,5669,10125,6017,6057,11688,6022,11308,6791,12634,3990,3072,9573,7596,13073,7358,7164,13520,10431,4339,5718,13110,14414,14235,2622,11107,9251,4311,2808,6106,3230,13351,5292,6744,12376,6219,9456,11277,8402,10567,12089,9045,5297,14786,4697,13672,3098,9918,8695,10562,5793,14729,12774,3108,6338,10314,3012,12261,14377,13796,12896,4326,3498,11556,10886,11881,9364,9818,4747,12013,6214,9003,11080,3382,14156,14200,13187,11468,8765,8568,4856,6759,10170,13152,3017,5550,7793,3848,14441,9956,14741,3217,3530,9526,6505,14602,12590,13442,11072,9127,2686,4575,8430,13623,3332,6246,3367,5755,6359,10358,8622,8981,7115,14665,11207,8747,14829,7096,11303,3446,7669,11288,4638,6416,12545,12865,13655,9000,5163,10940,8370,12398,5674,8947,7422,11513,6551,3121,7188,8881,11055,14689,9278,13145,13901,11756,7748,3717,13056,5192,14354,8752,12816,13488,5412,9672,5252,6251,9746,5476,7240,8165,4607,12879,4941,10351,7858,8911,4047,3103,13700,10368,13469,14203,10230,13452,10427,3236,3350,6466,13628,3545,9292,8086,7637,2985,11382,10599,13179,5518,14436,6872,6381,13997,11613,6887,9735,6623,5195,12303,12757,13083,7326,5825,5056,13378,12960,8671,8256,14716,9465,10559,14023,14677,14644,4963,12785,4156,5269,12324,9394,4610,9850,7592,10501,9946,7311,7628,10584,5352,4539,9067,5284,3148,12394,3891,5553,11426,9300,9056,7790,11949,13658,5429,5585,3976,2603,10935,3195,8500,9287,3425,14701,4866,11844,2735,13511,8967,6538,9828,2698,8875,3116,12832,9561,11913,12956,9332,6987,8357,3495,8515,6878,8806,3061,13619,13651,6066,3617,13241,14141,3485,4778,12407,2682,12065,11111,6676,14029,5160,3280,14923,10606,5640,3089,9668,6434,5289,11051,4568,8022,13275,5108,13906,5836,14228,5279,10655,5231,11232,4358,4622,8235,7997,2691,12682,3998,5355,13961,3374,11981,4353,11463,6905,11285,14455,7124,8310,8819,6149,6626,5604,4664,8571,6310,9941,14334,13580,4830,12621,4317,10982,11115,3734,3014,2730,9240,5746,8674,14019,5727,13927,9725,9039,8126,13263,10117,13044,4471,12657,8037,4771,10292,10682,4302,6487,7509,7112,3258,14751,12782,14051,13788,8870,11740,13786,13474,10025,5974,8293,13575,14061,12750,11838,10014,12981,7258,10309,5787,4411,10046,14034,14686,4205,8394,7268,13195,8190,3431,7786,7492,7144,4583,11064,11656,3199,9336,5888,12362,4173,5084,7564,14697,9490,4072,14056,4018,9330,10591,12453,11293,3295,9071,8627,6419,8934,12593,11891,5946,11676,4050,11215,9860,11389,10085,4724,7677,13414,11748,6054,8526,7317,3357,8018,5805,5311,6559,11446,3300,14238,11971,8759,6157,8479,9781,12041,10602,3851,4718,12638,6451,9167,10538,12554,13600,2965,14253,7408,8050,5059,12998,12485,9616,4935,4033,2618,3739,13305,8977,5096,11119,14410,13077,9743,14874,11384,4087,12315,7909,10405,6498,5246,10273,7954,10784,8686,5169,5897,6863,9341,13420,3756,14917,11408,11728,13833,2750,10233,7337,11954,11143,8939,7830,5137,11367,3870,3211,8094,3906,7760,4588,9272,7758,4211,9589,12306,14900,3184,9501,6860,4475,9584,10523,9738,8742,5961,7148,5875,5751,6064,5545,8668,11499,8867,8123,13440,7952,4700,10779,11597,9997,7657,11159,12747,7533,11121,4604,8170,14162,7849,5406,10943,11897,2910,7782,9571,8655,7471,3303,13408,7022,8927,8302,4888,10652,9440,6296,7550,10506,11550,10139,5017,8382,11170,6684,6139,12029,5697,13141,12446,12425,11672,9209,12474,14342,8613,3995,11324,6571,11069,5416,10165,4076,4370,2737,10947,6307,6884,8842,6741,12127,3418,9384,4925,13059,6092,3679,11545,9488,12159,13746,6820,13892,13649,3610,7640,4661,10278,10133,9036,13547,13260,4915,12542,8343,12437,13423,13126,12561,6079,8265,7703,3972,14357,14032,13301,8994,14766,10975,11766,9412,8476,7827,12510,6264,11037,8888,9949,4989,13572,5044,5349,7994,5266,11587,9031,13949,5956,7161,8856,6990,14075,11471,12809,14605,8724,5366,3233,7084,3371,5470,6915,11003,5102,4821,11908,13860,12058,6620,6582,7957,8683,13254,6629,7361,3894,14338,4740,6402,11420,4063,14789,5702,3980,5302,11570,14804,10330,5492,7842,13282,5465,10490,12340,10826,8651,6848,14926,14317,8942,9790,4757,11152,4947,3556,13536,13924,3578,13799,11249,9758,6708,10247,14681,9539,5534,7625,12692,12881,12025,14735,7545,13359,4402,9423,14167,6096,6392,6060,14894,11670,8847,7891,4104,10615,8226,2741,9613,13411,11602,8136,13853,12571,5330,8518,7686,8073,8155,8562,5798,3704,8884,14855,12796,8138,13981,8238,4808,8354,14380,6656,9814,8471,3699,10962,7281,7799,3909,9493,6413,12863,7329,12987,4957,7142,3831,2840,3482,5053,5221,3413,14327,10529,13006,6801,13222,6995,5006,7065,3862,11884,14629,6195,4108,6477,13904,13173,6603,8604,12506,4544,8319,9244,8931,13825,8984,8016,10152,10445,2724,4930,10434,3119,3746,10021,14413,14312,6919,11189,8800,13458,13735,6128,9603,7809,3176,9772,4291,8176,12768,6967,13527,13661,5588,4333,13790,4653,14914,7091,8544,3311,12151,8835,13635,14841,5166,6428,4276,12906,8864,13682,7631,3846,9397,5181,13291,7054,5496,13308,3622,5705,8251,6593,4721,12696,10391,13154,6642,6661,14598,5791,9426,14153,5620,3596,4938,10620,5263,7604,11229,11642,14110,8053,8132,9100,7930,11666,4054,3428,10688,7480,9085,6395,8346,14719,14104,7059,13184,7404,10239,7313,6275,4814,2978,9392,2649,10353,13539,8100,2836,6207,14352,8803,5479,3242,9200,11742,5576,5850,6134,12410,8219,8013,12859,11828,9348,7340,9012,8442,7878,14784,8891,14799,5374,6033,14655,7014,12429,2598,3354,14067,5380,12378,12164,9498,5234,14649,5498,11474,9581,6211,12558,4237,9630,3390,7495,10518,14494,13376,9053,8439,11184,8896,7385,10122,13680,10438,13277,10879,4231,13500,7086,14526,7913,5305,13167,6908,13943,10302,3409,11833,3692,10629,14634,12310,13731,14125,8090,10588,9598,13804,11610,13591,10180,8144,5369,13822,7826,13693,5026,4069,13340,3920,13490,12641,6533,13714,14216,11940,10819,6647,5249,14003,4535,8174,9534,5112,3903,5557,14657,7020,13507,13103,9468,8839,3563,12282,8247,8482,9094,7052,5090,7721,8512,4081,12736,14008,12891,8080,3173,9269,10377,3856,8422,9008,8923,5434,5964,13772,8955,9169,9171,8262,5419,11196,10951,5930,8945,9284,13137,13879,4036,14362,10090,3422,5513,6931,12823,6400,2995,3841,5295,7802,10190,9985,9562,12318,14085,4995,9517,7817,12677,12173,11692,4708,7706,5048,6192,14107,11165,4921,13444,9107,3660,6922,9237,3707,12106,6314,10703,10556,11506,12238,14638,12168,11710,10101,14762,11705,4872,13331,13455,9231,13201,5808,13544,4116,13989,4613,7128,6615,5762,10227,12982,7512,10202,5969,2717,14195,9203,8713,13584,10030,8290,7742,8040,7155,13896,12119,10079,6578,14469,13947,12265,13864,4562,11016,9021,14373,6243,7599,6001,3289,9853,6469,9404,3888,7382,6546,6228,5525,13849,4269,9451,3696,14776,11459,12778,5758,6422,13031,10890,13296,5598,12827,13559,7611,7860,12301,14021,3604,13685,9418,12441,3187,4998,10582,13471,5456,7968,2727,2970,14146,9010,9062,14523,8259,11105,8762,11566,3504,13972,11279,11836,5488,10547,6881,6510,6108,3240,2789,6312,10200,8349,5065,11615,11703,12038,5923,13550,7223,9025,7751,13157,3758,5940,3945,3283,4677,12958,9471,4122,10709,13569,9531,13033,9295,10700,14714,10242,13798,14731,12840,3900,13563,5050,5099,9521,12259,10461,8740,13809,6019,14642,9339,10127,12787,14044,6705,13132,3599,5427,10883,7191,10130,5578,14667,13908,8767,14268,4485,5033,3751,4127,14384,9587,5118,6937,8188,4796,3726,8432,8152,12067,10393,6667,12053,10183,7689,13459,13503,5595,13497,8629,8249,10640,11951,3208,13093,8877,4218,14608,12524,11201,10348,8000,7109,12451,4573,11370,14059,5190,12759,10938,2753,10493,5314,14183,4060,13984,7671,7536,5539,14587,8212,12146,5735,14549,9681,11841,8524,5158,14151,7062,6549,12280,5784,11618,6372,8010,12278,7315,11053,7865,10989,3170,6261,8244,12547,10056,13482,9670,14502,6144,11222,9623,9575,10236,5244,8970,5610,10457,13417,7158,3352,10088,7594,10448,4228,13876,5671,3251,13514,12990,2642,9454,2987,5520,2637,10204,9377,3551,4305,6443,10066,2774,6500,11092,11697,7379,7607,6112,13390,5827,14679,5853,12413,10564,3106,11733,9920,7255,8445,13794,4805,10037,8313,13705,3710,12337,13334,4616,5346,5093,5531,12136,2802,6154,10098,4300,6184,14048,12894,3586,5972,11883,7502,14042,5616,10696,6460,14053,6969,9206,10957,14063,6817,4554,14223,4694,14736,10450,7504,10645,9042,5511,6165,9857,14122,2812,13427,4420,13930,8633,7699,10397,4882,4009,7119,5730,14016,5082,9079,14699,10995,13857,9174,13734,9275,8103,7566,12044,11392,2780,4731,14178,10579,13272,5439,4264,4897,5286,3165,13777,14576,14892,7928,3192,8529,11519,3614,2593,3006,12899,5885,3583,12496,11387,10172,8473,9511,9528,9074,9674,6446,6568,12381,10004,7297,8340,13486,5838,13529,6376,10970,5987,7901,6345,12802,12534,10549,6151,14294,11607,13884,10119,13208,10499,10402,12680,12092,8853,4844,5254,6811,14329,13578,13963,5442,12432,6687,5372,6449,3838,8776,5377,9741,5482,7334,3917,11721,5516,7469,4085,11380,7647,13112,7960,13702,7911,4827,14660,11590,9916,12373,10979,8541,10264,4918,2633,3363,11605,9871,10063,13598,7852,5725,10424,8676,5299,10576,14675,6293,12308,4890,11193,7916,7507,14862,14739,13727,8990,14255,10692,4207,4868,9430,6659,7992,9678,8106,6083,3881,4331,3009,13268,9595,4405,9524,6890,2816,8965,5424,4394,10311,10824,5890,7490,4013,3936,7896,12492,5528,7571,4260,12978,6225,7650,4580,7975,10269,7681,3395,9514,9259,3161,10223,8160,13293,6088,7539,8116,6962,7151,13781,3146,14169,8789,10384,9943,14230,7420,7773,7122,6806,4113,13541,10788,9507,4355,13555,7718,11795,8020,6664,6998,5358,8194,4336,5003,4986,6557,11679,13189,11547,6202,12740,6875,9317,14417,10797,7475,9606,14444,3872,7724,4593,6012,4045,3988,7615,6362,8056,8593,5570,8905,5716,3376,10290,9794,5607,11327,6472,4360,9926,9847,11573,11857,13181,5125,6051,6934,11694,12139,4272,14336,13698,14562,13047,12313,10856,3214,13108,12271,3260,8598,3754,4922,14557,13759,2732,10684,13285,8163,5592,10371,3129,12807,3949,5523,2678,7045,10553,4641,5721,12873,11855,8096,9578,10521,129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).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11  % Problem  : SEU424+3 : TPTP v8.1.2. Released v3.4.0.
% 0.04/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu May 18 13:47:36 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.93/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 4.44/1.91  % [INFO] 	 Parsing done (1065ms). 
% 4.50/1.92  % [INFO] 	 Running in sequential loop mode. 
% 4.82/2.10  % [INFO] 	 eprover registered as external prover. 
% 4.82/2.11  % [INFO] 	 cvc4 registered as external prover. 
% 4.82/2.11  % [INFO] 	 Scanning for conjecture ... 
% 7.18/2.86  % [INFO] 	 Found a conjecture and 19088 axioms. Running axiom selection ... 
% 12.50/5.69  % [INFO] 	 Axiom selection finished. Selected 2590 axioms (removed 16498 axioms). 
% 15.14/6.67  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 15.31/6.73  % [INFO] 	 Type checking passed. 
% 15.31/6.74  % [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 ... 
% 60.78/21.26  % External prover 'cvc4' found a proof!
% 60.78/21.26  % [INFO] 	 Killing All external provers ... 
% 60.78/21.26  % Time passed: 20746ms (effective reasoning time: 19339ms)
% 60.78/21.26  % 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)>
% 60.78/21.27  % Axioms used in derivation (2590): rc2_setfam_1, t106_xboole_1, t158_relat_1, t39_relset_1, t63_mcart_1, t44_xboole_1, t6_funct_7, t36_funcop_1, t119_funct_2, t60_mcart_1, t72_xboole_1, t189_relat_1, t60_funct_4, d5_monoid_0, t15_finset_1, t44_enumset1, t62_partfun1, redefinition_k2_card_fil, t23_funct_2, rc2_lopclset, t38_funct_4, t61_classes2, t75_funct_3, t1_filter_2, fc1_cqc_lang, dt_k11_classes2, fraenkel_a_0_0_altcat_2, dt_m2_pua2mss1, t42_xboole_1, dt_k1_funct_3, dt_k15_domain_1, t34_subset_1, t75_enumset1, t34_sysrel, t14_realset1, d1_enumset1, t76_funct_3, t10_funct_7, free_g2_quantal1, redefinition_m2_relset_1, t56_funct_3, idempotence_k1_finsub_1, t41_finseq_3, fraenkel_a_1_0_domain_1, t51_partfun1, s1_altcat_2, t68_enumset1, cc1_pre_circ, t5_fraenkel, t32_funcop_1, t92_enumset1, t21_zfmisc_1, t5_boole, t84_finseq_2, fc2_altcat_1, t133_finseq_2, t13_zfmisc_1, t30_funct_2, existence_m1_triang_1, t55_funcop_1, t10_lattice2, t13_relset_1, t70_setwiseo, t128_partfun1, t38_funcop_1, t4_functor0, t19_yellow_9, t131_partfun1, redefinition_k1_functor0, redefinition_k1_oppcat_1, fc4_finset_1, fraenkel_a_4_2_domain_1, t16_finsub_1, t79_mcart_1, dt_k2_borsuk_1, t4_grcat_1, t48_funcop_1, fraenkel_a_4_0_pua2mss1, fraenkel_a_3_2_domain_1, t4_cantor_1, dt_k11_binop_2, fc1_zfmisc_1, t15_card_4, t45_setwiseo, free_g1_group_1, t1_altcat_2, redefinition_k1_metric_1, t25_mcart_1, dt_k7_vectsp_2, t19_xboole_1, t99_relat_1, t82_enumset1, d17_vectsp_2, t177_orders_1, t42_cqc_lang, t12_borsuk_1, s2_filter_1, t17_xboole_1, t90_relat_1, t4_funct_4, t112_xboole_1, t130_partfun1, t42_subset_1, t55_mcart_1, t30_setwiseo, t43_subset_1, commutativity_k3_setwiseo, t15_setwiseo, d1_funcsdom, t14_cantor_1, cc2_finset_1, t7_multop_1, t20_zfmisc_1, t54_relat_1, t35_subset_1, rc2_triang_1, d1_tarski, t4_pre_circ, t101_relat_1, t135_zfmisc_1, t17_zfmisc_1, fc11_finseq_1, t3_pre_circ, fc3_finset_1, d3_mcart_1, dt_k3_cantor_1, s1_setwiseo, t8_altcat_1, t25_relset_1, d20_binop_1, t66_funct_2, t57_classes2, t11_yellow_9, t67_relat_1, t18_finsub_1, t66_partfun1, t4_closure2, dt_k9_funct_3, t154_relat_1, t53_setwiseo, d4_ens_1, d4_funct_1, t60_funcop_1, t49_setfam_1, t70_funct_2, t23_ens_1, t6_setfam_1, cc2_tex_2, t35_funct_2, t14_finset_1, t20_mcart_1, t85_enumset1, t53_subset_1, redefinition_k4_finsub_1, t19_mcart_1, t14_finseq_2, t1_funct_4, t63_funcop_1, dt_k8_funcop_1, t67_enumset1, dt_k4_relset_1, d14_binop_1, dt_k9_domain_1, dt_k5_relset_1, dt_k8_ens_1, d5_relat_1, t15_finseq_1, t105_zfmisc_1, rc6_grcat_1, redefinition_k6_funct_3, t140_zfmisc_1, t49_setwiseo, d2_cqc_lang, redefinition_k12_mcart_1, commutativity_k1_finsub_1, d9_setfam_1, t1_closure3, t109_xboole_1, t66_mcart_1, idempotence_k3_xboole_0, t5_ens_1, t67_funcop_1, d1_funct_5, rc4_finset_1, redefinition_k9_domain_1, t110_xboole_1, t57_funcop_1, t47_relset_1, t13_sysrel, dt_k4_finsub_1, t1_boole, t62_relat_1, t7_subset_1, t92_xboole_1, t84_mcart_1, t2_realset1, t32_funct_2, t3_lattice5, s6_domain_1, rc3_triang_1, t86_mcart_1, t38_mcart_1, t66_xboole_1, t23_xboole_1, fc4_yellow_3, commutativity_k1_relset_2, fc37_membered, t79_funct_4, t75_relat_1, t27_funct_2, t14_funct_4, t50_relat_1, t16_cantor_1, t85_mcart_1, t195_orders_1, t29_mcart_1, redefinition_k5_subset_1, t16_yellow_9, t20_funct_2, t134_finseq_2, fraenkel_a_1_1_ens_1, redefinition_k8_relset_2, d1_cqc_lang, d13_ens_1, t73_xboole_1, s1_yellow_3, redefinition_m2_finseq_2, t9_setfam_1, dt_k7_setwiseo, t3_xboole_1, t97_xboole_1, t24_mcart_1, t3_realset1, d3_subset_1, dt_m1_functor0, t98_relat_1, t18_funcop_1, t113_xboole_1, t42_sysrel, dt_m1_triang_1, t56_partfun1, t8_subset_1, t4_ordinal1, s3_funct_2, t45_funcop_1, fc1_functor0, cc1_setfam_1, fc1_xboole_0, t6_ens_1, t97_funct_3, t10_tops_2, t62_enumset1, t47_enumset1, t77_enumset1, t25_funct_1, t7_mcart_1, d10_realset1, t73_funct_4, t113_zfmisc_1, t140_partfun1, fc43_membered, t16_funct_2, dt_k7_domain_1, idempotence_k5_setwiseo, t7_lattice2, t27_setwiseo, t48_domain_1, t92_funct_3, t4_altcat_1, t34_xboole_1, t8_zfrefle1, t89_enumset1, dt_k7_subset_1, rc7_finseq_1, t91_relat_1, t88_mcart_1, t14_yellow_9, t111_zfmisc_1, dt_k2_subset_1, t64_funct_5, d4_funct_4, d1_lattice2, d4_urysohn1, involutiveness_k8_binop_2, t102_finseq_3, t38_funct_1, t62_classes2, t53_funct_2, t76_mcart_1, t29_borsuk_1, d5_tarski, t13_funct_7, rc1_borsuk_1, t6_funct_4, t83_mcart_1, t15_funct_1, dt_k11_domain_1, fc4_relat_1, t37_funct_4, redefinition_k4_classes2, fc4_setfam_1, t156_funct_1, t101_xboole_1, t1_group_6, t59_partfun1, t72_funct_4, s12_funct_2, t53_funcop_1, t57_enumset1, t66_enumset1, t44_relat_1, fc4_funct_1, t1_subset, s3_filter_1, fraenkel_a_1_0_lattice5, redefinition_k7_funct_2, t147_relat_1, t10_partfun1, t158_partfun1, t12_yellow_9, dt_k2_card_fil, d5_xboole_0, dt_k7_relset_1, t32_mcart_1, t29_subset_1, d10_mcart_1, fc1_funct_4, t52_zfmisc_1, t144_relat_1, t57_domain_1, t33_setwiseo, t9_lattice2, fc4_subset_1, t71_funct_1, t10_mssubfam, dt_k2_cqc_lang, t22_funct_1, fc3_realset1, free_g3_vectsp_1, t83_funct_4, t9_borsuk_1, t79_funcop_1, fc1_numbers, dt_k3_funct_2, t31_funct_4, t74_funct_2, t168_funct_2, t43_xboole_1, fraenkel_a_8_0_domain_1, redefinition_k7_cat_1, t54_partfun1, t81_zfmisc_1, t16_fraenkel, t52_funct_4, fraenkel_a_0_0_pre_circ, t25_filter_1, fc3_functor0, t7_funct_2, d7_mcart_1, t10_relset_1, t135_partfun1, t55_domain_1, t146_funct_2, fc3_setfam_1, t10_funcop_1, t18_xboole_1, t42_setwiseo, t119_partfun1, t17_yellow_9, t36_sysrel, t4_funcop_1, d17_mcart_1, dt_k35_binop_2, t12_realset1, cc4_yellow21, t3_mcart_1, t78_funct_3, s23_fraenkel, t16_setwiseo, fc3_relat_1, t96_zfmisc_1, redefinition_k2_multop_1, t42_zfmisc_1, t18_cantor_1, t14_binop_1, dt_k9_relset_1, dt_k1_subset_1, t69_funct_3, t13_funcop_1, t6_xboole_1, t30_filter_1, t19_zfmisc_1, d8_funct_1, idempotence_k1_relset_2, dt_k5_urysohn1, t19_relat_1, t70_xboole_1, dt_m1_pua2mss1, d4_zfmisc_1, dt_k13_domain_1, s8_domain_1__e1_22__relset_2, dt_k2_urysohn1, t31_setwiseo, t33_mcart_1, t41_funct_2, t25_sysrel, t22_card_fil, t166_funct_2, t148_finseq_2, t11_altcat_1, t25_xboole_1, dt_m1_nat_lat, commutativity_k7_classes2, t1_qc_lang1, d9_monoid_0, redefinition_k9_classes2, t11_realset1, dt_k9_ens_1, t73_funcop_1, t47_relat_1, t148_partfun1, t36_partfun1, t53_funct_3, fc9_relat_1, t19_closure2, fc5_finset_1, t68_xboole_1, t21_membered, t41_mcart_1, d7_binop_1, t19_finset_1, t54_funct_4, t107_finseq_2, dt_k2_funct_4, t2_boole, dt_m1_filter_1, dt_k1_classes2, t35_zfmisc_1, t93_enumset1, t27_wellord2, t12_relset_2, d5_setfam_1, t28_funcop_1, t43_domain_1, t2_card_fil, t1_funcop_1, t11_pua2mss1, t82_relat_1, t20_yellow_9, t117_zfmisc_1, t29_funct_4, t65_partfun1, t186_partfun1, t44_funct_2, t5_yellow_6, free_g1_lattices, s1_filter_1, t16_finseq_1, involutiveness_k2_card_fil, t117_funct_1, dt_k4_realset1, dt_k4_subset_1, t71_xboole_1, t132_partfun1, t27_xboole_1, s1_group_5, t122_zfmisc_1, t4_mcart_1, t14_sysrel, t15_funct_5, redefinition_k1_pcomps_1, existence_m1_filter_1, t98_funct_3, fc6_funcop_1, dt_m1_realset1, t110_zfmisc_1, t65_classes2, fc3_card_3, t3_pralg_1, fraenkel_a_1_4_domain_1, dt_k19_pralg_1, t64_domain_1, t43_zfmisc_1, fraenkel_a_0_0_yellow_3, t55_funct_4, t29_numbers, rc2_partfun1, t18_relat_1, cc1_fraenkel, t5_card_fil, t162_partfun1, dt_m3_pboole, dt_k6_partfun1, t95_enumset1, t103_zfmisc_1, redefinition_k3_pre_circ, t59_mcart_1, t95_zfmisc_1, fc1_urysohn1, t63_partfun1, t63_setwiseo, t91_finseq_2, t78_funcop_1, t15_relset_1, redefinition_k3_setwiseo, t20_funct_3, redefinition_k8_classes2, t13_ens_1, fraenkel_a_1_2_domain_1, existence_m1_pua2mss1, t104_enumset1, dt_k1_funct_7, t99_zfmisc_1, t44_mcart_1, t10_functor0, t2_functor1, t61_subset_1, d9_funct_1, free_g1_vectsp_1, rc3_funct_1, t81_xboole_1, t47_setfam_1, t49_funct_2, dt_k17_domain_1, dt_k5_domain_1, t17_membered, fc1_funct_1, existence_m2_finseq_2, t27_finseq_2, rc3_finseq_1, t7_orders_1, t104_finseq_3, t121_partfun1, rc1_fraenkel, t5_funct_7, t1_yellow_3, s5_filter_1, t6_mssubfam, rc2_finseq_1, t64_funcop_1, fraenkel_a_3_3_domain_1, t45_zfmisc_1, t81_mcart_1, t51_enumset1, rc1_finseq_1, t57_funct_4, t9_cat_1, t50_funct_2, t63_domain_1, t75_funct_4, dt_k9_finseq_1, dt_m2_filter_1, rc4_triang_1, t70_zfmisc_1, t39_relat_1, dt_k3_metric_1, t69_zfmisc_1, t39_setwiseo, t10_metric_1, d7_partfun1, commutativity_k3_xboole_0, dt_k14_domain_1, t39_finseq_3, t25_setwiseo, t95_finseq_2, t56_relat_1, rc2_classes2, t93_funct_3, t41_relat_1, t27_zfmisc_1, t23_mcart_1, t84_funct_1, t18_ens_1, t37_xboole_1, t26_funct_2, t17_funct_1, t9_xboole_1, d1_card_fil, t82_funct_1, t59_subset_1, t41_zfmisc_1, fc2_functor0, dt_m2_relset_1, existence_m3_grcat_1, t10_borsuk_1, t9_mssubfam, t18_finset_1, t116_enumset1, t40_domain_1, t37_card_3, cc1_relat_1, t6_card_fil, t1_funct_3, dt_k7_funct_2, t131_zfmisc_1, d4_monoid_0, redefinition_k2_funct_2, t95_xboole_1, fraenkel_a_6_0_functor0, fc7_finseq_1, t11_funct_6, fc3_ens_1, t12_funct_5, idempotence_k5_subset_1, t50_zfmisc_1, t2_funct_1, t36_subset_1, fc8_finset_1, t16_funct_5, redefinition_k6_setfam_1, t40_finseq_2, t49_zfmisc_1, t45_yellow20, t102_relat_1, d17_ens_1, t1_waybel10, t42_yellow_9, t105_enumset1, t4_multop_1, t29_partfun1, t31_relset_1, t176_partfun1, t12_binop_1, t62_funct_2, t55_funct_1, dt_k2_realset1, commutativity_k7_domain_1, t49_enumset1, t70_partfun1, t88_finseq_2, d9_mcart_1, t3_funcop_1, fc28_membered, dt_k1_toler_1, t3_setfam_1, t130_funct_2, t152_funct_2, s13_funct_2, rc1_funct_1, d1_relset_2, t150_pboole, redefinition_m1_triang_1, d6_binop_1, t64_funct_2, t4_setwiseo, t15_mcart_1, t2_funct_6, t115_zfmisc_1, t52_funcop_1, existence_m2_card_fil, t62_funct_1, t76_funct_2, dt_k7_binop_2, t58_setwiseo, fraenkel_a_4_1_yellow_9, redefinition_k2_finsub_1, t80_funcop_1, t65_funct_2, fc30_membered, t19_funct_1, t56_setwiseo, fc42_membered, t68_mcart_1, free_g2_lattices, fc11_finset_1, dt_k14_mcart_1, t5_tex_2, dt_k8_relset_2, fraenkel_a_2_0_domain_1, t23_funct_7, t13_funct_4, d2_tarski, t24_funct_2, t29_finset_1, redefinition_k5_classes2, dt_k2_binop_1, t137_zfmisc_1, fraenkel_a_2_2_domain_1, t100_finseq_2, t129_zfmisc_1, d4_subset_1, t2_binop_1, t2_partfun1, t30_funcop_1, dt_k4_classes2, t86_xboole_1, involutiveness_k3_subset_1, t13_relat_1, t51_mcart_1, t89_xboole_1, redefinition_k14_domain_1, t83_funcop_1, t17_binop_1, redefinition_k2_cqc_lang, d1_fraenkel, t25_funct_2, fc2_xboole_0, fraenkel_a_4_0_domain_1, t11_finseq_2, t97_finseq_2, t15_binop_1, t26_finseq_1, dt_m2_realset1, t9_funct_3, t32_subset_1, t80_funct_3, t108_enumset1, dt_k32_binop_2, fraenkel_a_1_2_ens_1, t112_relat_1, t75_funct_2, t31_finset_1, t175_partfun1, t21_funct_4, t15_relat_1, t41_setwiseo, dt_k6_cqc_lang, t154_funct_2, t48_funct_2, fraenkel_a_3_7_domain_1, t12_funct_4, t49_mcart_1, t27_relat_1, t58_mcart_1, t156_funct_2, t18_funct_5, t78_funct_4, d1_xboole_0, t89_mcart_1, t71_funct_3, t5_mssubfam, free_g1_funcsdom, dt_m1_eqrel_1, t49_funct_1, d6_monoid_0, fc17_binop_2, cc7_tex_2, t108_xboole_1, dt_k4_finseq_1, t34_partfun1, s4_filter_1, d4_cantor_1, dt_k7_classes2, dt_k3_setwiseo, dt_k9_funct_2, s2_relset_1, redefinition_k1_nattra_1, t14_card_fil, t40_funct_1, redefinition_k8_funcop_1, t56_enumset1, t89_finseq_2, t2_mssubfam, t15_finsub_1, d2_tex_2, t29_setwiseo, t80_enumset1, t3_mssubfam, d7_ens_1, t2_zfrefle1, t3_waybel20, t64_relat_1, t138_zfmisc_1, rc6_finseq_1, t25_subset_1, t74_enumset1, fraenkel_a_2_0_borsuk_1, d5_urysohn1, t96_funct_3, t52_enumset1, d2_funcop_1, t16_pua2mss1, t12_functor0, t30_finset_1, d5_funcop_1, fraenkel_a_2_0_card_fil, fraenkel_a_1_5_domain_1, t23_funct_1, t130_zfmisc_1, t51_xboole_1, dt_k10_funcop_1, dt_k2_finsub_1, t20_functor0, t36_mcart_1, cc1_tex_2, t108_zfmisc_1, t96_relat_1, t28_funct_4, t165_funct_2, fc10_finset_1, t60_partfun1, t6_closure2, t56_zfmisc_1, t80_mcart_1, redefinition_m3_grcat_1, t27_relset_1, t12_mcart_1, t52_domain_1, t40_setwiseo, t102_finseq_2, t15_funcop_1, t79_funct_3, t11_pre_circ, t52_relset_1, dt_k8_classes2, t34_funct_1, t118_zfmisc_1, t55_partfun1, t2_mcart_1, s4_subset_1, t8_funct_2, dt_k4_setwiseo, t6_funct_3, t29_funct_2, t56_funct_4, dt_k4_ens_1, fraenkel_a_2_0_cantor_1, t118_funct_2, fc2_setfam_1, t126_partfun1, t14_relset_1, dt_m2_card_fil, dt_k1_card_fil, existence_m1_realset1, t26_finset_1, t73_funct_3, dt_k2_cat_5, t16_relset_1, t39_funct_4, fc3_lattice5, t107_enumset1, t53_relset_1, d6_enumset1, t30_sysrel, t6_mcart_1, redefinition_m1_orders_3, s1_funct_7, d3_enumset1, d13_relat_1, t46_zfmisc_1, t31_partfun1, t37_partfun1, dt_k2_relset_2, t171_partfun1, t164_funct_2, fc2_funct_2, t6_boole, t12_funct_1, t62_mcart_1, t10_funct_3, t4_orders_1, t67_setwiseo, t3_funct_2, t18_subset_1, t8_cat_1, dt_k1_functor0, rc2_subset_1, t1_closure2, fc9_finset_1, t46_mcart_1, t16_funct_7, t4_funct_5, t26_borsuk_1, t63_funct_1, t30_borsuk_1, t38_sysrel, t50_xboole_1, dt_k6_subset_1, t10_relat_1, t65_enumset1, t59_setfam_1, d1_relat_1, t24_finsub_1, existence_m2_pua2mss1, dt_k3_relset_2, t37_setwiseo, t185_partfun1, fraenkel_a_3_0_card_fil, t9_cantor_1, dt_k15_ens_1, d3_realset1, t1_funct_6, d6_mcart_1, t5_functor0, t55_relat_1, s17_fraenkel, redefinition_k13_mcart_1, t57_mcart_1, t1_xboole_1, redefinition_k4_relset_2, t87_mcart_1, redefinition_m1_nat_lat, t15_yellow_9, t26_relset_1, t72_relat_1, t66_funct_5, dt_k1_funct_4, t64_partfun1, fc3_cantor_1, t52_relat_1, t35_funcop_1, t77_funct_2, t59_domain_1, free_g1_pre_topc, dt_k5_ens_1, t20_funct_1, t82_finseq_2, t12_sysrel, rc2_waybel_7, dt_k4_card_fil, t104_relat_1, t28_wellord2, t69_funct_4, t39_funcop_1, fc1_fraenkel, d3_finseq_2, t32_relset_1, t17_domain_1, t7_setfam_1, t3_partfun1, dt_k10_binop_2, t59_setwiseo, t4_setfam_1, t39_finseq_2, t32_partfun1, redefinition_k4_funct_2, t56_yellow_0, t73_relat_1, t4_relat_1, fc5_funcop_1, t28_subset_1, t52_xboole_1, t185_relat_1, t21_finset_1, t44_finseq_2, t75_xboole_1, fraenkel_a_1_0_card_fil, fc17_finset_1, s5_domain_1, dt_k6_pralg_1, dt_k10_setwiseo, t34_funct_4, commutativity_k2_xboole_0, dt_k3_urysohn1, t15_domain_1, dt_k2_classes2, t128_zfmisc_1, t39_partfun1, t50_enumset1, t5_altcat_1, t142_finseq_2, fc3_subset_1, t5_subset, symmetry_r4_nattra_1, d9_realset1, t112_enumset1, dt_k9_classes2, t48_zfmisc_1, t7_mssubfam, t4_zfrefle1, t45_funct_2, t84_enumset1, existence_m1_cat_5, t100_enumset1, t25_zfmisc_1, d4_relat_1, t50_frechet2, t75_zfmisc_1, t94_zfmisc_1, t11_mcart_1, t8_mcart_1, t24_borsuk_1, t4_xboole_0, t41_funcop_1, d2_realset1, t81_enumset1, t32_sysrel, t3_functor0, t6_lattice2, d17_nattra_1, fc6_finset_1, free_g1_cat_1, t63_funct_5, t123_enumset1, t65_xboole_1, t43_funct_4, t122_partfun1, fraenkel_a_0_32_fraenkel, t1_triang_1, t38_card_3, t22_filter_1, fc17_finseq_1, t23_binop_1, d6_partfun1, t61_setwiseo, t150_relat_1, existence_m1_relset_1, t20_finseq_1, d11_mcart_1, d18_vectsp_2, commutativity_k5_subset_1, t55_setfam_1, t36_finseq_2, t1_zfmisc_1, t77_mcart_1, t68_funct_3, s8_domain_1, t46_partfun1, d2_enumset1, t12_setfam_1, t101_finseq_2, t3_funct_6, redefinition_k11_classes2, t5_setfam_1, t52_funct_1, d1_cantor_1, t163_relat_1, t28_mcart_1, s21_fraenkel, t3_fraenkel, t53_funct_4, rc3_setfam_1, t22_setwiseo, existence_m1_functor0, redefinition_k14_borsuk_1, t123_zfmisc_1, fc2_subset_1, t2_membered, t16_yellow20, t79_zfmisc_1, t12_lattice2, t5_funct_2, cc1_yellow13, dt_k8_funct_2, fraenkel_a_2_0_lattice5, t7_closure2, t50_setwiseo, d2_finseq_1, redefinition_k5_setwiseo, t18_setwiseo, d3_zfmisc_1, t72_mcart_1, s9_domain_1, t2_zfmisc_1, t9_altcat_1, fraenkel_a_1_6_domain_1, redefinition_k10_pboole, t167_funct_2, rc6_tex_2, t72_funct_3, t60_zfmisc_1, t24_filter_1, cc1_finseq_1, t24_finset_1, t1_pralg_3, fc1_orders_1, t97_zfmisc_1, redefinition_k7_domain_1, t11_funct_2, t21_funct_5, t28_partfun1, fc2_funct_1, d1_ens_1, t45_enumset1, t73_funct_1, dt_k3_realset1, t40_funct_2, t7_cat_1, fraenkel_a_0_0_domain_1, t4_waybel20, cc1_altcat_1, redefinition_k1_card_fil, t102_zfmisc_1, d2_ens_1, t102_xboole_1, t24_binop_1, t27_funcop_1, t28_relset_1, t24_domain_1, t72_partfun1, t8_funct_1, t51_funcop_1, t121_funct_1, t1_funct_7, existence_m1_orders_3, t9_relat_1, t2_tarski, t56_mcart_1, t23_setwiseo, t1_waybel14, t16_funct_1, t79_relat_1, t14_relat_1, t72_zfmisc_1, t25_finseq_3, t142_funct_2, t82_funct_2, fc6_subset_1, t28_zfmisc_1, t2_funcop_1, t33_xboole_1, t62_subset_1, t54_enumset1, t19_card_3, t122_funct_1, t13_setwiseo, t52_setfam_1, t25_borsuk_1, d1_filter_1, dt_k1_borsuk_1, t74_funct_3, t16_funct_4, t22_sysrel, t61_funcop_1, t114_xboole_1, t8_zfmisc_1, d6_realset1, t67_zfmisc_1, t74_funcop_1, d1_funct_4, dt_k1_partfun1, t11_tops_2, t61_funct_4, d2_fraenkel, t76_xboole_1, t71_setwiseo, cc1_funct_2, t32_xboole_1, t14_funct_1, d8_mcart_1, t52_subset_1, t5_ordinal1, t48_enumset1, t4_boole, t36_funct_2, t53_xboole_1, d2_funct_2, cc2_eqrel_1, t84_xboole_1, dt_k9_mcart_1, t23_zfmisc_1, t109_relat_1, t4_cat_1, t57_zfmisc_1, t125_funct_1, t46_funcop_1, d5_realset1, t21_xboole_1, t13_yellow_9, t98_zfmisc_1, t58_subset_1, dt_k11_relset_1, dt_k16_funct_3, dt_k5_metric_1, dt_k4_relat_1, t162_funct_1, t32_domain_1, t43_enumset1, dt_k9_relset_2, rc5_tex_2, t4_subset, dt_k10_cat_2, fc3_xboole_0, t22_ens_1, t29_sysrel, t38_subset_1, t176_orders_1, t16_funcop_1, fraenkel_a_1_3_domain_1, dt_k1_finsub_1, t169_funct_2, t33_sysrel, t29_funcop_1, d14_mcart_1, d2_xboole_0, t30_xboole_1, t99_enumset1, cc1_closure2, dt_k2_funct_1, t81_funct_4, dt_k8_domain_1, t15_realset1, t3_altcat_2, t74_zfmisc_1, t6_cqc_lang, t8_ens_1, t39_subset_1, t72_enumset1, t1_waybel20, t89_funct_3, t8_functor0, t76_relat_1, dt_k1_cat_5, t20_ens_1, d4_tarski, d5_partfun1, t43_funct_1, redefinition_k7_filter_1, dt_k14_funct_3, t141_zfmisc_1, rc2_realset1, t12_zfmisc_1, t26_mcart_1, commutativity_k10_classes2, fc1_qc_lang1, t96_xboole_1, s3_domain_1, t65_funcop_1, t5_filter_2, t80_xboole_1, t20_finsub_1, t58_funct_1, t50_domain_1, t25_finset_1, t88_enumset1, t9_zfmisc_1, t148_funct_2, t79_xboole_1, t106_relat_1, t51_funct_2, reflexivity_r2_zfrefle1, t38_finseq_3, t67_xboole_1, d12_binop_1, t35_setwiseo, fc1_rfinseq, reflexivity_r3_zfrefle1, t39_setfam_1, existence_m2_realset1, t61_enumset1, existence_m3_realset1, t119_enumset1, t12_tops_2, redefinition_k6_setwiseo, t10_mcart_1, t56_subset_1, redefinition_k10_relset_1, dt_k3_ens_1, s1_relset_1, redefinition_k14_mcart_1, t8_funct_5, redefinition_k5_setfam_1, t12_ens_1, s6_filter_1, t47_funcop_1, dt_k1_domain_1, t58_zfmisc_1, t41_enumset1, t20_borsuk_1, t21_funct_3, t17_funct_2, t3_grcat_1, t1_xboole_0, t21_finsub_1, t71_funct_4, involutiveness_k4_relat_1, t35_sysrel, d4_partfun1, t29_xboole_1, t50_funct_4, t5_orders_1, t17_finsub_1, t67_funct_4, t13_lattice2, rc5_triang_1, fc1_realset1, dt_k1_urysohn1, t63_classes2, t11_funct_5, t74_mcart_1, t7_realset1, dt_k6_relset_2, commutativity_k5_xboole_0, t59_funct_1, t145_finseq_2, t132_funct_2, t139_zfmisc_1, t36_setfam_1, fc4_qc_lang1, t143_relat_1, t77_relat_1, t13_finset_1, rc3_tex_2, t3_ordinal1, t32_lopclset, t6_realset1, t16_lattice2, t64_classes2, fc5_finseq_1, t7_boole, t7_altcat_1, t37_sysrel, t11_card_fil, t41_domain_1, dt_k4_closure2, cc1_funct_1, t51_finseq_2, t4_funct_2, t2_altcat_1, d2_filter_1, t24_funcop_1, t17_funct_5, t27_membered, t95_funct_3, t136_partfun1, rc3_realset1, d3_funcop_1, t111_finseq_2, fc6_finseq_1, s11_funct_2, t86_funct_3, t104_zfmisc_1, t11_binop_1, t42_mcart_1, t86_enumset1, t138_partfun1, t12_funct_7, t28_domain_1, s2_domain_1, dt_k7_mcart_1, t55_zfmisc_1, t42_finseq_3, d10_relat_1, t66_funct_4, t2_qc_lang1, d10_setfam_1, t1_t_0topsp, d2_subset_1, free_g1_metric_1, t66_zfmisc_1, d3_pboole, fc1_subset_1, t33_zfmisc_1, t29_finseq_1, t33_funct_4, fc29_membered, t22_relat_1, redefinition_k6_partfun1, t105_relat_1, redefinition_k3_classes2, d1_setwiseo, t91_funct_3, t48_xboole_1, dt_k6_domain_1, redefinition_m1_cat_5, t157_funct_1, t9_domain_1, fc38_membered, d5_mcart_1, t45_relset_1, t16_mcart_1, dt_k16_domain_1, t8_pua2mss1, dt_k4_urysohn1, fc2_membered, dt_k11_mcart_1, t6_funct_5, t158_funct_2, t74_relat_1, redefinition_k1_domain_1, t21_funct_2, t130_finseq_2, t20_cantor_1, t3_altcat_1, t14_functor0, t23_borsuk_1, t5_setwiseo, dt_k12_binop_2, t66_funcop_1, t16_subset_1, dt_k2_partfun1, dt_m1_card_fil, t26_zfmisc_1, t70_enumset1, t9_ens_1, t69_partfun1, dt_k9_binop_2, t38_relset_1, t65_funct_4, t7_ordinal1, t153_relat_1, rc2_funct_1, t49_partfun1, redefinition_k10_classes2, dt_k31_binop_2, t9_funct_2, t160_relat_1, cc2_setfam_1, reflexivity_r6_pboole, fc10_relat_1, t31_funct_2, rc1_subset_1, t64_funct_1, t149_funct_2, fc1_closure2, fc2_card_fil, t41_sysrel, t81_funcop_1, t187_relat_1, cc4_membered, t48_funct_1, fraenkel_a_0_0_group_5, t6_fraenkel, t49_relset_1, redefinition_k2_monoid_0, t7_relset_2, t54_setfam_1, t17_ens_1, t47_funct_1, d11_relat_1, fc1_yellow_3, t31_xboole_1, t1_functor1, t63_zfmisc_1, dt_k6_funcop_1, t4_subset_1, t88_xboole_1, t19_funct_2, t18_funct_4, fc1_partfun1, fc4_card_3, t51_funct_1, t26_filter_1, t13_borsuk_1, t8_fraenkel, t30_funct_4, fraenkel_a_3_0_domain_1, t85_xboole_1, t103_finseq_3, t7_funct_5, t22_finset_1, t67_funct_1, t8_lattice2, t90_funct_3, t42_funct_4, t30_relset_1, redefinition_k3_cat_5, t14_zfmisc_1, rc1_funct_2, t91_orders_1, t24_xboole_1, d7_realset1, dt_k10_funct_3, t76_funcop_1, d6_ens_1, t70_funct_4, t56_funct_1, t110_relat_1, t113_funct_2, t71_partfun1, t46_enumset1, fc8_finseq_1, dt_m1_pboole, t69_xboole_1, d5_funct_2, t17_fraenkel, t27_sysrel, t12_setwiseo, cc1_triang_1, d4_realset1, t59_funct_4, existence_m3_pboole, t94_finseq_2, t4_realset1, t11_fraenkel, t159_funct_2, t116_zfmisc_1, redefinition_k13_domain_1, t64_zfmisc_1, d7_xboole_0, redefinition_k6_relset_2, fc5_relat_1, t83_xboole_1, d6_setwiseo, t151_relat_1, redefinition_k7_classes2, t1_zfrefle1, t51_setfam_1, t4_borsuk_1, dt_m1_fraenkel, t45_relat_1, dt_m2_finseq_1, t2_lattice2, redefinition_k23_qc_lang1, d8_card_fil, t17_relset_2, t7_card_fil, t5_altcat_2, d1_tex_2, t4_ens_1, t14_funct_2, fc2_funct_7, t155_funct_2, t77_funct_4, t20_xboole_1, t178_orders_1, s2_subset_1, t6_tex_2, t12_funct_3, t50_mcart_1, commutativity_k3_setfam_1, t97_relat_1, d3_funct_4, t16_zfmisc_1, t17_cantor_1, t90_enumset1, t101_zfmisc_1, t4_isocat_2, d3_funct_2, t17_borsuk_1, t2_t_0topsp, redefinition_k8_domain_1, t65_funct_1, d2_funct_5, t134_pboole, t124_zfmisc_1, t188_relat_1, s10_funct_2, d9_binop_2, fraenkel_a_3_1_domain_1, t35_funct_4, t60_funct_2, d16_mcart_1, t82_xboole_1, existence_m1_pboole, t6_setwiseo, dt_k8_vectsp_2, t78_finseq_2, t4_filter_2, t107_relat_1, dt_k2_monoid_0, t32_zfmisc_1, t54_xboole_1, t186_relat_1, t46_setfam_1, t23_funct_4, t55_xboole_1, t3_multop_1, t56_funcop_1, d7_relat_1, t89_relat_1, t10_ens_1, cc2_funct_1, t120_zfmisc_1, t9_relset_2, t169_partfun1, t3_funct_3, t18_funct_1, redefinition_k1_cat_2, t5_realset1, t17_finset_1, dt_k8_setfam_1, t4_relset_1, t16_card_fil, dt_k4_funct_2, t31_subset_1, t2_filter_2, t3_subset, cc1_relset_1, cc1_eqrel_1, t22_relset_1, commutativity_k9_binop_2, t25_binop_1, t98_enumset1, s1_subset_1, t1_cantor_1, d2_binop_1, s1_domain_1, t31_sysrel, t78_relat_1, s4_funct_2, t8_mssubfam, t10_funct_5, t7_pua2mss1, t76_funct_1, t124_funct_1, fraenkel_a_3_1_pua2mss1, dt_k1_cantor_1, dt_k9_cat_2, t55_subset_1, t79_funct_2, t70_mcart_1, dt_k6_funct_3, t46_funct_1, t51_setwiseo, idempotence_k1_funct_4, dt_k6_setfam_1, d15_mcart_1, free_g3_quantal1, t44_setwiseo, t136_funct_2, t6_borsuk_1, fraenkel_a_2_1_domain_1, t14_relset_2, commutativity_k7_subset_1, d2_zfmisc_1, dt_k13_mcart_1, fc11_relat_1, t127_partfun1, t10_altcat_1, existence_m1_subset_1, fc5_subset_1, t1_waybel18, d2_mcart_1, t111_enumset1, d8_binop_2, t41_funct_4, t110_enumset1, commutativity_k2_tarski, t3_relat_1, t13_finseq_2, t26_funct_7, t24_relat_1, t14_funct_7, t8_relset_1, t68_funct_4, d6_xboole_0, t44_zfmisc_1, t14_finsub_1, redefinition_r6_pboole, redefinition_k5_domain_1, t17_relset_1, dt_k9_setwiseo, t91_enumset1, t25_domain_1, t35_xboole_1, t49_domain_1, fc3_yellow_3, t118_enumset1, t7_functor0, t106_zfmisc_1, dt_k11_setwiseo, t12_cantor_1, fraenkel_a_6_0_domain_1, t7_funct_7, fc2_qc_lang1, t16_relset_2, d5_card_3, t125_zfmisc_1, t73_funct_2, t30_subset_1, t8_setwiseo, d17_binop_1, t10_cqc_lang, t54_mcart_1, dt_k2_funct_2, fc3_qc_lang1, t84_funcop_1, commutativity_k5_classes2, dt_k7_relat_1, redefinition_k4_subset_1, t1_monoid_0, rc4_tex_2, t14_xboole_1, t44_setfam_1, t11_relset_1, t5_funct_5, t11_funct_4, rc5_orders_3, t155_relat_1, d8_relat_1, t2_pre_circ, t47_xboole_1, t109_enumset1, t19_numbers, t61_funct_1, commutativity_k8_classes2, d2_card_fil, fc1_finset_1, t15_subset_1, t99_funct_3, t5_grcat_1, t5_lattice2, free_g2_struct_0, t37_funct_2, t94_relat_1, t48_setfam_1, t5_isocat_2, t39_sysrel, t31_funcop_1, t118_funct_1, t132_zfmisc_1, t18_borsuk_1, d5_subset_1, t2_altcat_2, redefinition_k16_funct_3, t29_zfmisc_1, t9_zfrefle1, t146_relat_1, t92_zfmisc_1, redefinition_k4_setwiseo, t99_partfun1, t54_setwiseo, t107_zfmisc_1, redefinition_k2_classes2, t9_realset1, t9_funct_5, existence_m2_subset_1, t95_relat_1, d8_setfam_1, t100_zfmisc_1, t22_zfmisc_1, redefinition_k1_relset_2, t125_enumset1, redefinition_r2_subset_1, dt_k5_subset_1, dt_k9_funcop_1, t3_funct_7, t64_funct_4, t19_funct_5, t94_enumset1, t8_cantor_1, t64_setwiseo, t121_funct_2, t114_zfmisc_1, cc5_tex_2, fc3_urysohn1, t31_zfmisc_1, t70_funct_1, cc4_tex_2, s4_altcat_1, t58_partfun1, t60_setwiseo, redefinition_k7_pboole, t81_funct_3, t2_multop_1, d1_zfmisc_1, t16_xboole_1, free_g2_vectsp_1, t19_funcop_1, t106_finseq_3, t3_zfrefle1, t1_ens_1, t69_enumset1, t26_xboole_1, t69_mcart_1, t90_finseq_2, s24_fraenkel, t63_xboole_1, redefinition_k7_funcop_1, t26_domain_1, t7_tex_2, t15_xboole_1, t27_funct_4, redefinition_k8_waybel_5, t144_finseq_2, t57_setfam_1, t8_funct_4, t43_funct_2, commutativity_k4_subset_1, dt_k1_nattra_1, t96_finseq_2, t86_zfmisc_1, rc2_relat_1, existence_m2_relset_1, t98_xboole_1, t16_membered, t2_tex_2, d4_binop_1, t49_funcop_1, t54_domain_1, t38_zfmisc_1, t14_ens_1, t63_funct_4, dt_k13_ens_1, dt_k12_finseq_1, rc1_pua2mss1, t7_ens_1, redefinition_k7_subset_1, t15_cantor_1, t65_mcart_1, t16_ens_1, t4_funct_7, t34_funcop_1, t55_setwiseo, t31_yellow18, d8_ens_1, dt_k3_pre_circ, t37_mcart_1, t73_enumset1, d5_enumset1, t116_funct_2, d12_ens_1, fraenkel_a_3_6_domain_1, t9_functor0, t17_finseq_1, t73_partfun1, redefinition_k3_cantor_1, dt_k7_funcop_1, fc4_funcop_1, t6_funct_2, t69_funcop_1, fraenkel_a_1_0_pua2mss1, t28_finseq_2, t61_card_3, t72_funct_1, s4_domain_1, d14_ens_1, t168_partfun1, t1_isocat_1, t157_relat_1, cc3_finsub_1, t82_funct_3, s14_funct_2, redefinition_k4_domain_1, t62_setwiseo, t26_subset_1, redefinition_k2_binop_1, t6_grcat_1, existence_m2_filter_1, t51_subset_1, t21_subset_1, t111_xboole_1, rc1_triang_1, dt_k4_multop_1, t61_domain_1, t15_funct_3, t15_card_fil, involutiveness_k7_setfam_1, t22_xboole_1, t2_funct_3, t5_pua2mss1, involutiveness_k10_funcop_1, t64_enumset1, t84_zfmisc_1, t13_funct_5, t76_enumset1, t67_classes2, t27_borsuk_1, t62_funct_4, t113_enumset1, t40_sysrel, reflexivity_r1_filter_2, t3_pua2mss1, t8_setfam_1, t36_zfmisc_1, d4_classes2, d8_monoid_0, d7_monoid_0, t41_subset_1, t26_membered, redefinition_k5_funct_4, dt_k12_mcart_1, redefinition_k6_funcop_1, redefinition_k17_domain_1, t14_setwiseo, t73_finseq_1, t20_card_3, t100_xboole_1, t84_funct_3, t8_xboole_1, t8_realset1, t103_xboole_1, t25_ens_1, t58_funcop_1, t37_relat_1, rc2_cat_5, t6_relset_1, t78_xboole_1, t28_xboole_1, t16_borsuk_1, d1_relset_1, d3_tarski, d6_card_fil, t74_partfun1, t31_filter_1, t53_domain_1, d1_funct_3, t58_enumset1, d1_multop_1, t46_subset_1, t151_pboole, t18_binop_1, redefinition_k16_domain_1, cc6_funct_2, t74_funct_4, t43_funcop_1, dt_k8_binop_2, dt_k15_classes2, t76_funct_4, t33_domain_1, t60_subset_1, t39_zfmisc_1, d1_realset1, t15_funct_7, t19_functor0, t58_funct_4, t72_setwiseo, t131_funct_2, t119_zfmisc_1, dt_k7_pboole, t5_xboole_0, d8_realset1, d7_card_fil, redefinition_k1_cat_5, rc1_relat_1, t34_mcart_1, t13_xboole_1, t60_relat_1, t54_funct_1, t13_cantor_1, t42_funcop_1, t19_setwiseo, t83_zfmisc_1, t80_finseq_2, t40_subset_1, t2_monoid_0, t54_zfmisc_1, t13_card_fil, fraenkel_a_3_4_domain_1, s22_fraenkel, dt_k5_relat_1, t17_subset_1, t57_setwiseo, dt_k4_qc_lang1, t148_relat_1, reflexivity_r1_tarski, t9_funct_1, t6_orders_1, fraenkel_a_0_0_card_fil, symmetry_r2_subset_1, dt_k6_relat_1, t143_funct_2, t70_funct_3, fc2_urysohn1, t20_finset_1, t32_setwiseo, cc17_membered, t6_zfmisc_1, dt_k14_borsuk_1, t41_finseq_2, t1_mssubfam, t48_relat_1, dt_k10_relset_1, symmetry_r1_filter_2, d2_orders_1, t27_finsub_1, s3_subset_1, t5_mcart_1, t93_relat_1, t33_borsuk_1, t18_funct_2, redefinition_k1_classes2, dt_k4_relset_2, t121_zfmisc_1, t10_subset_1, t161_relat_1, dt_k7_filter_1, t19_ens_1, t51_funct_4, t139_finseq_2, t56_setfam_1, redefinition_k1_partfun1, rc2_setwiseo, t17_card_fil, t1_realset1, t7_cqc_lang, t36_setwiseo, t53_enumset1, reflexivity_r4_nattra_1, t2_xboole_1, t4_xboole_1, t57_partfun1, t141_partfun1, d12_funct_1, t9_relset_1, redefinition_k2_realset1, t17_funct_4, fc2_yellow_3, dt_k5_classes2, t9_mcart_1, t7_msualg_1, t11_funcop_1, dt_k5_funct_4, t34_setfam_1, t37_funcop_1, fraenkel_a_0_38_fraenkel, t59_zfmisc_1, fc6_relat_1, dt_k4_domain_1, free_g2_rlvect_1, s1_card_fil, t51_domain_1, t1_partfun1, existence_m4_realset1, t41_xboole_1, idempotence_k7_classes2, t79_enumset1, t34_funct_2, t11_funct_7, t83_enumset1, t57_subset_1, t47_zfmisc_1, d15_binop_1, t1_latsum_1, d1_funct_2, t12_funct_6, t3_lattice4, dt_k6_setwiseo, t2_setfam_1, t61_mcart_1, t18_zfmisc_1, t6_pua2mss1, t25_funct_4, t20_relat_1, t90_xboole_1, t8_relset_2, t51_relat_1, t2_ens_1, t31_domain_1, free_g3_lattices, redefinition_k11_domain_1, t46_relat_1, fc1_setfam_1, t39_mcart_1, d15_ens_1, d5_functor0, t66_funct_1, t3_card_fil, d1_funct_7, d4_xboole_0, redefinition_v1_yellow18, t7_funct_4, t43_setwiseo, t65_setwiseo, t68_setwiseo, t12_zfrefle1, t35_funct_1, t29_relset_1, rc1_realset1, dt_k11_ens_1, s4_multop_1, redefinition_k7_relset_1, t3_monoid_0, t3_isocat_2, t17_funcop_1, dt_k5_setfam_1, rc3_finset_1, t68_funct_1, t24_ens_1, d6_eqrel_1, dt_k2_nattra_1, dt_k5_setwiseo, existence_m1_eqrel_1, commutativity_k5_setwiseo, dt_k1_metric_1, t30_finseq_2, t45_partfun1, s2_pua2mss1, t36_xboole_1, t51_zfmisc_1, redefinition_k14_funct_3, dt_k8_subset_1, rc8_finseq_1, t3_ens_1, t144_partfun1, t20_funct_5, fc12_binop_2, existence_m1_nat_lat, t4_card_fil, t94_xboole_1, t73_zfmisc_1, t47_subset_1, redefinition_k4_multop_1, t123_partfun1, t151_funct_2, dt_k12_domain_1, t46_relset_1, t47_funct_4, t64_xboole_1, t49_xboole_1, dt_k1_cat_1, t64_mcart_1, t71_mcart_1, d5_binop_1, dt_m2_subset_1, dt_k5_numbers, t51_relset_1, dt_k8_setwiseo, dt_k6_ens_1, redefinition_k1_finsub_1, t19_borsuk_1, t18_yellow_9, t12_funct_2, d16_binop_1, t54_subset_1, t53_funct_1, t27_finseq_1, rc1_finset_1, dt_k7_setfam_1, t28_finsub_1, t127_zfmisc_1, d1_cat_1, t10_fraenkel, t123_funct_1, redefinition_k2_functor0, dt_k2_yellow_3, t70_funcop_1, t40_funct_4, t11_setfam_1, t50_relset_1, t44_subset_1, t87_relat_1, cc1_finset_1, commutativity_k11_binop_2, t14_mcart_1, t35_partfun1, d1_yellow18, d8_binop_1, t93_xboole_1, t5_cqc_lang, t21_funct_1, t50_funct_1, fc12_finset_1, t87_enumset1, t42_funct_1, t26_finsub_1, t8_card_fil, t73_mcart_1, t2_nattra_1, fc1_relat_1, d3_setwiseo, d10_binop_2, t4_mssubfam, t77_xboole_1, t10_setfam_1, cc6_membered, t8_boole, rc1_xboole_0, existence_m1_fraenkel, t108_finseq_3, fc1_waybel_2, t21_borsuk_1, t18_sysrel, t16_funct_3, t1_funct_5, t1_mcart_1, t103_enumset1, t11_xboole_1, t23_finset_1, t24_partfun1, redefinition_k8_funct_2, t35_mcart_1, t35_relset_1, d1_orders_1, t16_sysrel, d9_card_fil, dt_m2_finseq_2, t80_zfmisc_1, t18_card_3, t34_zfmisc_1, t18_functor0, fc3_funct_1, t6_functor0, t6_multop_1, t102_enumset1, t16_finseq_2, t60_enumset1, t26_setwiseo, t5_relat_1, t24_zfmisc_1, t68_zfmisc_1, rc2_tex_2, t22_membered, dt_k36_binop_2, dt_k6_mcart_1, rc7_tex_2, t1_functor0, t23_relat_1, dt_k7_metric_1, dt_m1_orders_1, dt_k12_funct_3, t54_funcop_1, t120_funct_2, d1_borsuk_1, t31_mcart_1, t67_mcart_1, t46_funct_4, involutiveness_k7_binop_2, redefinition_k9_relset_2, t59_funct_2, dt_k33_binop_2, t12_xboole_1, t22_funct_3, t10_zfmisc_1, t56_classes2, t2_subset, existence_m1_finseq_2, s1_binop_2, t100_funct_3, t20_sysrel, reflexivity_r1_partfun1, t38_funct_2, t33_partfun1, rc1_closure2, t34_finsub_1, d3_relat_1, t85_funct_2, fc1_tex_2, t45_domain_1, t12_altcat_1, t46_yellow20, t16_finset_1, t42_domain_1, dt_k6_classes2, d2_multop_1, fc2_yellow21, dt_k2_multop_1, t75_funcop_1, fc7_relat_1, t14_funcop_1, t4_qc_lang1, t47_mcart_1, s1_pre_circ, commutativity_k4_finsub_1, t60_funct_1, t111_relat_1, d11_ens_1, dt_k3_cat_5, dt_k8_mcart_1, t21_yellow_9, t24_funct_4, t11_functor0, fc2_relat_1, t14_finseq_1, t37_zfmisc_1, t52_setwiseo, t65_relat_1, t21_relat_1, t3_pboole, t156_relat_1, dt_k10_classes2, t23_finsub_1, t53_zfmisc_1, t30_finsub_1, fc1_funct_7, dt_k23_qc_lang1, t14_borsuk_1, d4_setwiseo, d4_mcart_1, t15_finseq_2, t109_zfmisc_1, redefinition_k6_cqc_lang, d10_lattice5, fraenkel_a_2_3_domain_1, t60_domain_1, t117_enumset1, t25_finsub_1, d1_setfam_1, t152_relat_1, symmetry_r1_xboole_0, t49_funct_4, t134_zfmisc_1, t86_relat_1, t28_finset_1, free_g1_rlvect_1, dt_k5_mcart_1, t100_relat_1, t78_mcart_1, t25_partfun1, t49_relat_1, d12_binop_2, t126_zfmisc_1, t12_domain_1, fraenkel_a_3_1_card_fil, rc3_closure2, dt_k2_cantor_1, t13_finsub_1, fc8_relat_1, t27_funct_1, t10_realset1, t92_relat_1, d11_binop_2, t82_funcop_1, redefinition_k2_cat_5, dt_k10_mcart_1, t175_orders_1, s10_fraenkel, dt_k3_binop_1, t15_functor0, t40_relat_1, fraenkel_a_0_18_fraenkel, t40_finseq_3, idempotence_k8_classes2, t75_mcart_1, fc2_funcop_1, t59_enumset1, fraenkel_a_2_1_card_fil, dt_k10_ens_1, t55_enumset1, t58_domain_1, t115_funct_2, free_g1_quantal1, t4_waybel18, idempotence_k2_xboole_0, t13_mcart_1, t48_funct_4, dt_k12_classes2, t32_finsub_1, t48_subset_1, t129_finseq_2, rc1_setwiseo, d18_pboole, dt_k1_pcomps_1, t28_relat_1, t17_mcart_1, d1_funct_1, d1_filter_2, t32_borsuk_1, t31_finseq_2, t1_pralg_1, t44_funct_4, dt_k1_relset_2, fc2_ens_1, dt_k5_relset_2, redefinition_k5_funcsdom, redefinition_k2_funct_3, redefinition_k10_cat_2, t145_relat_1, t50_subset_1, t1_nattra_1, t11_relset_2, t46_xboole_1, t107_xboole_1, d10_xboole_0, t1_tex_2, t27_filter_1, t149_relat_1, d3_pua2mss1, d11_setfam_1, dt_k2_qc_lang1, fc2_realset1, t2_lattice5, t74_xboole_1, fc2_finset_1, fraenkel_a_1_0_ens_1, fraenkel_a_0_33_fraenkel, redefinition_k18_group_2, redefinition_k10_domain_1, t7_xboole_1, t10_relset_2, t8_funct_7, t2_grcat_1, t37_funct_1, t59_classes2, t3_xboole_0, t67_partfun1, fc2_fraenkel, cc1_realset1, t58_setfam_1, t12_relset_1, t77_funcop_1, d2_funct_4, dt_k18_group_2, fc3_funcop_1, t5_xboole_1, fc4_binop_2, t49_subset_1, fc1_funcop_1, t44_funcop_1, t7_tarski, t15_borsuk_1, t108_relat_1, t33_funct_1, t145_funct_2, t141_funct_2, t43_mcart_1, t3_setwiseo, rc1_partfun1, redefinition_r1_filter_2, t40_ens_1, t28_setwiseo, redefinition_m1_pua2mss1, dt_k3_funct_4, redefinition_k5_relset_1, rc1_card_fil, redefinition_k2_nattra_1, t57_funct_1, t120_partfun1, fraenkel_a_3_0_ens_1, t27_partfun1, symmetry_r1_partfun1, d5_ens_1, t2_funct_7, t91_xboole_1, dt_k2_setwiseo, t23_filter_1, t3_boole, redefinition_k2_setwiseo, d8_funct_3, d9_funct_3, d5_funct_1, t48_mcart_1, t6_ordinal1, t53_mcart_1, t146_finseq_2, dt_k10_pboole, fc1_ens_1, redefinition_k6_subset_1, t93_zfmisc_1, dt_k2_funct_3, t140_finseq_2, redefinition_k4_relset_1, t44_funct_1, t10_finsub_1, cc5_funct_2, t48_relset_1, t57_sysrel, redefinition_m2_subset_1, t69_setwiseo, d4_enumset1, redefinition_k1_borsuk_1, t87_funct_3, t59_funcop_1, t25_relat_1, t22_funct_2, t62_finseq_3, t99_xboole_1, t4_pralg_1, t16_domain_1, fc1_sysrel, t5_funct_4, fc16_finset_1, t13_binop_1, dt_k34_binop_2, t83_funct_3, dt_k1_oppcat_1, d5_setwiseo, fc1_yellow21, t87_xboole_1, t67_funct_2, t26_partfun1, redefinition_k2_partfun1, fc14_finset_1, dt_k15_funct_3, t8_multop_1, fc4_realset1, t11_ens_1, t17_funct_3, t78_enumset1, t26_funct_4, t40_mcart_1, rc1_tex_2, t36_relset_1, t103_relat_1, dt_k5_finsub_1, t30_zfmisc_1, s2_multop_1, dt_k10_domain_1, t80_relat_1, cc16_membered, t15_sysrel, fraenkel_a_0_1_domain_1, t16_binop_1, fc13_finset_1, redefinition_k6_classes2, rc1_setfam_1, t45_mcart_1, t15_funct_4, t139_partfun1, fraenkel_a_4_0_relset_2, dt_k2_zfrefle1, d13_binop_1, t9_card_fil, fc7_finset_1, idempotence_k4_subset_1, t21_closure2, t34_setwiseo, d5_finsub_1, symmetry_r6_pboole, t26_sysrel, dt_k7_cat_1, t143_partfun1, d2_setwiseo, fraenkel_a_0_39_fraenkel, d10_ens_1, dt_k13_funct_3, d1_binop_1, t71_enumset1, t81_relat_1, t40_zfmisc_1, t72_funcop_1, t82_mcart_1, t22_funct_4, fc22_membered, rc2_xboole_0, dt_k3_card_fil, t174_partfun1, t55_funct_2, fraenkel_a_3_5_domain_1, t82_funct_4, redefinition_r4_nattra_1, t45_xboole_1, t66_relat_1, t38_partfun1, fc27_membered, existence_m1_card_fil, s7_domain_1, d3_monoid_0, t141_finseq_2, existence_m1_orders_1, symmetry_r2_zfrefle1, t112_zfmisc_1, t8_funct_3, t40_xboole_1, dt_m3_realset1, t5_closure2, t2_xboole_0, redefinition_k4_finseq_1, redefinition_k12_classes2, d3_xboole_0, d2_relat_1, d4_funcop_1, t71_relat_1, irreflexivity_r2_subset_1, t61_funct_2, t52_mcart_1, t36_funct_4, t62_domain_1, t10_xboole_1, redefinition_k12_domain_1, d3_binop_1, t28_funct_2, dt_k3_subset_1, fraenkel_a_0_2_domain_1, d2_relset_2, fc1_funct_2, existence_m2_finseq_1, t2_funct_4, fc23_membered, t147_finseq_2, t125_partfun1, t38_setwiseo, t96_enumset1, t66_classes2, cc1_binop_1, t6_relat_1, rc1_finseq_2, dt_k17_monoid_0, s18_fraenkel, t172_partfun1, t33_subset_1, t2_waybel18, t14_lattice2, t31_borsuk_1, t15_ens_1, t159_relat_1, dt_k3_qc_lang1, t10_card_fil, t32_funct_4, fraenkel_a_3_8_domain_1, t6_yellow21, t65_zfmisc_1, t30_partfun1, t80_funct_4, dt_k3_classes2, cc6_tex_2, t63_enumset1, redefinition_k9_funcop_1, t63_subset_1, t112_partfun1, fraenkel_a_4_1_domain_1, t38_xboole_1, t19_funct_4, redefinition_k9_cat_2, t39_xboole_1, redefinition_k8_setwiseo, t43_cqc_lang, t23_funcop_1, d7_binop_2, t20_funct_4, antisymmetry_r2_hidden, t23_relset_1, t15_relset_2, t88_funct_3, d1_mcart_1, dt_k1_setwiseo, t53_setfam_1, fc15_finset_1, t45_funct_4, t88_relat_1, redefinition_k15_domain_1, t26_relat_1, t42_enumset1, t18_mcart_1, t53_relat_1, fc3_binop_2, t21_lattice5, t22_subset_1, redefinition_k6_domain_1
% 60.78/21.27  % No. of inferences in proof: 5184
% 60.78/21.27  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 20746 ms resp. 19339 ms w/o parsing
% 63.22/22.23  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 63.32/22.24  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------