TSTP Solution File: SEU435+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU435+3 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 11:59:07 EDT 2023
% Result : Theorem 59.08s 20.23s
% Output : Refutation 61.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2900
% Syntax : Number of formulae : 5294 ( 437 unt; 508 typ; 0 def)
% Number of atoms : 26579 (4670 equ; 0 cnn)
% Maximal formula atoms : 47 ( 5 avg)
% Number of connectives : 100397 (3554 ~; 215 |;10779 &;75050 @)
% ( 428 <=>;10371 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1079 (1079 >; 0 *; 0 +; 0 <<)
% Number of symbols : 510 ( 508 usr; 112 con; 0-10 aty)
% Number of variables : 16081 ( 0 ^;15294 !; 787 ?;16081 :)
% Comments :
%------------------------------------------------------------------------------
thf(m1_subset_1_type,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_type,type,
k1_zfmisc_1: $i > $i ).
thf(k2_zfmisc_1_type,type,
k2_zfmisc_1: $i > $i > $i ).
thf(a_6_0_relset_2_type,type,
a_6_0_relset_2: $i > $i > $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_xboole_0_type,type,
v1_xboole_0: $i > $o ).
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(m2_relset_1_type,type,
m2_relset_1: $i > $i > $i > $o ).
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(k1_numbers_type,type,
k1_numbers: $i ).
thf(k9_binop_2_type,type,
k9_binop_2: $i > $i > $i ).
thf(v1_finset_1_type,type,
v1_finset_1: $i > $o ).
thf(m2_finseq_1_type,type,
m2_finseq_1: $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(k9_funct_7_type,type,
k9_funct_7: $i > $i > $i ).
thf(v1_relat_1_type,type,
v1_relat_1: $i > $o ).
thf(k7_relat_1_type,type,
k7_relat_1: $i > $i > $i ).
thf(m2_pua2mss1_type,type,
m2_pua2mss1: $i > $i > $o ).
thf(k3_funct_5_type,type,
k3_funct_5: $i > $i ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k3_partfun1_type,type,
k3_partfun1: $i > $i > $i > $i ).
thf(r1_tarski_type,type,
r1_tarski: $i > $i > $o ).
thf(k1_relat_1_type,type,
k1_relat_1: $i > $i ).
thf(r2_wellord2_type,type,
r2_wellord2: $i > $i > $o ).
thf(v2_relat_1_type,type,
v2_relat_1: $i > $o ).
thf(m1_pboole_type,type,
m1_pboole: $i > $i > $o ).
thf(k4_card_3_type,type,
k4_card_3: $i > $i ).
thf(v1_fraenkel_type,type,
v1_fraenkel: $i > $o ).
thf(r2_hidden_type,type,
r2_hidden: $i > $i > $o ).
thf(k1_setfam_1_type,type,
k1_setfam_1: $i > $i ).
thf(k4_relset_1_type,type,
k4_relset_1: $i > $i > $i > $i ).
thf(k2_relat_1_type,type,
k2_relat_1: $i > $i ).
thf(k3_xboole_0_type,type,
k3_xboole_0: $i > $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(k1_xboole_0_type,type,
k1_xboole_0: $i ).
thf(k6_relat_1_type,type,
k6_relat_1: $i > $i ).
thf(k5_funct_5_type,type,
k5_funct_5: $i > $i ).
thf(m3_pboole_type,type,
m3_pboole: $i > $i > $i > $i > $o ).
thf(k1_funct_1_type,type,
k1_funct_1: $i > $i > $i ).
thf(m1_card_fil_type,type,
m1_card_fil: $i > $i > $o ).
thf(k2_card_fil_type,type,
k2_card_fil: $i > $i > $i ).
thf(k7_setfam_1_type,type,
k7_setfam_1: $i > $i > $i ).
thf(r1_xboole_0_type,type,
r1_xboole_0: $i > $i > $o ).
thf(k1_setwiseo_type,type,
k1_setwiseo: $i > $i ).
thf(v2_membered_type,type,
v2_membered: $i > $o ).
thf(v1_membered_type,type,
v1_membered: $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(v1_binop_1_type,type,
v1_binop_1: $i > $i > $o ).
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(k2_tarski_type,type,
k2_tarski: $i > $i > $i ).
thf(k11_binop_2_type,type,
k11_binop_2: $i > $i > $i ).
thf(k5_funcop_1_type,type,
k5_funcop_1: $i > $i > $i > $i ).
thf(k7_pboole_type,type,
k7_pboole: $i > $i > $i > $i > $i ).
thf(v1_finseq_1_type,type,
v1_finseq_1: $i > $o ).
thf(k3_finseq_1_type,type,
k3_finseq_1: $i > $i ).
thf(k10_binop_2_type,type,
k10_binop_2: $i > $i > $i ).
thf(k1_tarski_type,type,
k1_tarski: $i > $i ).
thf(k1_funct_2_type,type,
k1_funct_2: $i > $i > $i ).
thf(m2_fraenkel_type,type,
m2_fraenkel: $i > $i > $i > $i > $o ).
thf(k1_fraenkel_type,type,
k1_fraenkel: $i > $i > $i ).
thf(m1_fraenkel_type,type,
m1_fraenkel: $i > $i > $i > $o ).
thf(k3_funcop_1_type,type,
k3_funcop_1: $i > $i > $i > $i ).
thf(k2_finseq_1_type,type,
k2_finseq_1: $i > $i ).
thf(k6_subset_1_type,type,
k6_subset_1: $i > $i > $i > $i ).
thf(k10_setwiseo_type,type,
k10_setwiseo: $i > $i > $i > $i > $i ).
thf(v2_funct_1_type,type,
v2_funct_1: $i > $o ).
thf(k3_funct_3_type,type,
k3_funct_3: $i > $i ).
thf(k5_relat_1_type,type,
k5_relat_1: $i > $i > $i ).
thf(k10_relat_1_type,type,
k10_relat_1: $i > $i > $i ).
thf(k2_funct_1_type,type,
k2_funct_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(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(v1_classes2_type,type,
v1_classes2: $i > $o ).
thf(k3_mcart_1_type,type,
k3_mcart_1: $i > $i > $i > $i ).
thf(k4_mcart_1_type,type,
k4_mcart_1: $i > $i > $i > $i > $i ).
thf(k3_pua2mss1_type,type,
k3_pua2mss1: $i > $i ).
thf(k4_finseq_1_type,type,
k4_finseq_1: $i > $i ).
thf(k10_funct_6_type,type,
k10_funct_6: $i > $i ).
thf(m1_relset_1_type,type,
m1_relset_1: $i > $i > $i > $o ).
thf(k1_cat_2_type,type,
k1_cat_2: $i > $i > $i > $i > $i > $i > $i ).
thf(r1_partfun1_type,type,
r1_partfun1: $i > $i > $o ).
thf(k1_funct_4_type,type,
k1_funct_4: $i > $i > $i ).
thf(m1_orders_1_type,type,
m1_orders_1: $i > $i > $o ).
thf(k3_tarski_type,type,
k3_tarski: $i > $i ).
thf(v1_realset1_type,type,
v1_realset1: $i > $o ).
thf(k3_pralg_3_type,type,
k3_pralg_3: $i > $i > $i ).
thf(m1_eqrel_1_type,type,
m1_eqrel_1: $i > $i > $o ).
thf(k1_partfun1_type,type,
k1_partfun1: $i > $i > $i > $i > $i > $i > $i ).
thf(k8_relat_1_type,type,
k8_relat_1: $i > $i > $i ).
thf(k7_funct_2_type,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(k4_tarski_type,type,
k4_tarski: $i > $i > $i ).
thf(k2_funct_4_type,type,
k2_funct_4: $i > $i ).
thf(k7_funct_6_type,type,
k7_funct_6: $i > $i ).
thf(k3_urysohn1_type,type,
k3_urysohn1: $i > $i ).
thf(k2_funcop_1_type,type,
k2_funcop_1: $i > $i > $i ).
thf(k2_funct_5_type,type,
k2_funct_5: $i > $i ).
thf(v3_binop_1_type,type,
v3_binop_1: $i > $i > $o ).
thf(m2_card_fil_type,type,
m2_card_fil: $i > $i > $o ).
thf(k15_funct_3_type,type,
k15_funct_3: $i > $i > $i ).
thf(k6_setfam_1_type,type,
k6_setfam_1: $i > $i > $i ).
thf(k2_cat_2_type,type,
k2_cat_2: $i > $i > $i > $i > $i ).
thf(k1_card_fil_type,type,
k1_card_fil: $i > $i > $i ).
thf(k5_partfun1_type,type,
k5_partfun1: $i > $i > $i > $i ).
thf(k3_setfam_1_type,type,
k3_setfam_1: $i > $i > $i ).
thf(k4_funcop_1_type,type,
k4_funcop_1: $i > $i > $i > $i ).
thf(k1_funct_3_type,type,
k1_funct_3: $i > $i ).
thf(k2_funcsdom_type,type,
k2_funcsdom: $i > $i > $i > $i > $i > $i > $i ).
thf(v1_setfam_1_type,type,
v1_setfam_1: $i > $o ).
thf(k1_domain_1_type,type,
k1_domain_1: $i > $i > $i > $i > $i ).
thf(k2_partfun1_type,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(a_2_1_pua2mss1_type,type,
a_2_1_pua2mss1: $i > $i > $i ).
thf(k6_partfun1_type,type,
k6_partfun1: $i > $i ).
thf(k7_ens_1_type,type,
k7_ens_1: $i > $i > $i > $i ).
thf(a_3_0_ens_1_type,type,
a_3_0_ens_1: $i > $i > $i > $i ).
thf(k3_cat_2_type,type,
k3_cat_2: $i > $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(k9_setwiseo_type,type,
k9_setwiseo: $i > $i ).
thf(k3_card_fil_type,type,
k3_card_fil: $i > $i > $i > $i ).
thf(k3_funcsdom_type,type,
k3_funcsdom: $i > $i > $i > $i ).
thf(v6_ordinal1_type,type,
v6_ordinal1: $i > $o ).
thf(k19_pralg_1_type,type,
k19_pralg_1: $i > $i > $i > $i ).
thf(k12_binop_2_type,type,
k12_binop_2: $i > $i > $i ).
thf(k1_orders_1_type,type,
k1_orders_1: $i > $i ).
thf(k1_isocat_2_type,type,
k1_isocat_2: $i > $i > $i > $i > $i ).
thf(k16_funct_3_type,type,
k16_funct_3: $i > $i > $i > $i > $i > $i > $i ).
thf(k1_funct_5_type,type,
k1_funct_5: $i > $i ).
thf(k3_subset_1_type,type,
k3_subset_1: $i > $i > $i ).
thf(r4_nattra_1_type,type,
r4_nattra_1: $i > $i > $i > $i > $i > $i > $o ).
thf(k2_funct_2_type,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(k1_enumset1_type,type,
k1_enumset1: $i > $i > $i > $i ).
thf(k6_domain_1_type,type,
k6_domain_1: $i > $i > $i ).
thf(k5_relset_1_type,type,
k5_relset_1: $i > $i > $i > $i ).
thf(k13_funct_3_type,type,
k13_funct_3: $i > $i > $i ).
thf(r5_binop_1_type,type,
r5_binop_1: $i > $i > $i > $o ).
thf(k7_filter_1_type,type,
k7_filter_1: $i > $i > $i > $i > $i ).
thf(k4_zfmisc_1_type,type,
k4_zfmisc_1: $i > $i > $i > $i > $i ).
thf(k3_zfmisc_1_type,type,
k3_zfmisc_1: $i > $i > $i > $i ).
thf(r2_binop_1_type,type,
r2_binop_1: $i > $i > $i > $o ).
thf(m1_nat_lat_type,type,
m1_nat_lat: $i > $i > $i > $i > $o ).
thf(k5_enumset1_type,type,
k5_enumset1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k4_enumset1_type,type,
k4_enumset1: $i > $i > $i > $i > $i > $i > $i ).
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(r6_binop_1_type,type,
r6_binop_1: $i > $i > $i > $o ).
thf(r4_binop_1_type,type,
r4_binop_1: $i > $i > $i > $o ).
thf(k3_enumset1_type,type,
k3_enumset1: $i > $i > $i > $i > $i > $i ).
thf(k6_enumset1_type,type,
k6_enumset1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k3_setwiseo_type,type,
k3_setwiseo: $i > $i > $i > $i ).
thf(k3_relset_2_type,type,
k3_relset_2: $i > $i > $i > $i > $i ).
thf(k11_relset_1_type,type,
k11_relset_1: $i > $i > $i > $i > $i ).
thf(k1_relset_2_type,type,
k1_relset_2: $i > $i > $i > $i ).
thf(k18_pralg_1_type,type,
k18_pralg_1: $i > $i > $i > $i ).
thf(k3_funct_2_type,type,
k3_funct_2: $i > $i > $i > $i > $i ).
thf(k5_relset_2_type,type,
k5_relset_2: $i > $i > $i ).
thf(k3_funct_4_type,type,
k3_funct_4: $i > $i > $i ).
thf(k6_pralg_1_type,type,
k6_pralg_1: $i > $i > $i ).
thf(k8_setwiseo_type,type,
k8_setwiseo: $i > $i > $i > $i > $i ).
thf(k8_binop_2_type,type,
k8_binop_2: $i > $i ).
thf(r6_pboole_type,type,
r6_pboole: $i > $i > $i > $o ).
thf(k6_funcop_1_type,type,
k6_funcop_1: $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(k4_domain_1_type,type,
k4_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k18_group_2_type,type,
k18_group_2: $i > $i > $i ).
thf(k2_mcart_1_type,type,
k2_mcart_1: $i > $i ).
thf(k2_borsuk_1_type,type,
k2_borsuk_1: $i > $i > $i ).
thf(k12_mcart_1_type,type,
k12_mcart_1: $i > $i > $i > $i > $i ).
thf(k9_funct_3_type,type,
k9_funct_3: $i > $i > $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(k4_setwiseo_type,type,
k4_setwiseo: $i > $i > $i > $i > $i ).
thf(k2_ens_1_type,type,
k2_ens_1: $i > $i ).
thf(k12_funct_3_type,type,
k12_funct_3: $i > $i ).
thf(v2_setfam_1_type,type,
v2_setfam_1: $i > $o ).
thf(k10_relset_1_type,type,
k10_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(k4_funct_2_type,type,
k4_funct_2: $i > $i > $i > $i ).
thf(k1_realset1_type,type,
k1_realset1: $i > $i > $i ).
thf(m1_realset1_type,type,
m1_realset1: $i > $i > $i > $o ).
thf(r1_filter_2_type,type,
r1_filter_2: $i > $i > $i > $o ).
thf(a_3_1_pua2mss1_type,type,
a_3_1_pua2mss1: $i > $i > $i > $i ).
thf(r2_wellord1_type,type,
r2_wellord1: $i > $i > $o ).
thf(k36_binop_2_type,type,
k36_binop_2: $i ).
thf(k13_pboole_type,type,
k13_pboole: $i > $i > $i ).
thf(k2_yellow_3_type,type,
k2_yellow_3: $i > $i > $i > $i > $i > $i > $i ).
thf(k1_yellow_3_type,type,
k1_yellow_3: $i > $i > $i ).
thf(k7_funcop_1_type,type,
k7_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k1_binop_1_type,type,
k1_binop_1: $i > $i > $i > $i ).
thf(m1_filter_1_type,type,
m1_filter_1: $i > $i > $i > $o ).
thf(k1_metric_1_type,type,
k1_metric_1: $i > $i > $i > $i > $i > $i ).
thf(k7_metric_1_type,type,
k7_metric_1: $i ).
thf(a_2_0_lattice5_type,type,
a_2_0_lattice5: $i > $i > $i ).
thf(k8_funcop_1_type,type,
k8_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k9_cat_2_type,type,
k9_cat_2: $i > $i > $i > $i > $i > $i > $i ).
thf(k4_qc_lang1_type,type,
k4_qc_lang1: $i ).
thf(k1_qc_lang1_type,type,
k1_qc_lang1: $i ).
thf(k8_eqrel_1_type,type,
k8_eqrel_1: $i > $i > $i ).
thf(k9_funcop_1_type,type,
k9_funcop_1: $i > $i > $i > $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(k11_setwiseo_type,type,
k11_setwiseo: $i > $i ).
thf(k14_funct_3_type,type,
k14_funct_3: $i > $i > $i > $i > $i > $i ).
thf(k7_binop_2_type,type,
k7_binop_2: $i > $i ).
thf(k5_subset_1_type,type,
k5_subset_1: $i > $i > $i > $i ).
thf(r1_zfrefle1_type,type,
r1_zfrefle1: $i > $i > $o ).
thf(k1_subset_1_type,type,
k1_subset_1: $i > $i ).
thf(k9_zf_lang_type,type,
k9_zf_lang: $i ).
thf(k2_cantor_1_type,type,
k2_cantor_1: $i > $i > $i ).
thf(k1_cantor_1_type,type,
k1_cantor_1: $i > $i > $i ).
thf(v1_tex_2_type,type,
v1_tex_2: $i > $i > $o ).
thf(r1_binop_1_type,type,
r1_binop_1: $i > $i > $i > $o ).
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(r7_relat_2_type,type,
r7_relat_2: $i > $i > $o ).
thf(k2_subset_1_type,type,
k2_subset_1: $i > $i ).
thf(k2_relset_2_type,type,
k2_relset_2: $i > $i > $i > $i > $i ).
thf(k1_ens_1_type,type,
k1_ens_1: $i > $i ).
thf(k3_cantor_1_type,type,
k3_cantor_1: $i > $i > $i > $i > $i > $i ).
thf(v4_finsub_1_type,type,
v4_finsub_1: $i > $o ).
thf(k33_binop_2_type,type,
k33_binop_2: $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(a_8_0_domain_1_type,type,
a_8_0_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k35_binop_2_type,type,
k35_binop_2: $i ).
thf(k2_altcat_1_type,type,
k2_altcat_1: $i > $i > $i ).
thf(k2_functor0_type,type,
k2_functor0: $i > $i > $i > $i > $i > $i > $i ).
thf(k17_mcart_1_type,type,
k17_mcart_1: $i > $i ).
thf(k18_mcart_1_type,type,
k18_mcart_1: $i > $i ).
thf(k19_mcart_1_type,type,
k19_mcart_1: $i > $i ).
thf(k10_funcop_1_type,type,
k10_funcop_1: $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(r1_lattice2_type,type,
r1_lattice2: $i > $i > $i > $o ).
thf(k1_nattra_1_type,type,
k1_nattra_1: $i > $i > $i > $i > $i ).
thf(m3_realset1_type,type,
m3_realset1: $i > $i > $i > $o ).
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(k4_card_fil_type,type,
k4_card_fil: $i > $i ).
thf(k1_eqrel_1_type,type,
k1_eqrel_1: $i > $i ).
thf(r7_binop_1_type,type,
r7_binop_1: $i > $i > $i > $o ).
thf(v1_yellow18_type,type,
v1_yellow18: $i > $i > $i > $i > $o ).
thf(k34_binop_2_type,type,
k34_binop_2: $i ).
thf(k8_setfam_1_type,type,
k8_setfam_1: $i > $i > $i ).
thf(v7_altcat_1_type,type,
v7_altcat_1: $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(k5_funcsdom_type,type,
k5_funcsdom: $i > $i > $i > $i > $i > $i ).
thf(m2_filter_1_type,type,
m2_filter_1: $i > $i > $i > $o ).
thf(k1_funcsdom_type,type,
k1_funcsdom: $i > $i > $i > $i > $i > $i ).
thf(k3_altcat_1_type,type,
k3_altcat_1: $i > $i > $i > $i ).
thf(a_4_0_relset_2_type,type,
a_4_0_relset_2: $i > $i > $i > $i > $i ).
thf(k2_funct_3_type,type,
k2_funct_3: $i > $i > $i > $i ).
thf(k3_metric_1_type,type,
k3_metric_1: $i ).
thf(a_3_8_domain_1_type,type,
a_3_8_domain_1: $i > $i > $i > $i ).
thf(p1_s3_domain_1_type,type,
p1_s3_domain_1: $i > $i > $i > $o ).
thf(a_1_0_domain_1_type,type,
a_1_0_domain_1: $i > $i ).
thf(k1_borsuk_1_type,type,
k1_borsuk_1: $i > $i > $i > $i ).
thf(k1_funct_7_type,type,
k1_funct_7: $i > $i > $i ).
thf(k4_subset_1_type,type,
k4_subset_1: $i > $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(r5_relat_2_type,type,
r5_relat_2: $i > $i > $o ).
thf(g1_group_1_type,type,
g1_group_1: $i > $i > $i ).
thf(r4_waybel_4_type,type,
r4_waybel_4: $i > $i > $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(g3_lattices_type,type,
g3_lattices: $i > $i > $i > $i ).
thf(k11_domain_1_type,type,
k11_domain_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k13_mcart_1_type,type,
k13_mcart_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k7_subset_1_type,type,
k7_subset_1: $i > $i > $i > $i ).
thf(a_3_6_domain_1_type,type,
a_3_6_domain_1: $i > $i > $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(a_4_2_relset_2_type,type,
a_4_2_relset_2: $i > $i > $i > $i > $i ).
thf(k8_relset_2_type,type,
k8_relset_2: $i > $i > $i > $i > $i ).
thf(r1_realset1_type,type,
r1_realset1: $i > $i > $i > $o ).
thf(a_2_1_domain_1_type,type,
a_2_1_domain_1: $i > $i > $i ).
thf(k2_qc_lang1_type,type,
k2_qc_lang1: $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(a_0_0_altcat_2_type,type,
a_0_0_altcat_2: $i ).
thf(g1_cat_1_type,type,
g1_cat_1: $i > $i > $i > $i > $i > $i > $i ).
thf(r2_relat_2_type,type,
r2_relat_2: $i > $i > $o ).
thf(g1_lattices_type,type,
g1_lattices: $i > $i > $i ).
thf(k4_relset_2_type,type,
k4_relset_2: $i > $i > $i > $i > $i ).
thf(k6_relset_2_type,type,
k6_relset_2: $i > $i > $i > $i ).
thf(m1_triang_1_type,type,
m1_triang_1: $i > $i > $i > $o ).
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(a_4_1_relset_2_type,type,
a_4_1_relset_2: $i > $i > $i > $i > $i ).
thf(a_4_1_yellow_9_type,type,
a_4_1_yellow_9: $i > $i > $i > $i > $i ).
thf(k6_funct_3_type,type,
k6_funct_3: $i > $i > $i ).
thf(k2_multop_1_type,type,
k2_multop_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k5_trees_3_type,type,
k5_trees_3: $i > $i ).
thf(a_2_0_card_fil_type,type,
a_2_0_card_fil: $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(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(a_3_5_domain_1_type,type,
a_3_5_domain_1: $i > $i > $i > $i ).
thf(k3_qc_lang1_type,type,
k3_qc_lang1: $i ).
thf(a_4_3_relset_2_type,type,
a_4_3_relset_2: $i > $i > $i > $i > $i ).
thf(g3_quantal1_type,type,
g3_quantal1: $i > $i > $i > $i > $i > $i > $i ).
thf(a_3_2_domain_1_type,type,
a_3_2_domain_1: $i > $i > $i > $i ).
thf(k5_urysohn1_type,type,
k5_urysohn1: $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(k31_binop_2_type,type,
k31_binop_2: $i ).
thf(g1_vectsp_1_type,type,
g1_vectsp_1: $i > $i > $i > $i ).
thf(k8_domain_1_type,type,
k8_domain_1: $i > $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(a_0_32_fraenkel_type,type,
a_0_32_fraenkel: $i ).
thf(f2_s17_fraenkel_type,type,
f2_s17_fraenkel: $i ).
thf(k1_pcomps_1_type,type,
k1_pcomps_1: $i > $i ).
thf(k2_monoid_0_type,type,
k2_monoid_0: $i > $i > $i > $i ).
thf(k14_borsuk_1_type,type,
k14_borsuk_1: $i > $i > $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(a_3_4_domain_1_type,type,
a_3_4_domain_1: $i > $i > $i > $i ).
thf(k14_mcart_1_type,type,
k14_mcart_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(g3_vectsp_1_type,type,
g3_vectsp_1: $i > $i > $i > $i > $i > $i ).
thf(a_4_0_pua2mss1_type,type,
a_4_0_pua2mss1: $i > $i > $i > $i > $i ).
thf(a_3_1_domain_1_type,type,
a_3_1_domain_1: $i > $i > $i > $i ).
thf(k1_cat_5_type,type,
k1_cat_5: $i > $i > $i > $i > $i ).
thf(r3_relat_2_type,type,
r3_relat_2: $i > $i > $o ).
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(a_4_1_domain_1_type,type,
a_4_1_domain_1: $i > $i > $i > $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(k15_domain_1_type,type,
k15_domain_1: $i > $i > $i > $i > $i ).
thf(g1_funcsdom_type,type,
g1_funcsdom: $i > $i > $i > $i > $i > $i > $i ).
thf(k9_domain_1_type,type,
k9_domain_1: $i > $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(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(r2_waybel_4_type,type,
r2_waybel_4: $i > $i > $i > $o ).
thf(a_3_3_domain_1_type,type,
a_3_3_domain_1: $i > $i > $i > $i ).
thf(p1_s1_funct_1_type,type,
p1_s1_funct_1: $i > $i > $o ).
thf(f1_s1_funct_1_type,type,
f1_s1_funct_1: $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(k10_domain_1_type,type,
k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).
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(k14_domain_1_type,type,
k14_domain_1: $i > $i > $i > $i > $i ).
thf(k7_relset_2_type,type,
k7_relset_2: $i > $i > $i > $i > $i ).
thf(a_3_7_domain_1_type,type,
a_3_7_domain_1: $i > $i > $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(m1_cantor_1_type,type,
m1_cantor_1: $i > $i > $o ).
thf(a_2_0_cantor_1_type,type,
a_2_0_cantor_1: $i > $i > $i ).
thf(k4_multop_1_type,type,
k4_multop_1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $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_1_card_fil_type,type,
a_2_1_card_fil: $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(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(a_2_0_relset_2_type,type,
a_2_0_relset_2: $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(k12_domain_1_type,type,
k12_domain_1: $i > $i > $i > $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_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(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_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(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(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(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(k9_relset_2_type,type,
k9_relset_2: $i > $i > $i > $i > $i > $i ).
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(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(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(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_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(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(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_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(f1_s2_altcat_1_type,type,
f1_s2_altcat_1: $i ).
thf(f2_s2_altcat_1_type,type,
f2_s2_altcat_1: $i ).
thf(f3_s2_altcat_1_type,type,
f3_s2_altcat_1: $i > $i > $i ).
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(k2_zfrefle1_type,type,
k2_zfrefle1: $i ).
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(p1_s10_fraenkel_type,type,
p1_s10_fraenkel: $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(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(722,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(5469,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_tarski @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(808,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_tex_2 @ B @ A )
<=> ( B
!= ( k3_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tex_2) ).
thf(5918,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)],[808]) ).
thf(1772,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/sandbox2/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(10577,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)],[1772]) ).
thf(2004,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/sandbox2/benchmark/theBenchmark.p',t35_subset_1) ).
thf(11922,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)],[2004]) ).
thf(688,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/sandbox2/benchmark/theBenchmark.p',t6_multop_1) ).
thf(5320,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)],[688]) ).
thf(1677,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/sandbox2/benchmark/theBenchmark.p',rc2_setwiseo) ).
thf(10134,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)],[1677]) ).
thf(1619,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/sandbox2/benchmark/theBenchmark.p',dt_k1_functor0) ).
thf(9864,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)],[1619]) ).
thf(1440,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k8_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_relat_1) ).
thf(9032,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k8_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440]) ).
thf(1635,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_3_domain_1) ).
thf(9929,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)],[1635]) ).
thf(1234,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/sandbox2/benchmark/theBenchmark.p',t21_finsub_1) ).
thf(8062,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)],[1234]) ).
thf(1096,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/sandbox2/benchmark/theBenchmark.p',commutativity_k3_setwiseo) ).
thf(7304,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)],[1096]) ).
thf(2237,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/sandbox2/benchmark/theBenchmark.p',t95_funct_3) ).
thf(13052,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)],[2237]) ).
thf(2292,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/sandbox2/benchmark/theBenchmark.p',t15_yellow_9) ).
thf(13266,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)],[2292]) ).
thf(442,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/sandbox2/benchmark/theBenchmark.p',fc8_finset_1) ).
thf(4188,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)],[442]) ).
thf(1109,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/sandbox2/benchmark/theBenchmark.p',t8_funct_3) ).
thf(7373,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)],[1109]) ).
thf(448,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/sandbox2/benchmark/theBenchmark.p',d2_relset_2) ).
thf(4201,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)],[448]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',t163_relat_1) ).
thf(2452,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)],[19]) ).
thf(1774,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/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(10609,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)],[1774]) ).
thf(2305,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/sandbox2/benchmark/theBenchmark.p',dt_k3_pre_circ) ).
thf(13321,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)],[2305]) ).
thf(908,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/sandbox2/benchmark/theBenchmark.p',t43_funct_1) ).
thf(6387,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)],[908]) ).
thf(1257,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/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(8186,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)],[1257]) ).
thf(643,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( B
= ( k8_relat_1 @ A @ C ) )
<=> ( ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
<=> ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ A ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_1) ).
thf(5116,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( B
= ( k8_relat_1 @ A @ C ) )
=> ( ! [D: $i] :
( ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ A ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ A ) )
=> ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) )
& ( ( ! [D: $i] :
( ( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ A ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ A ) )
=> ( r2_hidden @ D @ ( k1_relat_1 @ B ) ) ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) )
=> ( B
= ( k8_relat_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(1731,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_trees_3 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_pre_circ) ).
thf(10410,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)],[1731]) ).
thf(914,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 )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k1_tarski @ A ) ) @ ( k1_relat_1 @ D ) )
& ( C
= ( k4_funcop_1 @ D @ B @ A ) ) )
=> ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_finseq_2) ).
thf(6405,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 )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k2_relat_1 @ B ) @ ( k1_tarski @ A ) ) @ ( k1_relat_1 @ D ) )
& ( C
= ( k4_funcop_1 @ D @ B @ A ) ) )
=> ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k1_funct_2 @ A @ ( k1_funct_2 @ B @ C ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( r2_hidden @ ( k10_funct_6 @ D ) @ ( k1_funct_2 @ B @ ( k1_funct_2 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_6) ).
thf(2744,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k1_funct_2 @ A @ ( k1_funct_2 @ B @ C ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( r2_hidden @ ( k10_funct_6 @ D ) @ ( k1_funct_2 @ B @ ( k1_funct_2 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(2160,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 ) )
=> ( ( r4_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 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_binop_1) ).
thf(12710,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 ) )
=> ( ( ( r4_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 ) ) ) ) ) ) )
& ( ! [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 ) ) ) ) ) )
=> ( r4_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2160]) ).
thf(2136,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_card_fil) ).
thf(12607,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)],[2136]) ).
thf(1700,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/sandbox2/benchmark/theBenchmark.p',t47_subset_1) ).
thf(10259,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)],[1700]) ).
thf(1721,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/sandbox2/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(10373,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)],[1721]) ).
thf(1200,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/sandbox2/benchmark/theBenchmark.p',t130_funct_2) ).
thf(7890,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)],[1200]) ).
thf(1579,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/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(9653,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)],[1579]) ).
thf(1624,axiom,
! [A: $i] :
( ( ( k1_funct_5 @ A )
= k1_xboole_0 )
<=> ( ( k2_funct_5 @ A )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_5) ).
thf(9886,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)],[1624]) ).
thf(516,axiom,
( ( k4_card_3 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_card_3) ).
thf(4571,plain,
( ( k4_card_3 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(164,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 @ B @ ( k1_relat_1 @ ( k5_funct_5 @ C ) ) )
& ( v1_relat_1 @ ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_funct_5) ).
thf(3053,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 @ B @ ( k1_relat_1 @ ( k5_funct_5 @ C ) ) )
& ( v1_relat_1 @ ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(2162,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/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(12721,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)],[2162]) ).
thf(1688,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/sandbox2/benchmark/theBenchmark.p',t49_mcart_1) ).
thf(10177,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)],[1688]) ).
thf(802,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/sandbox2/benchmark/theBenchmark.p',fc2_realset1) ).
thf(5896,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)],[802]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k4_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(2778,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)],[99]) ).
thf(2329,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( m1_subset_1 @ ( a_1_2_domain_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_domain_1) ).
thf(13402,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)],[2329]) ).
thf(1999,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/sandbox2/benchmark/theBenchmark.p',dt_k14_borsuk_1) ).
thf(11895,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)],[1999]) ).
thf(1124,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t171_relat_1) ).
thf(7445,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(264,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/sandbox2/benchmark/theBenchmark.p',t31_funct_2) ).
thf(3434,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)],[264]) ).
thf(1208,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v4_finsub_1 @ A ) )
=> ( r2_hidden @ k1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finsub_1) ).
thf(7922,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)],[1208]) ).
thf(1326,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/sandbox2/benchmark/theBenchmark.p',t10_realset1) ).
thf(8514,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)],[1326]) ).
thf(440,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/sandbox2/benchmark/theBenchmark.p',t147_relat_1) ).
thf(4183,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)],[440]) ).
thf(1798,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ k1_numbers ) )
=> ( ( v1_membered @ A )
& ( v2_membered @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_membered) ).
thf(10730,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)],[1798]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= k1_xboole_0 )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(3698,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)],[328]) ).
thf(1875,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_lattice5) ).
thf(11164,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)],[1875]) ).
thf(1595,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ ( k9_relat_1 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_funct_1) ).
thf(9731,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ ( k9_relat_1 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1595]) ).
thf(581,axiom,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(4852,plain,
! [A: $i] : ( r1_xboole_0 @ A @ k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(1385,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/sandbox2/benchmark/theBenchmark.p',t17_relset_2) ).
thf(8784,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)],[1385]) ).
thf(1585,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/sandbox2/benchmark/theBenchmark.p',t152_relat_1) ).
thf(9685,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)],[1585]) ).
thf(1974,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/sandbox2/benchmark/theBenchmark.p',t48_funcop_1) ).
thf(11752,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)],[1974]) ).
thf(751,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/sandbox2/benchmark/theBenchmark.p',t2_nattra_1) ).
thf(5676,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)],[751]) ).
thf(42,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( m2_subset_1 @ ( k3_finseq_1 @ A ) @ k1_numbers @ k5_numbers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_finseq_1) ).
thf(2595,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ( m2_subset_1 @ ( k3_finseq_1 @ A ) @ k1_numbers @ k5_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(32,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/sandbox2/benchmark/theBenchmark.p',t81_xboole_1) ).
thf(2499,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)],[32]) ).
thf(2047,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_waybel_4 @ A @ B @ C )
<=> ( ( r2_hidden @ B @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( D != B )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d24_waybel_4) ).
thf(12148,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_waybel_4 @ A @ B @ C )
=> ( ( r2_hidden @ B @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( D != B )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ C ) ) ) )
& ( ( ( r2_hidden @ B @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( D != B )
& ( r2_hidden @ ( k4_tarski @ B @ D ) @ C ) ) )
=> ( r2_waybel_4 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2047]) ).
thf(1450,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/sandbox2/benchmark/theBenchmark.p',t89_relat_1) ).
thf(9076,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)],[1450]) ).
thf(1273,axiom,
( ( v1_relat_1 @ k1_xboole_0 )
& ( v1_funct_1 @ k1_xboole_0 )
& ( v1_finseq_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_finseq_1) ).
thf(8266,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)],[1273]) ).
thf(659,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/sandbox2/benchmark/theBenchmark.p',t20_ens_1) ).
thf(5205,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)],[659]) ).
thf(1663,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ ( k10_relat_1 @ C @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_borsuk_1) ).
thf(10081,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ ( k10_relat_1 @ C @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663]) ).
thf(988,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/sandbox2/benchmark/theBenchmark.p',t47_funct_4) ).
thf(6819,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)],[988]) ).
thf(848,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k1_relat_1 @ A ) )
& ( v1_relat_1 @ ( k1_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(6121,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)],[848]) ).
thf(267,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(3449,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(2090,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_eqrel_1) ).
thf(12383,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)],[2090]) ).
thf(951,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/sandbox2/benchmark/theBenchmark.p',t175_partfun1) ).
thf(6555,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)],[951]) ).
thf(1713,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/sandbox2/benchmark/theBenchmark.p',t16_domain_1) ).
thf(10319,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)],[1713]) ).
thf(767,axiom,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_zfmisc_1) ).
thf(5733,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)],[767]) ).
thf(1645,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/sandbox2/benchmark/theBenchmark.p',dt_k1_metric_1) ).
thf(9965,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)],[1645]) ).
thf(1091,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/sandbox2/benchmark/theBenchmark.p',t2_mcart_1) ).
thf(7285,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)],[1091]) ).
thf(1115,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/sandbox2/benchmark/theBenchmark.p',t10_borsuk_1) ).
thf(7396,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)],[1115]) ).
thf(1830,axiom,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(10901,plain,
? [A: $i] :
( ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1830]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relset_2 @ B @ D ) ) )
=> ( ( k1_funct_1 @ ( k5_relset_2 @ B @ D ) @ A )
= ( k9_relat_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_relset_2) ).
thf(4376,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_relset_2 @ B @ D ) ) )
=> ( ( k1_funct_1 @ ( k5_relset_2 @ B @ D ) @ A )
= ( k9_relat_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(51,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D )
& ( v1_finseq_1 @ D ) )
=> ! [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 )
=> ! [G: $i] :
( ( m2_finseq_1 @ G @ B )
=> ( ( ( ( k3_finseq_1 @ F )
= ( k3_finseq_1 @ G ) )
& ( D
= ( k3_funcop_1 @ E @ F @ G ) ) )
=> ( ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ F ) )
& ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_finseq_2) ).
thf(2622,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ~ ( v1_xboole_0 @ C )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D )
& ( v1_finseq_1 @ D ) )
=> ! [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 )
=> ! [G: $i] :
( ( m2_finseq_1 @ G @ B )
=> ( ( ( ( k3_finseq_1 @ F )
= ( k3_finseq_1 @ G ) )
& ( D
= ( k3_funcop_1 @ E @ F @ G ) ) )
=> ( ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ F ) )
& ( ( k3_finseq_1 @ D )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(1214,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/sandbox2/benchmark/theBenchmark.p',t68_xboole_1) ).
thf(7958,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)],[1214]) ).
thf(1589,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( E
= ( a_4_2_relset_2 @ A @ B @ C @ D ) )
=> ( ( k8_relset_2 @ A @ B @ ( k5_setfam_1 @ A @ D ) @ C )
= ( k8_setfam_1 @ B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_relset_2) ).
thf(9704,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( m2_relset_1 @ C @ A @ B )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) )
=> ( ( E
= ( a_4_2_relset_2 @ A @ B @ C @ D ) )
=> ( ( k8_relset_2 @ A @ B @ ( k5_setfam_1 @ A @ D ) @ C )
= ( k8_setfam_1 @ B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1589]) ).
thf(748,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/sandbox2/benchmark/theBenchmark.p',t12_funct_4) ).
thf(5669,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)],[748]) ).
thf(1657,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/sandbox2/benchmark/theBenchmark.p',t2_funct_1) ).
thf(10039,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)],[1657]) ).
thf(1297,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/sandbox2/benchmark/theBenchmark.p',t75_funct_2) ).
thf(8366,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)],[1297]) ).
thf(868,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( k1_fraenkel @ A @ B )
= ( k1_funct_2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_fraenkel) ).
thf(6214,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( k1_fraenkel @ A @ B )
= ( k1_funct_2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(1843,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/sandbox2/benchmark/theBenchmark.p',t159_relat_1) ).
thf(11008,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)],[1843]) ).
thf(1820,axiom,
? [A: $i] : ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(10844,plain,
? [A: $i] : ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1820]) ).
thf(854,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/sandbox2/benchmark/theBenchmark.p',d2_multop_1) ).
thf(6142,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)],[854]) ).
thf(1507,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/sandbox2/benchmark/theBenchmark.p',t6_pua2mss1) ).
thf(9342,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)],[1507]) ).
thf(2112,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/sandbox2/benchmark/theBenchmark.p',t16_setwiseo) ).
thf(12458,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)],[2112]) ).
thf(201,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/sandbox2/benchmark/theBenchmark.p',t25_funct_4) ).
thf(3185,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)],[201]) ).
thf(2133,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_cantor_1) ).
thf(12575,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)],[2133]) ).
thf(1910,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/sandbox2/benchmark/theBenchmark.p',t1_mssubfam) ).
thf(11352,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)],[1910]) ).
thf(2151,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/sandbox2/benchmark/theBenchmark.p',t64_funct_4) ).
thf(12674,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)],[2151]) ).
thf(1710,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/sandbox2/benchmark/theBenchmark.p',t51_funct_4) ).
thf(10299,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)],[1710]) ).
thf(1562,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r4_waybel_4 @ A @ B @ C )
<=> ( ( r2_hidden @ B @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( D != B )
& ( r2_hidden @ ( k4_tarski @ D @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d26_waybel_4) ).
thf(9573,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r4_waybel_4 @ A @ B @ C )
=> ( ( r2_hidden @ B @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( D != B )
& ( r2_hidden @ ( k4_tarski @ D @ B ) @ C ) ) ) )
& ( ( ( r2_hidden @ B @ A )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ A )
& ( D != B )
& ( r2_hidden @ ( k4_tarski @ D @ B ) @ C ) ) )
=> ( r4_waybel_4 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562]) ).
thf(2286,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/sandbox2/benchmark/theBenchmark.p',s1_yellow_3) ).
thf(13244,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)],[2286]) ).
thf(1106,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/sandbox2/benchmark/theBenchmark.p',t17_funct_2) ).
thf(7358,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)],[1106]) ).
thf(500,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/sandbox2/benchmark/theBenchmark.p',fc3_setfam_1) ).
thf(4500,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)],[500]) ).
thf(2358,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/sandbox2/benchmark/theBenchmark.p',s2_filter_1) ).
thf(13520,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)],[2358]) ).
thf(1738,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/sandbox2/benchmark/theBenchmark.p',rc3_triang_1) ).
thf(10431,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)],[1738]) ).
thf(472,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/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(4339,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)],[472]) ).
thf(2252,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/sandbox2/benchmark/theBenchmark.p',t69_setwiseo) ).
thf(13110,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)],[2252]) ).
thf(996,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/sandbox2/benchmark/theBenchmark.p',t3_altcat_2) ).
thf(6868,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)],[996]) ).
thf(757,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/sandbox2/benchmark/theBenchmark.p',t71_setwiseo) ).
thf(5696,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)],[757]) ).
thf(1390,axiom,
! [A: $i] :
( ( k2_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_subset_1) ).
thf(8797,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k1_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) )
= ( k3_partfun1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_partfun1) ).
thf(3762,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( ( k2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) )
= ( k3_partfun1 @ ( k2_funct_1 @ C ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(2149,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/sandbox2/benchmark/theBenchmark.p',t5_ens_1) ).
thf(12666,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)],[2149]) ).
thf(999,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/sandbox2/benchmark/theBenchmark.p',t19_relat_1) ).
thf(6883,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)],[999]) ).
thf(2313,axiom,
! [A: $i] :
( ( k1_eqrel_1 @ A )
= ( k2_zfmisc_1 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_eqrel_1) ).
thf(13341,plain,
! [A: $i] :
( ( k1_eqrel_1 @ A )
= ( k2_zfmisc_1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2313]) ).
thf(679,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/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_4) ).
thf(5292,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)],[679]) ).
thf(1766,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/sandbox2/benchmark/theBenchmark.p',d8_binop_2) ).
thf(10542,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)],[1766]) ).
thf(2088,axiom,
! [A: $i,B: $i] :
( ( v1_funct_1 @ k1_xboole_0 )
& ( m2_relset_1 @ k1_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_partfun1) ).
thf(12376,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)],[2088]) ).
thf(2069,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/sandbox2/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(12299,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)],[2069]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) )
= ( k1_funct_2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_funct_2) ).
thf(3417,plain,
! [A: $i,B: $i] :
( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) )
= ( k1_funct_2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(1534,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/sandbox2/benchmark/theBenchmark.p',t77_xboole_1) ).
thf(9456,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)],[1534]) ).
thf(1704,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/sandbox2/benchmark/theBenchmark.p',t57_mcart_1) ).
thf(10277,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)],[1704]) ).
thf(1924,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/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(11409,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)],[1924]) ).
thf(865,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/sandbox2/benchmark/theBenchmark.p',d4_monoid_0) ).
thf(6199,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)],[865]) ).
thf(1502,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/sandbox2/benchmark/theBenchmark.p',t62_funct_2) ).
thf(9324,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)],[1502]) ).
thf(480,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/sandbox2/benchmark/theBenchmark.p',t75_funct_3) ).
thf(4391,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)],[480]) ).
thf(271,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/sandbox2/benchmark/theBenchmark.p',t57_sysrel) ).
thf(3460,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)],[271]) ).
thf(570,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/sandbox2/benchmark/theBenchmark.p',t99_funct_3) ).
thf(4807,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)],[570]) ).
thf(987,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k8_relat_1 @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
<=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
thf(6798,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( C
= ( k8_relat_1 @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) ) )
& ( ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) ) )
& ( ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
=> ( C
= ( k8_relat_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(1358,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 ) )
=> ( m2_fraenkel @ ( k5_funcsdom @ A @ B @ C @ D @ E ) @ B @ A @ ( k1_fraenkel @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_funcsdom) ).
thf(8695,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 ) )
=> ( m2_fraenkel @ ( k5_funcsdom @ A @ B @ C @ D @ E ) @ B @ A @ ( k1_fraenkel @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ( v2_relat_1 @ B )
& ( m1_pboole @ B @ A ) )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_pboole) ).
thf(2676,plain,
! [A: $i,B: $i] :
( ( ( v2_relat_1 @ B )
& ( m1_pboole @ B @ A ) )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1769,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/sandbox2/benchmark/theBenchmark.p',t62_domain_1) ).
thf(10562,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)],[1769]) ).
thf(2296,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/sandbox2/benchmark/theBenchmark.p',dt_k10_domain_1) ).
thf(13283,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)],[2296]) ).
thf(2175,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_domain_1) ).
thf(12774,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)],[2175]) ).
thf(1084,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k8_relat_1 @ ( k2_relat_1 @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_relat_1) ).
thf(7253,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k8_relat_1 @ ( k2_relat_1 @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(2335,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/sandbox2/benchmark/theBenchmark.p',fc3_yellow_3) ).
thf(13424,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)],[2335]) ).
thf(178,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/sandbox2/benchmark/theBenchmark.p',t34_setfam_1) ).
thf(3108,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)],[178]) ).
thf(1067,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(7198,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k3_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v2_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_funcop_1) ).
thf(3012,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v2_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(2058,axiom,
( ! [A: $i,B: $i,C: $i] :
( ( ( p1_s1_funct_1 @ A @ B )
& ( p1_s1_funct_1 @ A @ C ) )
=> ( B = C ) )
=> ? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ! [B: $i,C: $i] :
( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
<=> ( ( r2_hidden @ B @ f1_s1_funct_1 )
& ( p1_s1_funct_1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_funct_1) ).
thf(12221,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( p1_s1_funct_1 @ A @ B )
& ( p1_s1_funct_1 @ A @ C ) )
=> ( B = C ) )
=> ? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ! [B: $i,C: $i] :
( ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ A )
=> ( ( r2_hidden @ B @ f1_s1_funct_1 )
& ( p1_s1_funct_1 @ B @ C ) ) )
& ( ( ( r2_hidden @ B @ f1_s1_funct_1 )
& ( p1_s1_funct_1 @ B @ C ) )
=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2058]) ).
thf(703,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/sandbox2/benchmark/theBenchmark.p',t2_lattice5) ).
thf(5405,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)],[703]) ).
thf(1893,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 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( r2_hidden @ C @ ( k8_relset_2 @ A @ B @ D @ E ) )
=> ! [F: $i] :
( ( r2_hidden @ F @ D )
=> ( r2_hidden @ C @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_relset_2) ).
thf(11266,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 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( r2_hidden @ C @ ( k8_relset_2 @ A @ B @ D @ E ) )
=> ! [F: $i] :
( ( r2_hidden @ F @ D )
=> ( r2_hidden @ C @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1893]) ).
thf(467,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m1_card_fil @ B @ A )
=> ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_card_fil) ).
thf(4326,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)],[467]) ).
thf(2178,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/sandbox2/benchmark/theBenchmark.p',t88_mcart_1) ).
thf(12789,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)],[2178]) ).
thf(277,axiom,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ~ ( r2_wellord2 @ A @ ( k2_finseq_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_finseq_1) ).
thf(3498,plain,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ~ ( r2_wellord2 @ A @ ( k2_finseq_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(1062,axiom,
! [A: $i,B: $i] :
( ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_zfmisc_1) ).
thf(7182,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)],[1062]) ).
thf(1424,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_funct_1 @ A @ C ) ) )
=> ( ( ( r2_hidden @ D @ ( k1_funct_1 @ A @ B ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) ) )
=> ( ( ( k4_card_3 @ A )
= k1_xboole_0 )
| ( E
= ( k1_funct_1 @ A @ C ) )
| ( ( r1_tarski @ ( k10_relat_1 @ ( k3_pralg_3 @ A @ B ) @ ( k1_tarski @ D ) ) @ ( k10_relat_1 @ ( k3_pralg_3 @ A @ C ) @ E ) )
<=> ( ( B = C )
& ( r2_hidden @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_yellow17) ).
thf(8943,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k1_funct_1 @ A @ C ) ) )
=> ( ( ( r2_hidden @ D @ ( k1_funct_1 @ A @ B ) )
& ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ C @ ( k1_relat_1 @ A ) ) )
=> ( ( ( k4_card_3 @ A )
= k1_xboole_0 )
| ( E
= ( k1_funct_1 @ A @ C ) )
| ( ( ( r1_tarski @ ( k10_relat_1 @ ( k3_pralg_3 @ A @ B ) @ ( k1_tarski @ D ) ) @ ( k10_relat_1 @ ( k3_pralg_3 @ A @ C ) @ E ) )
=> ( ( B = C )
& ( r2_hidden @ D @ E ) ) )
& ( ( ( B = C )
& ( r2_hidden @ D @ E ) )
=> ( r1_tarski @ ( k10_relat_1 @ ( k3_pralg_3 @ A @ B ) @ ( k1_tarski @ D ) ) @ ( k10_relat_1 @ ( k3_pralg_3 @ A @ C ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424]) ).
thf(1328,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/sandbox2/benchmark/theBenchmark.p',t4_functor0) ).
thf(8563,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)],[1328]) ).
thf(1103,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/sandbox2/benchmark/theBenchmark.p',t4_borsuk_1) ).
thf(7341,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)],[1103]) ).
thf(695,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/sandbox2/benchmark/theBenchmark.p',t28_funct_4) ).
thf(5348,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)],[695]) ).
thf(1465,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/sandbox2/benchmark/theBenchmark.p',t48_funct_4) ).
thf(9152,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)],[1465]) ).
thf(2275,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/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(13212,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)],[2275]) ).
thf(930,axiom,
! [A: $i,B: $i,C: $i] :
( ( k1_enumset1 @ A @ B @ C )
= ( k1_enumset1 @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_enumset1) ).
thf(6480,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)],[930]) ).
thf(523,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/sandbox2/benchmark/theBenchmark.p',redefinition_k18_group_2) ).
thf(4592,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)],[523]) ).
thf(1640,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/sandbox2/benchmark/theBenchmark.p',t1_realset1) ).
thf(9950,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)],[1640]) ).
thf(422,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/sandbox2/benchmark/theBenchmark.p',t99_partfun1) ).
thf(4105,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)],[422]) ).
thf(710,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/sandbox2/benchmark/theBenchmark.p',t73_partfun1) ).
thf(5425,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)],[710]) ).
thf(284,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/sandbox2/benchmark/theBenchmark.p',t63_funct_1) ).
thf(3530,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)],[284]) ).
thf(1476,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/sandbox2/benchmark/theBenchmark.p',t61_funct_2) ).
thf(9212,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)],[1476]) ).
thf(1282,axiom,
! [A: $i] :
( ( v2_setfam_1 @ A )
<=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( r2_hidden @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_setfam_1) ).
thf(8298,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)],[1282]) ).
thf(1262,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/sandbox2/benchmark/theBenchmark.p',t65_mcart_1) ).
thf(8204,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)],[1262]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ B @ A @ A ) @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_funct_2) ).
thf(3794,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ B @ A @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(533,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/sandbox2/benchmark/theBenchmark.p',t5_lattice2) ).
thf(4633,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)],[533]) ).
thf(182,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/sandbox2/benchmark/theBenchmark.p',t38_sysrel) ).
thf(3120,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)],[182]) ).
thf(1863,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/sandbox2/benchmark/theBenchmark.p',t17_cantor_1) ).
thf(11112,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)],[1863]) ).
thf(1993,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_4_domain_1) ).
thf(11848,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)],[1993]) ).
thf(2278,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/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(13219,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)],[2278]) ).
thf(1458,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/sandbox2/benchmark/theBenchmark.p',t23_relat_1) ).
thf(9127,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)],[1458]) ).
thf(47,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/sandbox2/benchmark/theBenchmark.p',t84_xboole_1) ).
thf(2607,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)],[47]) ).
thf(1481,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/sandbox2/benchmark/theBenchmark.p',t43_setwiseo) ).
thf(9233,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)],[1481]) ).
thf(1251,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(8150,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)],[1251]) ).
thf(1118,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/sandbox2/benchmark/theBenchmark.p',t13_funct_7) ).
thf(7405,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)],[1118]) ).
thf(1806,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/sandbox2/benchmark/theBenchmark.p',rc6_finseq_1) ).
thf(10772,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)],[1806]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v2_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_cantor_1) ).
thf(3135,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v2_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(387,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/sandbox2/benchmark/theBenchmark.p',t64_funct_2) ).
thf(3942,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)],[387]) ).
thf(1667,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/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(10093,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)],[1667]) ).
thf(1139,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/sandbox2/benchmark/theBenchmark.p',t34_mcart_1) ).
thf(7556,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)],[1139]) ).
thf(1444,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/sandbox2/benchmark/theBenchmark.p',t5_pua2mss1) ).
thf(9052,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)],[1444]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) )
=> ( ( v1_relat_1 @ ( k4_closure2 @ A @ B @ C ) )
& ( v2_relat_1 @ ( k4_closure2 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k4_closure2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_closure2) ).
thf(2740,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ~ ( v1_xboole_0 @ C )
& ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_closure2 @ A @ B ) ) ) )
=> ( ( v1_relat_1 @ ( k4_closure2 @ A @ B @ C ) )
& ( v2_relat_1 @ ( k4_closure2 @ A @ B @ C ) )
& ( v1_funct_1 @ ( k4_closure2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1826,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/sandbox2/benchmark/theBenchmark.p',t31_yellow18) ).
thf(10881,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)],[1826]) ).
thf(903,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( k1_relat_1 @ A )
= k1_xboole_0 )
<=> ( ( k2_relat_1 @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
thf(6359,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)],[903]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_partfun1) ).
thf(3044,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(678,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 ) )
=> ( ( ( r4_binop_1 @ A @ C @ D )
& ( r4_binop_1 @ B @ E @ F ) )
<=> ( r4_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_filter_1) ).
thf(5288,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 ) )
=> ( ( ( ( r4_binop_1 @ A @ C @ D )
& ( r4_binop_1 @ B @ E @ F ) )
=> ( r4_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) )
& ( ( r4_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) )
=> ( ( r4_binop_1 @ A @ C @ D )
& ( r4_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(1416,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/sandbox2/benchmark/theBenchmark.p',t169_partfun1) ).
thf(8913,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)],[1416]) ).
thf(1855,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/sandbox2/benchmark/theBenchmark.p',t14_setwiseo) ).
thf(11058,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)],[1855]) ).
thf(1190,axiom,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(7824,plain,
! [A: $i,B: $i] :
( ~ ( r2_hidden @ A @ B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(1417,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m1_card_fil @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_card_fil) ).
thf(8915,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m1_card_fil @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417]) ).
thf(850,axiom,
! [A: $i,B: $i] :
( ( k6_enumset1 @ A @ A @ A @ A @ A @ A @ A @ B )
= ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_enumset1) ).
thf(6127,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)],[850]) ).
thf(1232,axiom,
! [A: $i] :
( ( k1_enumset1 @ A @ A @ A )
= ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_enumset1) ).
thf(8057,plain,
! [A: $i] :
( ( k1_enumset1 @ A @ A @ A )
= ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(1035,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/sandbox2/benchmark/theBenchmark.p',fc5_funcop_1) ).
thf(7096,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)],[1035]) ).
thf(1294,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/sandbox2/benchmark/theBenchmark.p',t27_finseq_1) ).
thf(8353,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)],[1294]) ).
thf(266,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/sandbox2/benchmark/theBenchmark.p',t111_xboole_1) ).
thf(3446,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)],[266]) ).
thf(2037,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/sandbox2/benchmark/theBenchmark.p',free_g1_quantal1) ).
thf(12097,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)],[2037]) ).
thf(1352,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v7_altcat_1 @ A )
<=> ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( B
= ( k4_tarski @ D @ C ) )
& ( ( k1_funct_1 @ A @ B )
= ( k5_relat_1 @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_altcat_1) ).
thf(8667,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v7_altcat_1 @ A )
=> ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( B
= ( k4_tarski @ D @ C ) )
& ( ( k1_funct_1 @ A @ B )
= ( k5_relat_1 @ C @ D ) ) ) ) ) ) )
& ( ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( B
= ( k4_tarski @ D @ C ) )
& ( ( k1_funct_1 @ A @ B )
= ( k5_relat_1 @ C @ D ) ) ) ) ) )
=> ( v7_altcat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).
thf(1319,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k11_relset_1 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k11_relset_1) ).
thf(8490,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( m1_relset_1 @ C @ A @ B )
=> ( ( k11_relset_1 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(1327,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/sandbox2/benchmark/theBenchmark.p',d2_funct_2) ).
thf(8519,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)],[1327]) ).
thf(1560,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/sandbox2/benchmark/theBenchmark.p',rc1_pua2mss1) ).
thf(9565,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)],[1560]) ).
thf(139,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/sandbox2/benchmark/theBenchmark.p',t86_xboole_1) ).
thf(2933,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)],[139]) ).
thf(1606,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/sandbox2/benchmark/theBenchmark.p',t2_zfrefle1) ).
thf(9813,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)],[1606]) ).
thf(1678,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/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(10138,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)],[1678]) ).
thf(759,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/sandbox2/benchmark/theBenchmark.p',d6_monoid_0) ).
thf(5701,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)],[759]) ).
thf(1756,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/sandbox2/benchmark/theBenchmark.p',dt_m2_subset_1) ).
thf(10511,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)],[1756]) ).
thf(992,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/sandbox2/benchmark/theBenchmark.p',dt_k11_relset_1) ).
thf(6851,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)],[992]) ).
thf(1133,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/sandbox2/benchmark/theBenchmark.p',t97_funct_3) ).
thf(7467,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)],[1133]) ).
thf(1695,axiom,
! [A: $i] : ( m2_relset_1 @ ( k6_relat_1 @ A ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_relset_1) ).
thf(10209,plain,
! [A: $i] : ( m2_relset_1 @ ( k6_relat_1 @ A ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1695]) ).
thf(1298,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(8370,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)],[1298]) ).
thf(761,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/sandbox2/benchmark/theBenchmark.p',t20_borsuk_1) ).
thf(5713,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)],[761]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
<=> ( ( k4_xboole_0 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(2476,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)],[27]) ).
thf(2096,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/sandbox2/benchmark/theBenchmark.p',t5_filter_2) ).
thf(12398,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)],[2096]) ).
thf(750,axiom,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(5674,plain,
! [A: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',t37_sysrel) ).
thf(2459,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)],[22]) ).
thf(1264,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/sandbox2/benchmark/theBenchmark.p',t148_relat_1) ).
thf(8210,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)],[1264]) ).
thf(2253,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/sandbox2/benchmark/theBenchmark.p',t18_borsuk_1) ).
thf(13113,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)],[2253]) ).
thf(257,axiom,
! [A: $i] :
( ( k4_relat_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_relat_1) ).
thf(3414,plain,
! [A: $i] :
( ( k4_relat_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(949,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/sandbox2/benchmark/theBenchmark.p',t45_funct_4) ).
thf(6551,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)],[949]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ A ) )
<=> ~ ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(3481,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)],[273]) ).
thf(1797,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/sandbox2/benchmark/theBenchmark.p',fc1_closure2) ).
thf(10726,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)],[1797]) ).
thf(133,axiom,
( ( k4_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_relat_1) ).
thf(2901,plain,
( ( k4_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(1197,axiom,
! [A: $i] :
( ( v1_partfun1 @ ( k6_partfun1 @ A ) @ A @ A )
& ( m2_relset_1 @ ( k6_partfun1 @ A ) @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
thf(7871,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)],[1197]) ).
thf(239,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/sandbox2/benchmark/theBenchmark.p',t40_setwiseo) ).
thf(3313,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)],[239]) ).
thf(2050,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/sandbox2/benchmark/theBenchmark.p',t65_funcop_1) ).
thf(12165,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)],[2050]) ).
thf(1348,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/sandbox2/benchmark/theBenchmark.p',t86_relat_1) ).
thf(8650,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)],[1348]) ).
thf(1406,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/sandbox2/benchmark/theBenchmark.p',t187_relat_1) ).
thf(8881,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)],[1406]) ).
thf(1854,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/sandbox2/benchmark/theBenchmark.p',involutiveness_k10_funcop_1) ).
thf(11055,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)],[1854]) ).
thf(1529,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/sandbox2/benchmark/theBenchmark.p',t26_funct_7) ).
thf(9433,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)],[1529]) ).
thf(2259,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/sandbox2/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(13145,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)],[2259]) ).
thf(1485,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/sandbox2/benchmark/theBenchmark.p',t31_funcop_1) ).
thf(9246,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)],[1485]) ).
thf(611,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/sandbox2/benchmark/theBenchmark.p',t4_funcop_1) ).
thf(4980,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)],[611]) ).
thf(2238,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/sandbox2/benchmark/theBenchmark.p',t15_setwiseo) ).
thf(13056,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)],[2238]) ).
thf(656,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/sandbox2/benchmark/theBenchmark.p',t1_funct_7) ).
thf(5192,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)],[656]) ).
thf(1583,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/sandbox2/benchmark/theBenchmark.p',s1_setwiseo) ).
thf(9672,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)],[1583]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc37_membered) ).
thf(2575,plain,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k4_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(873,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 )
=> ( ( r5_binop_1 @ A @ C @ B )
<=> ( r4_binop_1 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_binop_1) ).
thf(6236,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 )
=> ( ( ( r5_binop_1 @ A @ C @ B )
=> ( r4_binop_1 @ A @ C @ B ) )
& ( ( r4_binop_1 @ A @ C @ B )
=> ( r5_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(217,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/sandbox2/benchmark/theBenchmark.p',t12_zfrefle1) ).
thf(3236,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)],[217]) ).
thf(456,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/sandbox2/benchmark/theBenchmark.p',t106_relat_1) ).
thf(4266,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)],[456]) ).
thf(2288,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_0_domain_1) ).
thf(13251,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)],[2288]) ).
thf(344,axiom,
! [A: $i] :
? [B: $i] : ( m2_pua2mss1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_pua2mss1) ).
thf(3777,plain,
! [A: $i] :
? [B: $i] : ( m2_pua2mss1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(2298,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_32_fraenkel) ).
thf(13287,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)],[2298]) ).
thf(1360,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/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_filter_2) ).
thf(8699,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)],[1360]) ).
thf(2030,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/sandbox2/benchmark/theBenchmark.p',t56_funct_4) ).
thf(12062,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)],[2030]) ).
thf(622,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/sandbox2/benchmark/theBenchmark.p',t2_funct_7) ).
thf(5024,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)],[622]) ).
thf(1717,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/sandbox2/benchmark/theBenchmark.p',dt_k34_binop_2) ).
thf(10351,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)],[1717]) ).
thf(1958,axiom,
( k5_urysohn1
= ( k4_subset_1 @ k1_numbers @ ( k4_subset_1 @ k1_numbers @ k1_urysohn1 @ k4_urysohn1 ) @ k2_urysohn1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_urysohn1) ).
thf(11684,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)],[1958]) ).
thf(853,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/sandbox2/benchmark/theBenchmark.p',t11_funct_6) ).
thf(6138,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)],[853]) ).
thf(411,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t174_relat_1) ).
thf(4047,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ~ ( ( A != k1_xboole_0 )
& ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(2109,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/sandbox2/benchmark/theBenchmark.p',existence_m1_triang_1) ).
thf(12447,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)],[2109]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k5_partfun1 @ A @ A @ ( k3_partfun1 @ B @ A @ A ) )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t162_funct_2) ).
thf(3103,plain,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( v1_funct_2 @ B @ A @ A )
& ( m2_relset_1 @ B @ A @ A ) )
=> ( ( k5_partfun1 @ A @ A @ ( k3_partfun1 @ B @ A @ A ) )
= ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(290,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/sandbox2/benchmark/theBenchmark.p',t32_funct_2) ).
thf(3545,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)],[290]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_relset_2) ).
thf(2723,plain,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1906,axiom,
! [A: $i] :
( ( v1_fraenkel @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_fraenkel) ).
thf(11335,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)],[1906]) ).
thf(2206,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/sandbox2/benchmark/theBenchmark.p',s3_funct_2) ).
thf(12929,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)],[2206]) ).
thf(820,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/sandbox2/benchmark/theBenchmark.p',t16_funct_1) ).
thf(5977,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)],[820]) ).
thf(12,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k3_funct_5 @ A ) )
& ( v1_funct_1 @ ( k3_funct_5 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_funct_5) ).
thf(2432,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k3_funct_5 @ A ) )
& ( v1_funct_1 @ ( k3_funct_5 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k4_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(2491,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)],[30]) ).
thf(1241,axiom,
( ( k2_funct_4 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_funct_5) ).
thf(8086,plain,
( ( k2_funct_4 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(1412,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/sandbox2/benchmark/theBenchmark.p',t51_funct_2) ).
thf(8898,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)],[1412]) ).
thf(2182,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/sandbox2/benchmark/theBenchmark.p',t58_partfun1) ).
thf(12833,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)],[2182]) ).
thf(1988,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/sandbox2/benchmark/theBenchmark.p',dt_k9_funcop_1) ).
thf(11834,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)],[1988]) ).
thf(1287,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/sandbox2/benchmark/theBenchmark.p',t3_pre_circ) ).
thf(8325,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)],[1287]) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k10_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t154_funct_1) ).
thf(3502,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k9_relat_1 @ B @ A )
= ( k10_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(2356,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/sandbox2/benchmark/theBenchmark.p',dt_k17_domain_1) ).
thf(13516,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)],[2356]) ).
thf(1832,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/sandbox2/benchmark/theBenchmark.p',free_g1_vectsp_1) ).
thf(10908,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)],[1832]) ).
thf(2171,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(12763,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2171]) ).
thf(1597,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/sandbox2/benchmark/theBenchmark.p',t31_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 ) )
=> ( ( ( 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)],[1597]) ).
thf(657,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/sandbox2/benchmark/theBenchmark.p',rc2_finseq_1) ).
thf(5195,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)],[657]) ).
thf(1047,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/sandbox2/benchmark/theBenchmark.p',redefinition_k9_funcop_1) ).
thf(7136,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)],[1047]) ).
thf(2327,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(13392,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)],[2327]) ).
thf(1467,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/sandbox2/benchmark/theBenchmark.p',t37_funct_1) ).
thf(9159,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)],[1467]) ).
thf(1266,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ ( k7_relat_1 @ B @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_partfun1) ).
thf(8239,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)],[1266]) ).
thf(237,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 )
& ( v1_finseq_1 @ C ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C )
& ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_finseq_2) ).
thf(3308,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 )
& ( v1_finseq_1 @ C ) )
=> ( ( ( r1_tarski @ A @ C )
& ( r1_tarski @ B @ C )
& ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(428,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/sandbox2/benchmark/theBenchmark.p',t10_funcop_1) ).
thf(4124,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)],[428]) ).
thf(1080,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/sandbox2/benchmark/theBenchmark.p',t100_funct_3) ).
thf(7240,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)],[1080]) ).
thf(1004,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/sandbox2/benchmark/theBenchmark.p',rc1_borsuk_1) ).
thf(6904,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)],[1004]) ).
thf(787,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/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(5825,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)],[787]) ).
thf(1402,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ A ) )
=> ( ( ( k1_relat_1 @ ( k9_funct_7 @ A @ B ) )
= ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k9_funct_7 @ A @ B ) ) @ ( k1_relat_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_funct_7) ).
thf(8866,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( r1_tarski @ ( k2_relat_1 @ A ) @ ( k1_relat_1 @ A ) )
=> ( ( ( k1_relat_1 @ ( k9_funct_7 @ A @ B ) )
= ( k1_relat_1 @ A ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k9_funct_7 @ A @ B ) ) @ ( k1_relat_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402]) ).
thf(2211,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/sandbox2/benchmark/theBenchmark.p',rc5_triang_1) ).
thf(12960,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)],[2211]) ).
thf(1847,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/sandbox2/benchmark/theBenchmark.p',t15_domain_1) ).
thf(11024,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)],[1847]) ).
thf(1590,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/sandbox2/benchmark/theBenchmark.p',t15_ens_1) ).
thf(9708,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)],[1590]) ).
thf(682,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/sandbox2/benchmark/theBenchmark.p',t12_funct_3) ).
thf(5301,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)],[682]) ).
thf(447,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/sandbox2/benchmark/theBenchmark.p',t57_setwiseo) ).
thf(4198,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)],[447]) ).
thf(1362,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_funct_4 @ k1_xboole_0 @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_4) ).
thf(8705,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)],[1362]) ).
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/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setwiseo) ).
thf(2400,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(1762,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(10530,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1762]) ).
thf(931,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/sandbox2/benchmark/theBenchmark.p',t76_funct_1) ).
thf(6483,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)],[931]) ).
thf(2281,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(13223,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)],[2281]) ).
thf(2177,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(12785,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_xboole_0 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2177]) ).
thf(675,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/sandbox2/benchmark/theBenchmark.p',t137_zfmisc_1) ).
thf(5269,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)],[675]) ).
thf(2074,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/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_3) ).
thf(12324,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)],[2074]) ).
thf(890,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/sandbox2/benchmark/theBenchmark.p',d5_funcop_1) ).
thf(6291,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)],[890]) ).
thf(527,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/sandbox2/benchmark/theBenchmark.p',dt_k3_funct_4) ).
thf(4610,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)],[527]) ).
thf(2315,axiom,
! [A: $i] : ( m1_subset_1 @ ( k8_subset_1 @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_subset_1) ).
thf(13346,plain,
! [A: $i] : ( m1_subset_1 @ ( k8_subset_1 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2315]) ).
thf(1682,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(10153,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ~ ( r2_hidden @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1682]) ).
thf(325,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/sandbox2/benchmark/theBenchmark.p',t64_classes2) ).
thf(3688,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)],[325]) ).
thf(1098,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/sandbox2/benchmark/theBenchmark.p',t25_borsuk_1) ).
thf(7311,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)],[1098]) ).
thf(1777,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/sandbox2/benchmark/theBenchmark.p',t25_filter_1) ).
thf(10633,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)],[1777]) ).
thf(126,axiom,
! [A: $i] : ( r1_tarski @ ( k1_setfam_1 @ A ) @ ( k3_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_setfam_1) ).
thf(2869,plain,
! [A: $i] : ( r1_tarski @ ( k1_setfam_1 @ A ) @ ( k3_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(2193,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/sandbox2/benchmark/theBenchmark.p',t68_setwiseo) ).
thf(12879,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)],[2193]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_partfun1) ).
thf(2957,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(2161,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/sandbox2/benchmark/theBenchmark.p',t9_relset_2) ).
thf(12718,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)],[2161]) ).
thf(866,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k10_relat_1 @ ( k13_funct_3 @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
= ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_funct_3) ).
thf(6208,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k10_relat_1 @ ( k13_funct_3 @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
= ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(791,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( v2_funct_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_partfun1) ).
thf(5836,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)],[791]) ).
thf(1112,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/sandbox2/benchmark/theBenchmark.p',fc30_membered) ).
thf(7386,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)],[1112]) ).
thf(1643,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/sandbox2/benchmark/theBenchmark.p',dt_m1_nat_lat) ).
thf(9960,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)],[1643]) ).
thf(2082,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/sandbox2/benchmark/theBenchmark.p',t3_fraenkel) ).
thf(12351,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)],[2082]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(3248,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)],[221]) ).
thf(815,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k1_tarski @ B ) )
<=> ( ( A = k1_xboole_0 )
| ( A
= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(5953,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)],[815]) ).
thf(2270,axiom,
m1_subset_1 @ k1_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_urysohn1) ).
thf(13191,plain,
m1_subset_1 @ k1_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2270]) ).
thf(775,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/sandbox2/benchmark/theBenchmark.p',t13_funct_4) ).
thf(5765,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)],[775]) ).
thf(223,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/sandbox2/benchmark/theBenchmark.p',redefinition_k4_finseq_1) ).
thf(3263,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)],[223]) ).
thf(2302,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/sandbox2/benchmark/theBenchmark.p',t13_cantor_1) ).
thf(13313,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)],[2302]) ).
thf(1836,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/sandbox2/benchmark/theBenchmark.p',t3_funct_3) ).
thf(10955,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)],[1836]) ).
thf(1705,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_pboole) ).
thf(10286,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)],[1705]) ).
thf(1152,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/sandbox2/benchmark/theBenchmark.p',t15_realset1) ).
thf(7620,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)],[1152]) ).
thf(1674,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/sandbox2/benchmark/theBenchmark.p',t9_mcart_1) ).
thf(10121,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)],[1674]) ).
thf(1652,axiom,
~ ( v1_xboole_0 @ k1_qc_lang1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_qc_lang1) ).
thf(9989,plain,
~ ( v1_xboole_0 @ k1_qc_lang1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1652]) ).
thf(506,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/sandbox2/benchmark/theBenchmark.p',t14_funct_4) ).
thf(4524,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)],[506]) ).
thf(1496,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/sandbox2/benchmark/theBenchmark.p',t115_funct_2) ).
thf(9287,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)],[1496]) ).
thf(1206,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/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(7914,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)],[1206]) ).
thf(2013,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/sandbox2/benchmark/theBenchmark.p',redefinition_k15_domain_1) ).
thf(11976,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)],[2013]) ).
thf(684,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/sandbox2/benchmark/theBenchmark.p',t27_funcop_1) ).
thf(5306,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)],[684]) ).
thf(589,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 ) ) )
=> ( ( ( r4_binop_1 @ A @ C @ D )
=> ( r4_binop_1 @ B @ E @ F ) )
& ( ( r5_binop_1 @ A @ C @ D )
=> ( r5_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_filter_2) ).
thf(4896,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 ) ) )
=> ( ( ( r4_binop_1 @ A @ C @ D )
=> ( r4_binop_1 @ B @ E @ F ) )
& ( ( r5_binop_1 @ A @ C @ D )
=> ( r5_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(875,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/sandbox2/benchmark/theBenchmark.p',t39_funct_4) ).
thf(6242,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)],[875]) ).
thf(1991,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/sandbox2/benchmark/theBenchmark.p',dt_k7_setwiseo) ).
thf(11844,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)],[1991]) ).
thf(1086,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/sandbox2/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
thf(7262,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)],[1086]) ).
thf(2209,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/sandbox2/benchmark/theBenchmark.p',t22_filter_1) ).
thf(12943,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)],[2209]) ).
thf(1430,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/sandbox2/benchmark/theBenchmark.p',t15_sysrel) ).
thf(8967,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)],[1430]) ).
thf(1169,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/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).
thf(7696,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)],[1169]) ).
thf(1524,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/sandbox2/benchmark/theBenchmark.p',t88_funct_3) ).
thf(9410,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)],[1524]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_fraenkel @ C @ A @ B ) )
=> ! [D: $i] :
( ( m2_fraenkel @ D @ A @ B @ C )
<=> ( m1_subset_1 @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
thf(3275,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_fraenkel @ C @ A @ B ) )
=> ! [D: $i] :
( ( ( m2_fraenkel @ D @ A @ B @ C )
=> ( m1_subset_1 @ D @ C ) )
& ( ( m1_subset_1 @ D @ C )
=> ( m2_fraenkel @ D @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(1320,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/sandbox2/benchmark/theBenchmark.p',t74_partfun1) ).
thf(8494,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)],[1320]) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',t61_funct_1) ).
thf(2698,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)],[73]) ).
thf(1432,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/sandbox2/benchmark/theBenchmark.p',t15_funct_4) ).
thf(8996,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)],[1432]) ).
thf(945,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/sandbox2/benchmark/theBenchmark.p',t56_subset_1) ).
thf(6538,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)],[945]) ).
thf(185,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m2_pua2mss1 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( v2_relat_1 @ B )
& ( v2_funct_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_pua2mss1) ).
thf(3131,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m2_pua2mss1 @ B @ A )
=> ( ~ ( v1_xboole_0 @ B )
& ( v2_relat_1 @ B )
& ( v2_funct_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(1404,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) )
=> ( ( k3_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) )
= ( k10_relat_1 @ B @ ( k3_tarski @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_funct_3) ).
thf(8875,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) )
=> ( ( k3_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) )
= ( k10_relat_1 @ B @ ( k3_tarski @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( m2_finseq_1 @ B @ ( k3_pua2mss1 @ A ) )
=> ? [C: $i] :
( ( m2_finseq_1 @ C @ A )
& ( ( k4_card_3 @ B )
= ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_pua2mss1) ).
thf(3116,plain,
! [A: $i,B: $i] :
( ( m2_finseq_1 @ B @ ( k3_pua2mss1 @ A ) )
=> ? [C: $i] :
( ( m2_finseq_1 @ C @ A )
& ( ( k4_card_3 @ B )
= ( k1_tarski @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(64,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_xboole_1) ).
thf(2667,plain,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1117,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/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(7401,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)],[1117]) ).
thf(1840,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/sandbox2/benchmark/theBenchmark.p',redefinition_k8_domain_1) ).
thf(10997,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)],[1840]) ).
thf(2337,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/sandbox2/benchmark/theBenchmark.p',redefinition_k13_mcart_1) ).
thf(13429,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)],[2337]) ).
thf(434,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/sandbox2/benchmark/theBenchmark.p',t122_zfmisc_1) ).
thf(4151,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)],[434]) ).
thf(1801,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/sandbox2/benchmark/theBenchmark.p',t11_funct_2) ).
thf(10751,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)],[1801]) ).
thf(1751,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/sandbox2/benchmark/theBenchmark.p',t55_setfam_1) ).
thf(10486,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)],[1751]) ).
thf(163,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 )
& ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_wellord2 @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ C @ D ) ) ) )
=> ( r2_wellord2 @ ( k4_card_3 @ B ) @ ( k4_card_3 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_funct_6) ).
thf(3046,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 )
& ! [D: $i] :
( ( r2_hidden @ D @ A )
=> ( r2_wellord2 @ ( k1_funct_1 @ B @ D ) @ ( k1_funct_1 @ C @ D ) ) ) )
=> ( r2_wellord2 @ ( k4_card_3 @ B ) @ ( k4_card_3 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(2001,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/sandbox2/benchmark/theBenchmark.p',t62_relat_1) ).
thf(11913,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)],[2001]) ).
thf(774,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/sandbox2/benchmark/theBenchmark.p',t45_funct_2) ).
thf(5759,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)],[774]) ).
thf(1453,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/sandbox2/benchmark/theBenchmark.p',d9_funct_3) ).
thf(9084,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)],[1453]) ).
thf(846,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/sandbox2/benchmark/theBenchmark.p',t49_funct_1) ).
thf(6095,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)],[846]) ).
thf(1658,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/sandbox2/benchmark/theBenchmark.p',t14_yellow_9) ).
thf(10053,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)],[1658]) ).
thf(1505,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/sandbox2/benchmark/theBenchmark.p',t14_lattice2) ).
thf(9332,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)],[1505]) ).
thf(276,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k3_funct_3 @ A ) )
& ( v1_funct_1 @ ( k3_funct_3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_funct_3) ).
thf(3495,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k3_funct_3 @ A ) )
& ( v1_funct_1 @ ( k3_funct_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(1588,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/sandbox2/benchmark/theBenchmark.p',t52_subset_1) ).
thf(9693,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)],[1588]) ).
thf(2025,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/sandbox2/benchmark/theBenchmark.p',t48_relset_1) ).
thf(12046,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)],[2025]) ).
thf(555,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) )
= ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_relat_1) ).
thf(4761,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) )
= ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(654,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/sandbox2/benchmark/theBenchmark.p',t26_funct_4) ).
thf(5188,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)],[654]) ).
thf(75,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/sandbox2/benchmark/theBenchmark.p',t22_setwiseo) ).
thf(2708,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)],[75]) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',t1_monoid_0) ).
thf(2501,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)],[33]) ).
thf(2011,axiom,
! [A: $i] : ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relset_1) ).
thf(11966,plain,
! [A: $i] : ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k2_zfmisc_1 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2011]) ).
thf(537,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_relat_1) ).
thf(4654,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v2_relat_1 @ B )
& ( m1_pboole @ B @ A ) )
=> ( ~ ( v1_xboole_0 @ ( k4_card_3 @ B ) )
& ( v1_fraenkel @ ( k4_card_3 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_pralg_1) ).
thf(2444,plain,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v2_relat_1 @ B )
& ( m1_pboole @ B @ A ) )
=> ( ~ ( v1_xboole_0 @ ( k4_card_3 @ B ) )
& ( v1_fraenkel @ ( k4_card_3 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(470,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/sandbox2/benchmark/theBenchmark.p',t99_relat_1) ).
thf(4334,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)],[470]) ).
thf(1425,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_zfmisc_1) ).
thf(8951,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)],[1425]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(3148,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)],[191]) ).
thf(937,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/sandbox2/benchmark/theBenchmark.p',t75_enumset1) ).
thf(6506,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)],[937]) ).
thf(1386,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/sandbox2/benchmark/theBenchmark.p',t1_altcat_2) ).
thf(8787,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)],[1386]) ).
thf(560,axiom,
! [A: $i] : ( v2_funct_1 @ ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_1) ).
thf(4778,plain,
! [A: $i] : ( v2_funct_1 @ ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(1556,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/sandbox2/benchmark/theBenchmark.p',t93_funct_3) ).
thf(9552,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)],[1556]) ).
thf(1009,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
<=> ( r1_tarski @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relset_2) ).
thf(6968,plain,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) )
& ( ( r1_tarski @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(183,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_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( v1_finseq_1 @ E ) )
=> ! [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 )
=> ( ( E
= ( k4_funcop_1 @ F @ G @ D ) )
=> ( ( k3_finseq_1 @ E )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_finseq_2) ).
thf(3125,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_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( v1_finseq_1 @ E ) )
=> ! [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 )
=> ( ( E
= ( k4_funcop_1 @ F @ G @ D ) )
=> ( ( k3_finseq_1 @ E )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(2222,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/sandbox2/benchmark/theBenchmark.p',t32_borsuk_1) ).
thf(12993,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)],[2222]) ).
thf(2031,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/sandbox2/benchmark/theBenchmark.p',t20_cantor_1) ).
thf(12065,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)],[2031]) ).
thf(1881,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/sandbox2/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(11200,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)],[1881]) ).
thf(430,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/sandbox2/benchmark/theBenchmark.p',t14_relset_2) ).
thf(4130,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)],[430]) ).
thf(1349,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/sandbox2/benchmark/theBenchmark.p',t8_functor0) ).
thf(8654,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)],[1349]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t135_relat_1) ).
thf(4275,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C )
= ( k3_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(255,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_funct_3) ).
thf(3410,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( r2_wellord2 @ ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_card_1) ).
thf(3280,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ C @ B ) )
=> ( r2_wellord2 @ ( k4_xboole_0 @ B @ ( k1_tarski @ A ) ) @ ( k4_xboole_0 @ B @ ( k1_tarski @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1631,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/sandbox2/benchmark/theBenchmark.p',t55_funct_2) ).
thf(9909,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)],[1631]) ).
thf(1655,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/sandbox2/benchmark/theBenchmark.p',t1_t_0topsp) ).
thf(10010,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)],[1655]) ).
thf(2264,axiom,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(13170,plain,
! [A: $i] :
? [B: $i] : ( m1_subset_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2264]) ).
thf(1715,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r7_relat_2 @ A @ B )
<=> ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ~ ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ~ ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_2) ).
thf(10337,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( r7_relat_2 @ A @ B )
=> ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ~ ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ~ ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) )
& ( ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ~ ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ~ ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
=> ( r7_relat_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1715]) ).
thf(403,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/sandbox2/benchmark/theBenchmark.p',t27_xboole_1) ).
thf(4023,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)],[403]) ).
thf(29,axiom,
! [A: $i] :
( ( k1_setwiseo @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setwiseo) ).
thf(2488,plain,
! [A: $i] :
( ( k1_setwiseo @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(132,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 @ B @ A ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ A ) @ C ) )
=> ( ( v1_funct_1 @ ( k5_funct_5 @ D ) )
& ( v1_funct_2 @ ( k5_funct_5 @ D ) @ A @ ( k1_fraenkel @ B @ C ) )
& ( m2_relset_1 @ ( k5_funct_5 @ D ) @ A @ ( k1_fraenkel @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_cat_2) ).
thf(2897,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 @ B @ A ) @ C )
& ( m2_relset_1 @ D @ ( k2_zfmisc_1 @ B @ A ) @ C ) )
=> ( ( v1_funct_1 @ ( k5_funct_5 @ D ) )
& ( v1_funct_2 @ ( k5_funct_5 @ D ) @ A @ ( k1_fraenkel @ B @ C ) )
& ( m2_relset_1 @ ( k5_funct_5 @ D ) @ A @ ( k1_fraenkel @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1582,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/sandbox2/benchmark/theBenchmark.p',d2_realset1) ).
thf(9668,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)],[1582]) ).
thf(900,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ ( k3_pua2mss1 @ B ) )
<=> ? [C: $i] :
( ( A
= ( k1_tarski @ C ) )
& ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_relset_2) ).
thf(6332,plain,
! [A: $i,B: $i] :
( ( ( r2_hidden @ A @ ( k3_pua2mss1 @ B ) )
=> ? [C: $i] :
( ( A
= ( k1_tarski @ C ) )
& ( r2_hidden @ C @ B ) ) )
& ( ? [C: $i] :
( ( A
= ( k1_tarski @ C ) )
& ( r2_hidden @ C @ B ) )
=> ( r2_hidden @ A @ ( k3_pua2mss1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(968,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/sandbox2/benchmark/theBenchmark.p',dt_k2_realset1) ).
thf(6662,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)],[968]) ).
thf(1605,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_domain_1) ).
thf(9805,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)],[1605]) ).
thf(940,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/sandbox2/benchmark/theBenchmark.p',t5_yellow_6) ).
thf(6519,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)],[940]) ).
thf(1480,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/sandbox2/benchmark/theBenchmark.p',t77_funcop_1) ).
thf(9230,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)],[1480]) ).
thf(2241,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/sandbox2/benchmark/theBenchmark.p',t9_card_fil) ).
thf(13067,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)],[2241]) ).
thf(1950,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/sandbox2/benchmark/theBenchmark.p',t2_functor1) ).
thf(11628,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)],[1950]) ).
thf(851,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/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).
thf(6130,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)],[851]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ A @ ( k4_relset_1 @ B @ C @ ( k3_partfun1 @ D @ B @ C ) ) )
<=> ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_partfun1) ).
thf(2703,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r2_hidden @ A @ ( k4_relset_1 @ B @ C @ ( k3_partfun1 @ D @ B @ C ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) ) )
& ( ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( r2_hidden @ A @ B )
& ( r2_hidden @ ( k1_funct_1 @ D @ A ) @ C ) )
=> ( r2_hidden @ A @ ( k4_relset_1 @ B @ C @ ( k3_partfun1 @ D @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(2156,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/sandbox2/benchmark/theBenchmark.p',d20_binop_1) ).
thf(12693,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)],[2156]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( m2_pua2mss1 @ B @ A )
=> ( ( v2_relat_1 @ B )
& ( v2_funct_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_pua2mss1) ).
thf(2713,plain,
! [A: $i,B: $i] :
( ( m2_pua2mss1 @ B @ A )
=> ( ( v2_relat_1 @ B )
& ( v2_funct_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(980,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/sandbox2/benchmark/theBenchmark.p',t76_xboole_1) ).
thf(6781,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)],[980]) ).
thf(1972,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/sandbox2/benchmark/theBenchmark.p',t119_funct_2) ).
thf(11741,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)],[1972]) ).
thf(1539,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/sandbox2/benchmark/theBenchmark.p',t11_pre_circ) ).
thf(9475,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)],[1539]) ).
thf(1272,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] :
( ( r2_hidden @ E @ ( k10_relat_1 @ D @ C ) )
<=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_2) ).
thf(8257,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] :
( ( ( r2_hidden @ E @ ( k10_relat_1 @ D @ C ) )
=> ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ C ) ) )
& ( ( ( r2_hidden @ E @ A )
& ( r2_hidden @ ( k1_funct_1 @ D @ E ) @ C ) )
=> ( r2_hidden @ E @ ( k10_relat_1 @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(1414,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/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).
thf(8907,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)],[1414]) ).
thf(1193,axiom,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_subset_1) ).
thf(7835,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(1222,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/sandbox2/benchmark/theBenchmark.p',d16_binop_1) ).
thf(7997,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)],[1222]) ).
thf(826,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/sandbox2/benchmark/theBenchmark.p',t74_funcop_1) ).
thf(6010,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)],[826]) ).
thf(175,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_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( v1_finseq_1 @ E ) )
=> ! [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 )
=> ( ( E
= ( k5_funcop_1 @ F @ D @ G ) )
=> ( ( k3_finseq_1 @ E )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_finseq_2) ).
thf(3099,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_relat_1 @ E )
& ( v1_funct_1 @ E )
& ( v1_finseq_1 @ E ) )
=> ! [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 )
=> ( ( E
= ( k5_funcop_1 @ F @ D @ G ) )
=> ( ( k3_finseq_1 @ E )
= ( k3_finseq_1 @ G ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(1231,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/sandbox2/benchmark/theBenchmark.p',fc4_funcop_1) ).
thf(8054,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)],[1231]) ).
thf(249,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( C
= ( k3_pralg_3 @ A @ B ) )
<=> ( ( ( k1_relat_1 @ C )
= ( k4_card_3 @ A ) )
& ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ D @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_pralg_3) ).
thf(3374,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( C
= ( k3_pralg_3 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= ( k4_card_3 @ A ) )
& ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ D @ B ) ) ) ) ) )
& ( ( ( ( k1_relat_1 @ C )
= ( k4_card_3 @ A ) )
& ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ D @ B ) ) ) ) )
=> ( C
= ( k3_pralg_3 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(1172,axiom,
! [A: $i] :
( ( k6_enumset1 @ A @ A @ A @ A @ A @ A @ A @ A )
= ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_enumset1) ).
thf(7711,plain,
! [A: $i] :
( ( k6_enumset1 @ A @ A @ A @ A @ A @ A @ A @ A )
= ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(971,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/sandbox2/benchmark/theBenchmark.p',t25_partfun1) ).
thf(6681,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)],[971]) ).
thf(927,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/sandbox2/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
thf(6470,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)],[927]) ).
thf(1569,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/sandbox2/benchmark/theBenchmark.p',t36_mcart_1) ).
thf(9612,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)],[1569]) ).
thf(564,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(4788,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)],[564]) ).
thf(1304,axiom,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ~ ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_realset1) ).
thf(8389,plain,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ~ ( v1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).
thf(923,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/sandbox2/benchmark/theBenchmark.p',t13_finsub_1) ).
thf(6455,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)],[923]) ).
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/sandbox2/benchmark/theBenchmark.p',d9_monoid_0) ).
thf(2403,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(530,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( v1_setfam_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_eqrel_1) ).
thf(4617,plain,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( v1_setfam_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(1892,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/sandbox2/benchmark/theBenchmark.p',t44_funct_2) ).
thf(11264,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)],[1892]) ).
thf(911,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/sandbox2/benchmark/theBenchmark.p',t59_subset_1) ).
thf(6396,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)],[911]) ).
thf(445,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/sandbox2/benchmark/theBenchmark.p',t54_setwiseo) ).
thf(4194,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)],[445]) ).
thf(1758,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/sandbox2/benchmark/theBenchmark.p',existence_m1_functor0) ).
thf(10516,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)],[1758]) ).
thf(2282,axiom,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset_1) ).
thf(13226,plain,
! [A: $i] : ( m1_subset_1 @ k1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2282]) ).
thf(1671,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/sandbox2/benchmark/theBenchmark.p',dt_k1_borsuk_1) ).
thf(10110,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)],[1671]) ).
thf(857,axiom,
! [A: $i] :
( ( k1_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_subset_1) ).
thf(6149,plain,
! [A: $i] :
( ( k1_subset_1 @ A )
= ( k3_subset_1 @ A @ ( k2_subset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(1466,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/sandbox2/benchmark/theBenchmark.p',t52_mcart_1) ).
thf(9155,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)],[1466]) ).
thf(1827,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/sandbox2/benchmark/theBenchmark.p',dt_k9_cat_2) ).
thf(10891,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)],[1827]) ).
thf(1330,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/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
thf(8571,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)],[1330]) ).
thf(540,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/sandbox2/benchmark/theBenchmark.p',t24_borsuk_1) ).
thf(4664,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)],[540]) ).
thf(1366,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_realset1 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_tex_2) ).
thf(8717,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)],[1366]) ).
thf(745,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/sandbox2/benchmark/theBenchmark.p',t11_relset_1) ).
thf(5604,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)],[745]) ).
thf(1614,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/sandbox2/benchmark/theBenchmark.p',t16_yellow_9) ).
thf(9843,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)],[1614]) ).
thf(1637,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/sandbox2/benchmark/theBenchmark.p',t34_subset_1) ).
thf(9941,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)],[1637]) ).
thf(1312,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/sandbox2/benchmark/theBenchmark.p',t80_funct_3) ).
thf(8468,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)],[1312]) ).
thf(1886,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/sandbox2/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(11247,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)],[1886]) ).
thf(702,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/sandbox2/benchmark/theBenchmark.p',t84_mcart_1) ).
thf(5397,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)],[702]) ).
thf(383,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A )
& ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(3919,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)],[383]) ).
thf(1122,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/sandbox2/benchmark/theBenchmark.p',t158_partfun1) ).
thf(7436,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)],[1122]) ).
thf(318,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 ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ ( k3_partfun1 @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_partfun1) ).
thf(3657,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 ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ ( k3_partfun1 @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(2189,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(12864,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2189]) ).
thf(2018,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/sandbox2/benchmark/theBenchmark.p',t16_subset_1) ).
thf(11991,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)],[2018]) ).
thf(84,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/sandbox2/benchmark/theBenchmark.p',t34_sysrel) ).
thf(2730,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)],[84]) ).
thf(771,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/sandbox2/benchmark/theBenchmark.p',t15_funct_5) ).
thf(5746,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)],[771]) ).
thf(2350,axiom,
? [A: $i] :
( ( m1_pboole @ A @ ( k2_zfmisc_1 @ f1_s2_altcat_1 @ f2_s2_altcat_1 ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s2_altcat_1 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f2_s2_altcat_1 )
=> ( ( k1_binop_1 @ A @ B @ C )
= ( f3_s2_altcat_1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_altcat_1) ).
thf(13489,plain,
? [A: $i] :
( ( m1_pboole @ A @ ( k2_zfmisc_1 @ f1_s2_altcat_1 @ f2_s2_altcat_1 ) )
& ! [B: $i] :
( ( m1_subset_1 @ B @ f1_s2_altcat_1 )
=> ! [C: $i] :
( ( m1_subset_1 @ C @ f2_s2_altcat_1 )
=> ( ( k1_binop_1 @ A @ B @ C )
= ( f3_s2_altcat_1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2350]) ).
thf(359,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k1_relat_1 @ ( k10_funct_6 @ A ) ) )
=> ( ( v1_relat_1 @ ( k1_funct_1 @ ( k10_funct_6 @ A ) @ B ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k10_funct_6 @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_funct_6) ).
thf(3835,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k1_relat_1 @ ( k10_funct_6 @ A ) ) )
=> ( ( v1_relat_1 @ ( k1_funct_1 @ ( k10_funct_6 @ A ) @ B ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k10_funct_6 @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(330,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( v2_relat_1 @ A )
<=> ~ ( r2_hidden @ k1_xboole_0 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_1) ).
thf(3708,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( ( v2_relat_1 @ A )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k2_relat_1 @ A ) ) )
& ( ~ ( r2_hidden @ k1_xboole_0 @ ( k2_relat_1 @ A ) )
=> ( v2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(765,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/sandbox2/benchmark/theBenchmark.p',d5_setwiseo) ).
thf(5727,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)],[765]) ).
thf(1345,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) )
& ( v1_finset_1 @ ( k2_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finset_1) ).
thf(8632,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)],[1345]) ).
thf(2235,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( A = k1_xboole_0 )
| ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finset_1) ).
thf(13044,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)],[2235]) ).
thf(492,axiom,
! [A: $i,B: $i] :
( ( ( k3_xboole_0 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ B ) )
=> ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(4471,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)],[492]) ).
thf(726,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k1_yellow_3 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_3) ).
thf(5493,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k1_yellow_3 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(1371,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_realset1) ).
thf(8738,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ~ ( v1_realset1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).
thf(906,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/sandbox2/benchmark/theBenchmark.p',t10_funct_7) ).
thf(6382,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)],[906]) ).
thf(225,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/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(3268,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)],[225]) ).
thf(2124,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/sandbox2/benchmark/theBenchmark.p',t67_setwiseo) ).
thf(12517,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)],[2124]) ).
thf(2176,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/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(12782,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)],[2176]) ).
thf(1803,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/sandbox2/benchmark/theBenchmark.p',dt_m1_triang_1) ).
thf(10764,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)],[1803]) ).
thf(1403,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/sandbox2/benchmark/theBenchmark.p',t41_sysrel) ).
thf(8870,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)],[1403]) ).
thf(1179,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( r2_hidden @ C @ B )
& ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ~ ( ( ( k1_funct_1 @ ( k5_funct_5 @ D ) @ C )
= E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ ( k2_relat_1 @ D ) )
& ! [F: $i] :
( ( r2_hidden @ F @ A )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ ( k4_tarski @ F @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_funct_5) ).
thf(7733,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( r2_hidden @ C @ B )
& ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ~ ( ( ( k1_funct_1 @ ( k5_funct_5 @ D ) @ C )
= E )
& ( ( k1_relat_1 @ E )
= A )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ ( k2_relat_1 @ D ) )
& ! [F: $i] :
( ( r2_hidden @ F @ A )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ ( k4_tarski @ F @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(1078,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/sandbox2/benchmark/theBenchmark.p',t71_funct_3) ).
thf(7236,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)],[1078]) ).
thf(904,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t151_funct_1) ).
thf(6364,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(349,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 ) )
=> ( ( ( ( k2_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_finseq_1) ).
thf(3788,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 ) )
=> ( ( ( ( k2_relat_1 @ A )
= ( k2_relat_1 @ B ) )
& ( v2_funct_1 @ A )
& ( v2_funct_1 @ B ) )
=> ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(524,axiom,
! [A: $i] : ( r2_hidden @ ( k6_relat_1 @ A ) @ ( k1_funct_2 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_altcat_1) ).
thf(4595,plain,
! [A: $i] : ( r2_hidden @ ( k6_relat_1 @ A ) @ ( k1_funct_2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',t7_setfam_1) ).
thf(2456,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)],[21]) ).
thf(1574,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/sandbox2/benchmark/theBenchmark.p',t54_domain_1) ).
thf(9636,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)],[1574]) ).
thf(2081,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/sandbox2/benchmark/theBenchmark.p',dt_k32_binop_2) ).
thf(12347,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)],[2081]) ).
thf(374,axiom,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k4_tarski @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_sysrel) ).
thf(3887,plain,
! [A: $i] :
( ( k6_relat_1 @ ( k1_tarski @ A ) )
= ( k1_tarski @ ( k4_tarski @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(551,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/sandbox2/benchmark/theBenchmark.p',t33_funct_1) ).
thf(4733,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)],[551]) ).
thf(395,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/sandbox2/benchmark/theBenchmark.p',d2_funct_4) ).
thf(3973,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)],[395]) ).
thf(685,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ? [C: $i] : ( m1_filter_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_filter_1) ).
thf(5311,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)],[685]) ).
thf(880,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/sandbox2/benchmark/theBenchmark.p',t146_funct_2) ).
thf(6259,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)],[880]) ).
thf(1617,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/sandbox2/benchmark/theBenchmark.p',t67_partfun1) ).
thf(9854,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)],[1617]) ).
thf(614,axiom,
! [A: $i,B: $i] :
( ( ( v2_relat_1 @ B )
& ( m1_pboole @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k4_card_3 @ B ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k1_relat_1 @ B ) )
& ! [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ E ) @ ( k1_funct_1 @ B @ E ) ) ) )
=> ( m1_subset_1 @ ( k1_funct_4 @ D @ C ) @ ( k4_card_3 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_pre_circ) ).
thf(4988,plain,
! [A: $i,B: $i] :
( ( ( v2_relat_1 @ B )
& ( m1_pboole @ B @ A ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k4_card_3 @ B ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k1_relat_1 @ B ) )
& ! [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ C ) )
=> ( r2_hidden @ ( k1_funct_1 @ C @ E ) @ ( k1_funct_1 @ B @ E ) ) ) )
=> ( m1_subset_1 @ ( k1_funct_4 @ D @ C ) @ ( k4_card_3 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(823,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/sandbox2/benchmark/theBenchmark.p',d1_multop_1) ).
thf(6002,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)],[823]) ).
thf(1499,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/sandbox2/benchmark/theBenchmark.p',t26_borsuk_1) ).
thf(9298,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)],[1499]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k2_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) )
= ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_zfmisc_1) ).
thf(4396,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)],[482]) ).
thf(2272,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/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(13195,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)],[2272]) ).
thf(1088,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/sandbox2/benchmark/theBenchmark.p',t12_funct_1) ).
thf(7268,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)],[1088]) ).
thf(1278,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/sandbox2/benchmark/theBenchmark.p',d3_realset1) ).
thf(8284,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)],[1278]) ).
thf(1779,axiom,
( ~ ( v1_xboole_0 @ k4_urysohn1 )
& ( v1_membered @ k4_urysohn1 )
& ( v2_membered @ k4_urysohn1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_urysohn1) ).
thf(10641,plain,
( ~ ( v1_xboole_0 @ k4_urysohn1 )
& ( v1_membered @ k4_urysohn1 )
& ( v2_membered @ k4_urysohn1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1779]) ).
thf(800,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/sandbox2/benchmark/theBenchmark.p',t13_relset_1) ).
thf(5892,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)],[800]) ).
thf(2204,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_fraenkel @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_fraenkel) ).
thf(12924,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_fraenkel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2204]) ).
thf(1800,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/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
thf(10746,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)],[1800]) ).
thf(2263,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/sandbox2/benchmark/theBenchmark.p',s4_altcat_1) ).
thf(13166,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)],[2263]) ).
thf(590,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/sandbox2/benchmark/theBenchmark.p',t135_partfun1) ).
thf(4903,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)],[590]) ).
thf(2033,axiom,
( ( v1_finset_1 @ f2_s21_fraenkel )
=> ( v1_finset_1 @ a_0_38_fraenkel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s21_fraenkel) ).
thf(12069,plain,
( ( v1_finset_1 @ f2_s21_fraenkel )
=> ( v1_finset_1 @ a_0_38_fraenkel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2033]) ).
thf(1140,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/sandbox2/benchmark/theBenchmark.p',t33_mcart_1) ).
thf(7564,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)],[1140]) ).
thf(1121,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/sandbox2/benchmark/theBenchmark.p',t30_funct_2) ).
thf(7423,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)],[1121]) ).
thf(401,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/sandbox2/benchmark/theBenchmark.p',t16_funct_7) ).
thf(4018,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)],[401]) ).
thf(583,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/sandbox2/benchmark/theBenchmark.p',d4_urysohn1) ).
thf(4857,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)],[583]) ).
thf(1095,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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_partfun1) ).
thf(7300,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)],[1095]) ).
thf(1082,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/sandbox2/benchmark/theBenchmark.p',fc4_binop_2) ).
thf(7245,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)],[1082]) ).
thf(1218,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/sandbox2/benchmark/theBenchmark.p',t176_orders_1) ).
thf(7969,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)],[1218]) ).
thf(233,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/sandbox2/benchmark/theBenchmark.p',t2_monoid_0) ).
thf(3295,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)],[233]) ).
thf(1934,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/sandbox2/benchmark/theBenchmark.p',t3_card_fil) ).
thf(11500,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)],[1934]) ).
thf(2006,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/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(11926,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)],[2006]) ).
thf(1448,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(9071,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k3_xboole_0 @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448]) ).
thf(2388,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/sandbox2/benchmark/theBenchmark.p',t5_tex_2) ).
thf(13647,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)],[2388]) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',fc1_urysohn1) ).
thf(2893,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)],[131]) ).
thf(690,axiom,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relset_2) ).
thf(5333,plain,
! [A: $i,B: $i] :
( ( k3_pua2mss1 @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_pua2mss1 @ A ) @ ( k3_pua2mss1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(574,axiom,
! [A: $i] :
( ~ ( v2_setfam_1 @ A )
=> ~ ( v1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_setfam_1) ).
thf(4820,plain,
! [A: $i] :
( ~ ( v2_setfam_1 @ A )
=> ~ ( v1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(942,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/sandbox2/benchmark/theBenchmark.p',t151_relat_1) ).
thf(6523,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)],[942]) ).
thf(1037,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/sandbox2/benchmark/theBenchmark.p',t27_partfun1) ).
thf(7104,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)],[1037]) ).
thf(1872,axiom,
! [A: $i] :
( ( v1_relat_1 @ ( k6_relat_1 @ A ) )
& ( v1_funct_1 @ ( k6_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(11154,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)],[1872]) ).
thf(1185,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/sandbox2/benchmark/theBenchmark.p',t76_funct_2) ).
thf(7775,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)],[1185]) ).
thf(1421,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 ) )
=> ( ( r4_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 )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d18_binop_1) ).
thf(8929,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 ) )
=> ( ( ( r4_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 )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ B @ 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 @ B @ D @ ( k2_binop_1 @ A @ A @ A @ C @ E @ F ) )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ E ) @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) ) ) ) ) )
=> ( r4_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421]) ).
thf(1110,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/sandbox2/benchmark/theBenchmark.p',fc2_funcop_1) ).
thf(7376,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)],[1110]) ).
thf(580,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/sandbox2/benchmark/theBenchmark.p',t39_relset_1) ).
thf(4847,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)],[580]) ).
thf(752,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/sandbox2/benchmark/theBenchmark.p',t9_borsuk_1) ).
thf(5680,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)],[752]) ).
thf(862,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(6187,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(893,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/sandbox2/benchmark/theBenchmark.p',fc2_altcat_1) ).
thf(6300,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)],[893]) ).
thf(412,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/sandbox2/benchmark/theBenchmark.p',t50_frechet2) ).
thf(4050,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)],[412]) ).
thf(2068,axiom,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_relat_1) ).
thf(12296,plain,
! [A: $i] :
( ( k9_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2068]) ).
thf(1802,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/sandbox2/benchmark/theBenchmark.p',dt_k10_funct_3) ).
thf(10757,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)],[1802]) ).
thf(1665,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ A @ B )
=> ( ( v1_xboole_0 @ B )
| ( r2_hidden @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(10085,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)],[1665]) ).
thf(1235,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k2_ens_1 @ A )
= ( a_1_1_ens_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ens_1) ).
thf(8065,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)],[1235]) ).
thf(1921,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/sandbox2/benchmark/theBenchmark.p',t132_funct_2) ).
thf(11398,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)],[1921]) ).
thf(991,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/sandbox2/benchmark/theBenchmark.p',t91_orders_1) ).
thf(6841,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)],[991]) ).
thf(2158,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/sandbox2/benchmark/theBenchmark.p',t23_funct_7) ).
thf(12703,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)],[2158]) ).
thf(2067,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_zfmisc_1 @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( r1_tarski @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(12276,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)],[2067]) ).
thf(173,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 ) )
=> ( ( k2_cat_2 @ A @ B @ C @ D )
= ( k3_funct_5 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_cat_2) ).
thf(3093,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 ) )
=> ( ( k2_cat_2 @ A @ B @ C @ D )
= ( k3_funct_5 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(425,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/sandbox2/benchmark/theBenchmark.p',t74_enumset1) ).
thf(4115,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)],[425]) ).
thf(1723,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/sandbox2/benchmark/theBenchmark.p',t2_funct_3) ).
thf(10378,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)],[1723]) ).
thf(1378,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/sandbox2/benchmark/theBenchmark.p',redefinition_k7_relset_1) ).
thf(8759,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)],[1378]) ).
thf(1048,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(7139,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)],[1048]) ).
thf(2134,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/sandbox2/benchmark/theBenchmark.p',t84_funct_3) ).
thf(12582,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)],[2134]) ).
thf(1316,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/sandbox2/benchmark/theBenchmark.p',t50_funct_2) ).
thf(8479,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)],[1316]) ).
thf(562,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/sandbox2/benchmark/theBenchmark.p',t46_subset_1) ).
thf(4783,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)],[562]) ).
thf(342,axiom,
! [A: $i] :
( ( k2_funct_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_funct_1) ).
thf(3771,plain,
! [A: $i] :
( ( k2_funct_1 @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(571,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k3_tarski @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) @ ( k10_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_funct_3) ).
thf(4810,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k3_tarski @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) @ ( k10_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(2195,axiom,
v1_xboole_0 @ k1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(12888,plain,
v1_xboole_0 @ k1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2195]) ).
thf(1849,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_sysrel) ).
thf(11036,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1849]) ).
thf(2217,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/sandbox2/benchmark/theBenchmark.p',s4_domain_1) ).
thf(12981,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)],[2217]) ).
thf(1951,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 ) )
=> ( ( r5_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 @ ( 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/sandbox2/benchmark/theBenchmark.p',d10_binop_1) ).
thf(11632,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 ) )
=> ( ( ( r5_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 @ ( 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 @ ( k1_binop_1 @ C @ D @ E ) @ F )
= ( k1_binop_1 @ C @ ( k1_binop_1 @ B @ D @ F ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) )
=> ( r5_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1951]) ).
thf(1903,axiom,
! [A: $i] : ( m2_relset_1 @ ( k1_eqrel_1 @ A ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_eqrel_1) ).
thf(11325,plain,
! [A: $i] : ( m2_relset_1 @ ( k1_eqrel_1 @ A ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1903]) ).
thf(1332,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/sandbox2/benchmark/theBenchmark.p',t9_mssubfam) ).
thf(8575,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)],[1332]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',t6_setfam_1) ).
thf(2483,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)],[28]) ).
thf(576,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ ( k1_relat_1 @ A ) )
= ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
thf(4825,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)],[576]) ).
thf(90,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/sandbox2/benchmark/theBenchmark.p',idempotence_k5_setwiseo) ).
thf(2750,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)],[90]) ).
thf(250,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 ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
& ( D
= ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ D ) )
& ( ( k1_funct_1 @ D @ B )
= ( k1_funct_1 @ C @ ( k4_tarski @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_5) ).
thf(3389,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 ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
& ( D
= ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ D ) )
& ( ( k1_funct_1 @ D @ B )
= ( k1_funct_1 @ C @ ( k4_tarski @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1230,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/sandbox2/benchmark/theBenchmark.p',t78_finseq_2) ).
thf(8050,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)],[1230]) ).
thf(959,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( r2_hidden @ C @ A )
& ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ~ ( ( ( k1_funct_1 @ ( k3_funct_5 @ D ) @ C )
= E )
& ( ( k1_relat_1 @ E )
= B )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ ( k2_relat_1 @ D ) )
& ! [F: $i] :
( ( r2_hidden @ F @ B )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ ( k4_tarski @ C @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_funct_5) ).
thf(6591,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
& ( ( k1_relat_1 @ D )
= ( k2_zfmisc_1 @ A @ B ) )
& ( r2_hidden @ C @ A )
& ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ~ ( ( ( k1_funct_1 @ ( k3_funct_5 @ D ) @ C )
= E )
& ( ( k1_relat_1 @ E )
= B )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ ( k2_relat_1 @ D ) )
& ! [F: $i] :
( ( r2_hidden @ F @ B )
=> ( ( k1_funct_1 @ E @ F )
= ( k1_funct_1 @ D @ ( k4_tarski @ C @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(2120,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(12504,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)],[2120]) ).
thf(811,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k1_funct_2 @ A @ ( k1_funct_2 @ B @ C ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ! [F: $i] :
( ( ( v1_relat_1 @ F )
& ( v1_funct_1 @ F ) )
=> ! [G: $i,H: $i] :
( ( ( r2_hidden @ G @ A )
& ( r2_hidden @ H @ B )
& ( ( k1_funct_1 @ D @ G )
= E )
& ( ( k1_funct_1 @ ( k10_funct_6 @ D ) @ H )
= F ) )
=> ( ( ( k1_funct_1 @ F @ G )
= ( k1_funct_1 @ E @ H ) )
& ( ( k1_relat_1 @ F )
= A )
& ( ( k1_relat_1 @ E )
= B )
& ( r1_tarski @ ( k2_relat_1 @ F ) @ C )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_funct_6) ).
thf(5929,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k1_funct_2 @ A @ ( k1_funct_2 @ B @ C ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ! [F: $i] :
( ( ( v1_relat_1 @ F )
& ( v1_funct_1 @ F ) )
=> ! [G: $i,H: $i] :
( ( ( r2_hidden @ G @ A )
& ( r2_hidden @ H @ B )
& ( ( k1_funct_1 @ D @ G )
= E )
& ( ( k1_funct_1 @ ( k10_funct_6 @ D ) @ H )
= F ) )
=> ( ( ( k1_funct_1 @ F @ G )
= ( k1_funct_1 @ E @ H ) )
& ( ( k1_relat_1 @ F )
= A )
& ( ( k1_relat_1 @ E )
= B )
& ( r1_tarski @ ( k2_relat_1 @ F ) @ C )
& ( r1_tarski @ ( k2_relat_1 @ E ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1729,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/sandbox2/benchmark/theBenchmark.p',t19_setwiseo) ).
thf(10404,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)],[1729]) ).
thf(2152,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/sandbox2/benchmark/theBenchmark.p',dt_k10_setwiseo) ).
thf(12678,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)],[2152]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( m1_subset_1 @ B @ k5_numbers ) )
=> ( ( v1_relat_1 @ ( k9_funct_7 @ A @ B ) )
& ( v1_funct_1 @ ( k9_funct_7 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_funct_7) ).
thf(2437,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( m1_subset_1 @ B @ k5_numbers ) )
=> ( ( v1_relat_1 @ ( k9_funct_7 @ A @ B ) )
& ( v1_funct_1 @ ( k9_funct_7 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1023,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/sandbox2/benchmark/theBenchmark.p',t85_mcart_1) ).
thf(7036,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)],[1023]) ).
thf(1784,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
thf(10670,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1784]) ).
thf(1627,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/sandbox2/benchmark/theBenchmark.p',cc7_tex_2) ).
thf(9897,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)],[1627]) ).
thf(697,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/sandbox2/benchmark/theBenchmark.p',t11_funct_4) ).
thf(5353,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)],[697]) ).
thf(1680,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(10145,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1680]) ).
thf(1368,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/sandbox2/benchmark/theBenchmark.p',t63_funct_5) ).
thf(8727,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)],[1368]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_fraenkel @ C @ A @ B ) )
=> ! [D: $i] :
( ( m2_fraenkel @ D @ A @ B @ C )
=> ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ A @ B )
& ( m2_relset_1 @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_fraenkel) ).
thf(2618,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_fraenkel @ C @ A @ B ) )
=> ! [D: $i] :
( ( m2_fraenkel @ D @ 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)],[50]) ).
thf(116,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 ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ ( k1_relat_1 @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( ( k5_funct_5 @ C )
= ( k5_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_5) ).
thf(2833,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 ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ ( k1_relat_1 @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( ( k5_funct_5 @ C )
= ( k5_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(203,axiom,
( ( ( k3_funct_5 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k5_funct_5 @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_funct_5) ).
thf(3189,plain,
( ( ( k3_funct_5 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k5_funct_5 @ k1_xboole_0 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(1711,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/sandbox2/benchmark/theBenchmark.p',t49_funcop_1) ).
thf(10303,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)],[1711]) ).
thf(578,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k10_relat_1 @ B @ ( k10_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t181_relat_1) ).
thf(4842,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ A )
= ( k10_relat_1 @ B @ ( k10_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(1382,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/sandbox2/benchmark/theBenchmark.p',t32_setwiseo) ).
thf(8774,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)],[1382]) ).
thf(661,axiom,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(5210,plain,
! [A: $i] :
( ( k3_tarski @ ( k1_zfmisc_1 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(1647,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/sandbox2/benchmark/theBenchmark.p',t2_mssubfam) ).
thf(9970,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)],[1647]) ).
thf(1488,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/sandbox2/benchmark/theBenchmark.p',d8_realset1) ).
thf(9255,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)],[1488]) ).
thf(847,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/sandbox2/benchmark/theBenchmark.p',t136_funct_2) ).
thf(6110,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)],[847]) ).
thf(1469,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/sandbox2/benchmark/theBenchmark.p',t34_funct_4) ).
thf(9167,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)],[1469]) ).
thf(279,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/sandbox2/benchmark/theBenchmark.p',dt_k4_finseq_1) ).
thf(3505,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)],[279]) ).
thf(2347,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/sandbox2/benchmark/theBenchmark.p',s4_filter_1) ).
thf(13479,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)],[2347]) ).
thf(1101,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/sandbox2/benchmark/theBenchmark.p',redefinition_k1_functor0) ).
thf(7336,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)],[1101]) ).
thf(2392,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/sandbox2/benchmark/theBenchmark.p',s23_fraenkel) ).
thf(13668,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)],[2392]) ).
thf(777,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k3_funct_2 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_funct_2) ).
thf(5772,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ C )
& ( m1_relset_1 @ C @ A @ B ) )
=> ( ( k3_funct_2 @ A @ B @ C @ D )
= ( k10_relat_1 @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(355,axiom,
! [A: $i,B: $i] :
( ( r2_wellord2 @ A @ ( k1_tarski @ B ) )
<=> ? [C: $i] :
( A
= ( k1_tarski @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_card_1) ).
thf(3808,plain,
! [A: $i,B: $i] :
( ( ( r2_wellord2 @ A @ ( k1_tarski @ B ) )
=> ? [C: $i] :
( A
= ( k1_tarski @ C ) ) )
& ( ? [C: $i] :
( A
= ( k1_tarski @ C ) )
=> ( r2_wellord2 @ A @ ( k1_tarski @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(1982,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/sandbox2/benchmark/theBenchmark.p',t16_cantor_1) ).
thf(11806,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)],[1982]) ).
thf(1461,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/sandbox2/benchmark/theBenchmark.p',t43_funcop_1) ).
thf(9140,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)],[1461]) ).
thf(1925,axiom,
r1_tarski @ k1_qc_lang1 @ ( k12_mcart_1 @ k1_numbers @ k1_numbers @ k5_numbers @ k5_numbers ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_qc_lang1) ).
thf(11413,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)],[1925]) ).
thf(2073,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_domain_1) ).
thf(12315,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)],[2073]) ).
thf(1205,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/sandbox2/benchmark/theBenchmark.p',t29_funct_2) ).
thf(7909,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)],[1205]) ).
thf(463,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k3_funct_3 @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) )
& ! [C: $i] :
( ( r1_tarski @ C @ ( k2_relat_1 @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( k10_relat_1 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_funct_3) ).
thf(4307,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k3_funct_3 @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) )
& ! [C: $i] :
( ( r1_tarski @ C @ ( k2_relat_1 @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( k10_relat_1 @ A @ C ) ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) )
& ! [C: $i] :
( ( r1_tarski @ C @ ( k2_relat_1 @ A ) )
=> ( ( k1_funct_1 @ B @ C )
= ( k10_relat_1 @ A @ C ) ) ) )
=> ( B
= ( k3_funct_3 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(1292,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/sandbox2/benchmark/theBenchmark.p',t27_setwiseo) ).
thf(8347,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)],[1292]) ).
thf(1213,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/sandbox2/benchmark/theBenchmark.p',t11_realset1) ).
thf(7954,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)],[1213]) ).
thf(1809,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/sandbox2/benchmark/theBenchmark.p',dt_k4_funct_2) ).
thf(10784,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)],[1809]) ).
thf(2243,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/sandbox2/benchmark/theBenchmark.p',t1_yellow_3) ).
thf(13072,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)],[2243]) ).
thf(694,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/sandbox2/benchmark/theBenchmark.p',t149_funct_2) ).
thf(5343,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)],[694]) ).
thf(2062,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/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(12249,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)],[2062]) ).
thf(650,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/sandbox2/benchmark/theBenchmark.p',t27_funct_1) ).
thf(5169,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)],[650]) ).
thf(1441,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/sandbox2/benchmark/theBenchmark.p',t70_funcop_1) ).
thf(9035,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)],[1441]) ).
thf(2328,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/sandbox2/benchmark/theBenchmark.p',s3_filter_1) ).
thf(13397,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)],[2328]) ).
thf(1828,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/sandbox2/benchmark/theBenchmark.p',t60_funct_2) ).
thf(10895,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)],[1828]) ).
thf(1309,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/sandbox2/benchmark/theBenchmark.p',redefinition_k16_funct_3) ).
thf(8459,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)],[1309]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( v2_relat_1 @ B )
<=> ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( v1_xboole_0 @ ( k1_funct_1 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_pboole) ).
thf(3243,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( ( v2_relat_1 @ B )
=> ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( v1_xboole_0 @ ( k1_funct_1 @ B @ C ) ) ) )
& ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( v1_xboole_0 @ ( k1_funct_1 @ B @ C ) ) )
=> ( v2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k4_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_relat_1) ).
thf(2809,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)],[109]) ).
thf(1073,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/sandbox2/benchmark/theBenchmark.p',t22_relset_1) ).
thf(7213,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)],[1073]) ).
thf(408,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/sandbox2/benchmark/theBenchmark.p',t70_funct_3) ).
thf(4038,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)],[408]) ).
thf(1513,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/sandbox2/benchmark/theBenchmark.p',redefinition_k1_partfun1) ).
thf(9368,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)],[1513]) ).
thf(1482,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/sandbox2/benchmark/theBenchmark.p',redefinition_k1_borsuk_1) ).
thf(9236,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)],[1482]) ).
thf(1895,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/sandbox2/benchmark/theBenchmark.p',t78_funct_3) ).
thf(11270,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)],[1895]) ).
thf(1771,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ( k9_relat_1 @ ( k5_setfam_1 @ ( k2_zfmisc_1 @ A @ B ) @ D ) @ C )
= ( k3_tarski @ ( a_4_3_relset_2 @ A @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_relset_2) ).
thf(10574,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ( ( k9_relat_1 @ ( k5_setfam_1 @ ( k2_zfmisc_1 @ A @ B ) @ D ) @ C )
= ( k3_tarski @ ( a_4_3_relset_2 @ A @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1771]) ).
thf(2009,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/sandbox2/benchmark/theBenchmark.p',dt_k16_funct_3) ).
thf(11954,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)],[2009]) ).
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] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',t82_funct_4) ).
thf(8892,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)],[1410]) ).
thf(148,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/sandbox2/benchmark/theBenchmark.p',t155_relat_1) ).
thf(2965,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)],[148]) ).
thf(1943,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_0_pua2mss1) ).
thf(11596,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)],[1943]) ).
thf(504,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/sandbox2/benchmark/theBenchmark.p',t94_relat_1) ).
thf(4519,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)],[504]) ).
thf(1869,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
<=> ( v1_finset_1 @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_finset_1) ).
thf(11143,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)],[1869]) ).
thf(1915,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/sandbox2/benchmark/theBenchmark.p',t42_yellow_9) ).
thf(11367,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)],[1915]) ).
thf(477,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/sandbox2/benchmark/theBenchmark.p',t8_relset_1) ).
thf(4379,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)],[477]) ).
thf(1436,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_funct_5 @ B ) ) )
& ( C
= ( k1_funct_1 @ ( k5_funct_5 @ B ) @ A ) ) )
=> ( ( ( k1_relat_1 @ C )
= ( k1_funct_5 @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k2_zfmisc_1 @ ( k1_funct_5 @ ( k1_relat_1 @ B ) ) @ ( k1_tarski @ A ) ) ) ) )
& ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k1_funct_5 @ ( k1_relat_1 @ B ) ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k2_relat_1 @ B ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ ( k4_tarski @ D @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ D @ A ) @ ( k1_relat_1 @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_funct_5) ).
thf(9007,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_funct_5 @ B ) ) )
& ( C
= ( k1_funct_1 @ ( k5_funct_5 @ B ) @ A ) ) )
=> ( ( ( k1_relat_1 @ C )
= ( k1_funct_5 @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k2_zfmisc_1 @ ( k1_funct_5 @ ( k1_relat_1 @ B ) ) @ ( k1_tarski @ A ) ) ) ) )
& ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k1_funct_5 @ ( k1_relat_1 @ B ) ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k2_relat_1 @ B ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ ( k4_tarski @ D @ A ) ) )
& ( r2_hidden @ ( k4_tarski @ D @ A ) @ ( k1_relat_1 @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436]) ).
thf(785,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/sandbox2/benchmark/theBenchmark.p',t13_setwiseo) ).
thf(5819,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)],[785]) ).
thf(1634,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/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).
thf(9923,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)],[1634]) ).
thf(1166,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/sandbox2/benchmark/theBenchmark.p',t14_relat_1) ).
thf(7688,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)],[1166]) ).
thf(1493,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ k1_numbers )
=> ( m1_subset_1 @ ( k7_binop_2 @ A ) @ k1_numbers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_binop_2) ).
thf(9272,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)],[1493]) ).
thf(1130,axiom,
! [A: $i,B: $i] :
( ( k1_funct_2 @ A @ ( k1_tarski @ B ) )
= ( k1_tarski @ ( k2_funcop_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_5) ).
thf(7460,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)],[1130]) ).
thf(1912,axiom,
! [A: $i,B: $i] :
( ( ( k3_zfmisc_1 @ A @ A @ A )
= ( k3_zfmisc_1 @ B @ B @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_mcart_1) ).
thf(11357,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)],[1912]) ).
thf(818,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k8_relat_1 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
thf(5970,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k8_relat_1 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(995,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/sandbox2/benchmark/theBenchmark.p',t25_finset_1) ).
thf(6860,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)],[995]) ).
thf(129,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k5_funct_5 @ A )
= ( k3_funct_5 @ ( k2_funct_4 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_5) ).
thf(2884,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k5_funct_5 @ A )
= ( k3_funct_5 @ ( k2_funct_4 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(2287,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/sandbox2/benchmark/theBenchmark.p',redefinition_k16_domain_1) ).
thf(13248,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)],[2287]) ).
thf(496,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/sandbox2/benchmark/theBenchmark.p',t58_zfmisc_1) ).
thf(4483,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)],[496]) ).
thf(1564,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_2_domain_1) ).
thf(9584,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)],[1564]) ).
thf(1076,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/sandbox2/benchmark/theBenchmark.p',t11_funcop_1) ).
thf(7230,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)],[1076]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $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 ) )
=> ( m2_fraenkel @ ( k3_funcsdom @ A @ B @ C ) @ A @ B @ ( k1_fraenkel @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_funcsdom) ).
thf(3510,plain,
! [A: $i,B: $i,C: $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 ) )
=> ( m2_fraenkel @ ( k3_funcsdom @ A @ B @ C ) @ A @ B @ ( k1_fraenkel @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(416,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/sandbox2/benchmark/theBenchmark.p',t83_mcart_1) ).
thf(4065,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)],[416]) ).
thf(1598,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/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
thf(9738,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)],[1598]) ).
thf(2352,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
thf(13494,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)],[2352]) ).
thf(2285,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/sandbox2/benchmark/theBenchmark.p',s11_funct_2) ).
thf(13231,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)],[2285]) ).
thf(1325,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/sandbox2/benchmark/theBenchmark.p',fc17_binop_2) ).
thf(8508,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)],[1325]) ).
thf(1593,axiom,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(9720,plain,
! [A: $i] : ( r1_tarski @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1593]) ).
thf(647,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/sandbox2/benchmark/theBenchmark.p',fc3_functor0) ).
thf(5157,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)],[647]) ).
thf(1420,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/sandbox2/benchmark/theBenchmark.p',t93_relat_1) ).
thf(8927,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)],[1420]) ).
thf(1755,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/sandbox2/benchmark/theBenchmark.p',t8_altcat_1) ).
thf(10506,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)],[1755]) ).
thf(972,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/sandbox2/benchmark/theBenchmark.p',fc6_funcop_1) ).
thf(6684,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)],[972]) ).
thf(2077,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/sandbox2/benchmark/theBenchmark.p',s3_domain_1) ).
thf(12333,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)],[2077]) ).
thf(2205,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/sandbox2/benchmark/theBenchmark.p',cc1_tex_2) ).
thf(12927,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)],[2205]) ).
thf(878,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/sandbox2/benchmark/theBenchmark.p',t132_partfun1) ).
thf(6250,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)],[878]) ).
thf(1475,axiom,
! [A: $i,B: $i] :
( ( k2_funcop_1 @ ( k1_tarski @ A ) @ B )
= ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_4) ).
thf(9209,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)],[1475]) ).
thf(739,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/sandbox2/benchmark/theBenchmark.p',t143_partfun1) ).
thf(5562,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)],[739]) ).
thf(1930,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/sandbox2/benchmark/theBenchmark.p',d4_cantor_1) ).
thf(11456,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)],[1930]) ).
thf(518,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k5_relat_1 @ A @ ( k2_funcop_1 @ B @ C ) )
= ( k2_funcop_1 @ ( k10_relat_1 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funcop_1) ).
thf(4576,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k5_relat_1 @ A @ ( k2_funcop_1 @ B @ C ) )
= ( k2_funcop_1 @ ( k10_relat_1 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(1697,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_0_yellow_3) ).
thf(10216,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)],[1697]) ).
thf(681,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/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(5298,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)],[681]) ).
thf(1438,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/sandbox2/benchmark/theBenchmark.p',t64_funcop_1) ).
thf(9026,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)],[1438]) ).
thf(887,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/sandbox2/benchmark/theBenchmark.p',t7_msualg_1) ).
thf(6282,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)],[887]) ).
thf(1376,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/sandbox2/benchmark/theBenchmark.p',t72_funct_3) ).
thf(8751,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)],[1376]) ).
thf(1654,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/sandbox2/benchmark/theBenchmark.p',free_g1_cat_1) ).
thf(9997,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)],[1654]) ).
thf(1159,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/sandbox2/benchmark/theBenchmark.p',dt_k4_domain_1) ).
thf(7657,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)],[1159]) ).
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 ) )
=> ( ( r1_tarski @ A @ C )
=> ( ( k2_partfun1 @ A @ B @ D @ C )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_2) ).
thf(11159,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)],[1873]) ).
thf(1538,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/sandbox2/benchmark/theBenchmark.p',t66_funct_2) ).
thf(9472,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)],[1538]) ).
thf(1632,axiom,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(9917,plain,
! [A: $i] :
( ( r1_tarski @ A @ ( k2_zfmisc_1 @ A @ A ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1632]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ B )
=> ( ( ( k8_relat_1 @ B @ ( k8_relat_1 @ A @ C ) )
= ( k8_relat_1 @ A @ C ) )
& ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_funct_1) ).
thf(3899,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ A @ B )
=> ( ( ( k8_relat_1 @ B @ ( k8_relat_1 @ A @ C ) )
= ( k8_relat_1 @ A @ C ) )
& ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(1433,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/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_4) ).
thf(8999,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)],[1433]) ).
thf(1939,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/sandbox2/benchmark/theBenchmark.p',t17_funct_5) ).
thf(11555,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)],[1939]) ).
thf(2311,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ D ) ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_domain_1__e1_46__relset_2) ).
thf(13337,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
& ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ D ) ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2311]) ).
thf(2000,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/sandbox2/benchmark/theBenchmark.p',d2_card_fil) ).
thf(11897,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)],[2000]) ).
thf(953,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/sandbox2/benchmark/theBenchmark.p',t177_orders_1) ).
thf(6560,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)],[953]) ).
thf(588,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/sandbox2/benchmark/theBenchmark.p',redefinition_k3_setwiseo) ).
thf(4893,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)],[588]) ).
thf(466,axiom,
! [A: $i,B: $i] :
( ( k5_enumset1 @ A @ A @ A @ A @ A @ A @ B )
= ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_enumset1) ).
thf(4323,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)],[466]) ).
thf(1187,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/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(7782,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)],[1187]) ).
thf(1061,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/sandbox2/benchmark/theBenchmark.p',t26_setwiseo) ).
thf(7179,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)],[1061]) ).
thf(2283,axiom,
m1_subset_1 @ a_0_0_domain_1 @ ( k1_zfmisc_1 @ f1_s7_domain_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s7_domain_1) ).
thf(13228,plain,
m1_subset_1 @ a_0_0_domain_1 @ ( k1_zfmisc_1 @ f1_s7_domain_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2283]) ).
thf(607,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k8_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(4962,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k8_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(1347,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/sandbox2/benchmark/theBenchmark.p',t73_finseq_1) ).
thf(8640,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)],[1347]) ).
thf(829,axiom,
! [A: $i] :
( ( k4_enumset1 @ A @ A @ A @ A @ A @ A )
= ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_enumset1) ).
thf(6020,plain,
! [A: $i] :
( ( k4_enumset1 @ A @ A @ A @ A @ A @ A )
= ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(486,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/sandbox2/benchmark/theBenchmark.p',t165_funct_2) ).
thf(4407,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)],[486]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_card_fil) ).
thf(2473,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)],[26]) ).
thf(1501,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/sandbox2/benchmark/theBenchmark.p',t42_zfmisc_1) ).
thf(9308,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)],[1501]) ).
thf(2228,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/sandbox2/benchmark/theBenchmark.p',t4_cantor_1) ).
thf(13017,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)],[2228]) ).
thf(2229,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/sandbox2/benchmark/theBenchmark.p',d1_filter_2) ).
thf(13019,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)],[2229]) ).
thf(1300,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/sandbox2/benchmark/theBenchmark.p',t18_relat_1) ).
thf(8375,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)],[1300]) ).
thf(705,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/sandbox2/benchmark/theBenchmark.p',t44_funct_4) ).
thf(5411,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)],[705]) ).
thf(1177,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/sandbox2/benchmark/theBenchmark.p',t38_card_3) ).
thf(7725,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)],[1177]) ).
thf(1238,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( k8_relat_1 @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t125_relat_1) ).
thf(8078,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ A )
=> ( ( k8_relat_1 @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(495,axiom,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(4480,plain,
! [A: $i,B: $i] :
( ( k2_tarski @ A @ B )
= ( k2_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(835,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ ( k3_xboole_0 @ B @ C ) )
=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_xboole_1) ).
thf(6047,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)],[835]) ).
thf(2234,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/sandbox2/benchmark/theBenchmark.p',t63_partfun1) ).
thf(13038,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)],[2234]) ).
thf(841,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/sandbox2/benchmark/theBenchmark.p',t53_funct_2) ).
thf(6064,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)],[841]) ).
thf(649,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finseq_1) ).
thf(5167,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)],[649]) ).
thf(1985,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/sandbox2/benchmark/theBenchmark.p',t21_borsuk_1) ).
thf(11820,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)],[1985]) ).
thf(2336,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k8_relset_2 @ A @ B @ C @ ( k5_subset_1 @ ( k2_zfmisc_1 @ A @ B ) @ D @ E ) )
= ( k5_subset_1 @ B @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k8_relset_2 @ A @ B @ C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_relset_2) ).
thf(13426,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k8_relset_2 @ A @ B @ C @ ( k5_subset_1 @ ( k2_zfmisc_1 @ A @ B ) @ D @ E ) )
= ( k5_subset_1 @ B @ ( k8_relset_2 @ A @ B @ C @ D ) @ ( k8_relset_2 @ A @ B @ C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2336]) ).
thf(475,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/sandbox2/benchmark/theBenchmark.p',t5_mcart_1) ).
thf(4370,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)],[475]) ).
thf(593,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/sandbox2/benchmark/theBenchmark.p',t1_tex_2) ).
thf(4910,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)],[593]) ).
thf(2132,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
<=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(12565,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)],[2132]) ).
thf(2219,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(12985,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2219]) ).
thf(733,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/sandbox2/benchmark/theBenchmark.p',t49_funct_2) ).
thf(5540,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)],[733]) ).
thf(405,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/sandbox2/benchmark/theBenchmark.p',t50_relset_1) ).
thf(4031,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)],[405]) ).
thf(1586,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/sandbox2/benchmark/theBenchmark.p',redefinition_k8_setwiseo) ).
thf(9688,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)],[1586]) ).
thf(2043,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/sandbox2/benchmark/theBenchmark.p',s14_funct_2) ).
thf(12127,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)],[2043]) ).
thf(62,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k3_funct_3 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k3_funct_3 @ B ) @ ( k3_funct_3 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_3) ).
thf(2660,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k3_funct_3 @ ( k5_relat_1 @ A @ B ) )
= ( k5_relat_1 @ ( k3_funct_3 @ B ) @ ( k3_funct_3 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(415,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/sandbox2/benchmark/theBenchmark.p',d15_binop_1) ).
thf(4059,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)],[415]) ).
thf(1748,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/sandbox2/benchmark/theBenchmark.p',t12_tops_2) ).
thf(10477,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)],[1748]) ).
thf(1443,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_8_domain_1) ).
thf(9041,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)],[1443]) ).
thf(135,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/sandbox2/benchmark/theBenchmark.p',t62_finseq_3) ).
thf(2905,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)],[135]) ).
thf(2051,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_3_domain_1) ).
thf(12169,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)],[2051]) ).
thf(919,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/sandbox2/benchmark/theBenchmark.p',t23_funcop_1) ).
thf(6442,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)],[919]) ).
thf(617,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/sandbox2/benchmark/theBenchmark.p',t83_zfmisc_1) ).
thf(4999,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)],[617]) ).
thf(1882,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/sandbox2/benchmark/theBenchmark.p',t10_tops_2) ).
thf(11202,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)],[1882]) ).
thf(1518,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/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
thf(9384,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)],[1518]) ).
thf(2387,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/sandbox2/benchmark/theBenchmark.p',t53_setfam_1) ).
thf(13644,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)],[2387]) ).
thf(1623,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/sandbox2/benchmark/theBenchmark.p',t1_funct_4) ).
thf(9881,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)],[1623]) ).
thf(1963,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_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k1_binop_1 @ ( k18_pralg_1 @ A @ B @ C ) @ E @ D )
= ( k1_binop_1 @ C @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_altcat_2) ).
thf(11698,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_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ B )
=> ( ( k1_binop_1 @ ( k18_pralg_1 @ A @ B @ C ) @ E @ D )
= ( k1_binop_1 @ C @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1963]) ).
thf(1898,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/sandbox2/benchmark/theBenchmark.p',t61_domain_1) ).
thf(11292,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)],[1898]) ).
thf(2039,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/sandbox2/benchmark/theBenchmark.p',t75_relat_1) ).
thf(12110,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)],[2039]) ).
thf(849,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/sandbox2/benchmark/theBenchmark.p',dt_m2_card_fil) ).
thf(6124,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)],[849]) ).
thf(2214,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/sandbox2/benchmark/theBenchmark.p',dt_m1_filter_1) ).
thf(12970,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)],[2214]) ).
thf(1340,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/sandbox2/benchmark/theBenchmark.p',t100_relat_1) ).
thf(8608,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)],[1340]) ).
thf(1775,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/sandbox2/benchmark/theBenchmark.p',dt_k3_binop_1) ).
thf(10612,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)],[1775]) ).
thf(2155,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/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(12687,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)],[2155]) ).
thf(1239,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/sandbox2/benchmark/theBenchmark.p',t28_partfun1) ).
thf(8081,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)],[1239]) ).
thf(934,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/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funcop_1) ).
thf(6496,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)],[934]) ).
thf(938,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) )
& ( v1_realset1 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_realset1) ).
thf(6509,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)],[938]) ).
thf(2361,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/sandbox2/benchmark/theBenchmark.p',s4_subset_1) ).
thf(13547,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)],[2361]) ).
thf(1178,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/sandbox2/benchmark/theBenchmark.p',t49_funct_4) ).
thf(7730,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)],[1178]) ).
thf(967,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/sandbox2/benchmark/theBenchmark.p',d7_monoid_0) ).
thf(6652,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)],[967]) ).
thf(2289,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/sandbox2/benchmark/theBenchmark.p',dt_k9_relset_2) ).
thf(13260,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)],[2289]) ).
thf(595,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/sandbox2/benchmark/theBenchmark.p',t124_zfmisc_1) ).
thf(4915,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)],[595]) ).
thf(2107,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/sandbox2/benchmark/theBenchmark.p',t6_fraenkel) ).
thf(12437,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)],[2107]) ).
thf(1594,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_domain_1) ).
thf(9722,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)],[1594]) ).
thf(2091,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/sandbox2/benchmark/theBenchmark.p',t49_relat_1) ).
thf(12385,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)],[2091]) ).
thf(902,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/sandbox2/benchmark/theBenchmark.p',t74_mcart_1) ).
thf(6343,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)],[902]) ).
thf(843,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ A )
=> ( ( k5_relat_1 @ ( k6_partfun1 @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_functor0) ).
thf(6079,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)],[843]) ).
thf(45,axiom,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(2601,plain,
! [A: $i] :
( ( k4_xboole_0 @ A @ k1_xboole_0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(331,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k5_funct_5 @ A ) )
& ( v1_funct_1 @ ( k5_funct_5 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_funct_5) ).
thf(3711,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k5_funct_5 @ A ) )
& ( v1_funct_1 @ ( k5_funct_5 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(85,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/sandbox2/benchmark/theBenchmark.p',t39_partfun1) ).
thf(2733,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)],[85]) ).
thf(2225,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/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(13002,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)],[2225]) ).
thf(877,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/sandbox2/benchmark/theBenchmark.p',t29_setwiseo) ).
thf(6247,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)],[877]) ).
thf(618,axiom,
! [A: $i] : ( v3_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_setwiseo) ).
thf(5002,plain,
! [A: $i] : ( v3_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(1315,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/sandbox2/benchmark/theBenchmark.p',t75_funcop_1) ).
thf(8476,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)],[1315]) ).
thf(782,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/sandbox2/benchmark/theBenchmark.p',t16_pua2mss1) ).
thf(5794,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)],[782]) ).
thf(2148,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/sandbox2/benchmark/theBenchmark.p',t1_cantor_1) ).
thf(12664,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)],[2148]) ).
thf(1377,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_tex_2) ).
thf(8756,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377]) ).
thf(2157,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/sandbox2/benchmark/theBenchmark.p',t1_waybel20) ).
thf(12700,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)],[2157]) ).
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/sandbox2/benchmark/theBenchmark.p',t70_partfun1) ).
thf(6773,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(943,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ ( k7_funct_6 @ ( k2_funcop_1 @ A @ B ) ) )
= ( k1_funct_2 @ A @ ( k1_relat_1 @ B ) ) )
& ( ( k2_relat_1 @ ( k7_funct_6 @ ( k2_funcop_1 @ A @ B ) ) )
= ( k1_funct_2 @ A @ ( k2_relat_1 @ B ) ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ ( k7_funct_6 @ ( k2_funcop_1 @ A @ B ) ) @ C )
= ( k5_relat_1 @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_funct_6) ).
thf(6528,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k1_relat_1 @ ( k7_funct_6 @ ( k2_funcop_1 @ A @ B ) ) )
= ( k1_funct_2 @ A @ ( k1_relat_1 @ B ) ) )
& ( ( k2_relat_1 @ ( k7_funct_6 @ ( k2_funcop_1 @ A @ B ) ) )
= ( k1_funct_2 @ A @ ( k2_relat_1 @ B ) ) )
& ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ C @ ( k1_funct_2 @ A @ ( k1_relat_1 @ B ) ) )
=> ( ( k1_funct_1 @ ( k7_funct_6 @ ( k2_funcop_1 @ A @ B ) ) @ C )
= ( k5_relat_1 @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(2268,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/sandbox2/benchmark/theBenchmark.p',s2_domain_1) ).
thf(13186,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)],[2268]) ).
thf(2364,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/sandbox2/benchmark/theBenchmark.p',t44_setfam_1) ).
thf(13572,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)],[2364]) ).
thf(1221,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 @ ( k2_zfmisc_1 @ C @ D ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_relset_1 @ E @ ( k2_zfmisc_1 @ C @ D ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_subset_1 @ F @ ( k2_zfmisc_1 @ C @ D ) ) )
=> ( ( k2_funcsdom @ A @ B @ C @ D @ E @ F )
= ( k1_funct_1 @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funcsdom) ).
thf(7994,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 @ ( k2_zfmisc_1 @ C @ D ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_relset_1 @ E @ ( k2_zfmisc_1 @ C @ D ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_subset_1 @ F @ ( k2_zfmisc_1 @ C @ D ) ) )
=> ( ( k2_funcsdom @ A @ B @ C @ D @ E @ F )
= ( k1_funct_1 @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(674,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/sandbox2/benchmark/theBenchmark.p',redefinition_k1_cat_2) ).
thf(5266,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)],[674]) ).
thf(1334,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/sandbox2/benchmark/theBenchmark.p',t10_funct_3) ).
thf(8582,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)],[1334]) ).
thf(2053,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 )
=> ( m1_subset_1 @ ( a_4_0_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relset_2) ).
thf(12190,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)],[2053]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k1_funct_2 @ A @ ( k1_funct_2 @ B @ C ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( ( k10_funct_6 @ ( k10_funct_6 @ D ) )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_funct_6) ).
thf(3022,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k1_funct_2 @ A @ ( k1_funct_2 @ B @ C ) ) )
=> ( ( A = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( ( k10_funct_6 @ ( k10_funct_6 @ D ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(719,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/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(5455,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)],[719]) ).
thf(1995,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/sandbox2/benchmark/theBenchmark.p',t148_funct_2) ).
thf(11865,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)],[1995]) ).
thf(1367,axiom,
! [A: $i,B: $i] :
( ( k1_funct_2 @ A @ B )
= ( k4_card_3 @ ( k2_funcop_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_card_3) ).
thf(8724,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)],[1367]) ).
thf(700,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/sandbox2/benchmark/theBenchmark.p',t26_funct_2) ).
thf(5366,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)],[700]) ).
thf(1415,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/sandbox2/benchmark/theBenchmark.p',t16_xboole_1) ).
thf(8910,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)],[1415]) ).
thf(1616,axiom,
! [A: $i,B: $i,C: $i] :
( ( m2_relset_1 @ C @ A @ B )
<=> ( m1_relset_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(9849,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)],[1616]) ).
thf(2341,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ E ) ) )
=> ( ( r2_hidden @ A @ ( a_6_0_relset_2 @ B @ C @ D @ E @ F @ G ) )
<=> ? [H: $i] :
( ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ E @ F ) ) )
& ( A
= ( k8_relset_2 @ E @ F @ G @ H ) )
& ( r2_hidden @ H @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_6_0_relset_2) ).
thf(13443,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ C ) ) ) )
& ( m1_subset_1 @ G @ ( k1_zfmisc_1 @ E ) ) )
=> ( ( ( r2_hidden @ A @ ( a_6_0_relset_2 @ B @ C @ D @ E @ F @ G ) )
=> ? [H: $i] :
( ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ E @ F ) ) )
& ( A
= ( k8_relset_2 @ E @ F @ G @ H ) )
& ( r2_hidden @ H @ D ) ) )
& ( ? [H: $i] :
( ( m1_subset_1 @ H @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ E @ F ) ) )
& ( A
= ( k8_relset_2 @ E @ F @ G @ H ) )
& ( r2_hidden @ H @ D ) )
=> ( r2_hidden @ A @ ( a_6_0_relset_2 @ B @ C @ D @ E @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2341]) ).
thf(449,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/sandbox2/benchmark/theBenchmark.p',t51_partfun1) ).
thf(4204,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)],[449]) ).
thf(373,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/sandbox2/benchmark/theBenchmark.p',t4_grcat_1) ).
thf(3884,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)],[373]) ).
thf(1219,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/sandbox2/benchmark/theBenchmark.p',t35_funct_2) ).
thf(7984,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)],[1219]) ).
thf(2246,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k1_funct_7 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_7) ).
thf(13078,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k1_funct_7 @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2246]) ).
thf(1600,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/sandbox2/benchmark/theBenchmark.p',d5_binop_1) ).
thf(9745,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)],[1600]) ).
thf(320,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/sandbox2/benchmark/theBenchmark.p',t59_funct_1) ).
thf(3664,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)],[320]) ).
thf(1405,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/sandbox2/benchmark/theBenchmark.p',t3_funcop_1) ).
thf(8878,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)],[1405]) ).
thf(1879,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/sandbox2/benchmark/theBenchmark.p',free_g1_rlvect_1) ).
thf(11191,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)],[1879]) ).
thf(2250,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/sandbox2/benchmark/theBenchmark.p',dt_k9_setwiseo) ).
thf(13094,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)],[2250]) ).
thf(1916,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(11371,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1916]) ).
thf(2365,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/sandbox2/benchmark/theBenchmark.p',dt_k7_subset_1) ).
thf(13583,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)],[2365]) ).
thf(2024,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/sandbox2/benchmark/theBenchmark.p',t4_multop_1) ).
thf(12037,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)],[2024]) ).
thf(402,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/sandbox2/benchmark/theBenchmark.p',t92_relat_1) ).
thf(4021,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)],[402]) ).
thf(2382,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/sandbox2/benchmark/theBenchmark.p',dt_k3_cat_5) ).
thf(13622,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)],[2382]) ).
thf(2029,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/sandbox2/benchmark/theBenchmark.p',t27_filter_1) ).
thf(12058,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)],[2029]) ).
thf(794,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( k10_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
thf(5843,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k10_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) ) )
& ( ( ( r2_hidden @ D @ ( k1_relat_1 @ A ) )
& ( r2_hidden @ ( k1_funct_1 @ A @ D ) @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k10_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(956,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/sandbox2/benchmark/theBenchmark.p',t21_closure2) ).
thf(6582,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)],[956]) ).
thf(2125,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/sandbox2/benchmark/theBenchmark.p',free_g2_lattices) ).
thf(12525,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)],[2125]) ).
thf(1374,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/sandbox2/benchmark/theBenchmark.p',t16_funct_3) ).
thf(8746,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)],[1374]) ).
thf(410,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/sandbox2/benchmark/theBenchmark.p',t97_relat_1) ).
thf(4044,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)],[410]) ).
thf(809,axiom,
! [A: $i] :
( ~ ( v2_setfam_1 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ A )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_setfam_1) ).
thf(5924,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)],[809]) ).
thf(1478,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/sandbox2/benchmark/theBenchmark.p',t28_wellord2) ).
thf(9217,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)],[1478]) ).
thf(444,axiom,
! [A: $i] :
( ( v1_realset1 @ A )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow13) ).
thf(4192,plain,
! [A: $i] :
( ( v1_realset1 @ A )
=> ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(1752,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/sandbox2/benchmark/theBenchmark.p',free_g2_rlvect_1) ).
thf(10490,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)],[1752]) ).
thf(1871,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/sandbox2/benchmark/theBenchmark.p',fc6_subset_1) ).
thf(11152,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)],[1871]) ).
thf(755,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/sandbox2/benchmark/theBenchmark.p',t87_funct_3) ).
thf(5690,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)],[755]) ).
thf(1554,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r5_relat_2 @ A @ B )
<=> ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_2) ).
thf(9539,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( r5_relat_2 @ A @ B )
=> ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) )
& ( ! [C: $i,D: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A )
& ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
=> ( r5_relat_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1554]) ).
thf(1571,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/sandbox2/benchmark/theBenchmark.p',t4_isocat_2) ).
thf(9626,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)],[1571]) ).
thf(1896,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/sandbox2/benchmark/theBenchmark.p',t1_functor0) ).
thf(11284,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)],[1896]) ).
thf(845,axiom,
! [A: $i] :
( ( v1_setfam_1 @ A )
<=> ~ ( r2_hidden @ k1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_setfam_1) ).
thf(6090,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)],[845]) ).
thf(230,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 ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
& ( D
= ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( ( k1_funct_1 @ D @ A )
= ( k1_funct_1 @ C @ ( k4_tarski @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_funct_5) ).
thf(3282,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 ) )
=> ( ( ( r2_hidden @ ( k4_tarski @ A @ B ) @ ( k1_relat_1 @ C ) )
& ( D
= ( k1_funct_1 @ ( k5_funct_5 @ C ) @ B ) ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ D ) )
& ( ( k1_funct_1 @ D @ A )
= ( k1_funct_1 @ C @ ( k4_tarski @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(1490,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/sandbox2/benchmark/theBenchmark.p',t17_funct_4) ).
thf(9264,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)],[1490]) ).
thf(776,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/sandbox2/benchmark/theBenchmark.p',t56_funcop_1) ).
thf(5769,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)],[776]) ).
thf(1796,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/sandbox2/benchmark/theBenchmark.p',t9_altcat_1) ).
thf(10721,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)],[1796]) ).
thf(226,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/sandbox2/benchmark/theBenchmark.p',t97_finseq_2) ).
thf(3271,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)],[226]) ).
thf(1394,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/sandbox2/benchmark/theBenchmark.p',t24_funct_4) ).
thf(8810,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)],[1394]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',d18_pboole) ).
thf(2464,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)],[24]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t76_partfun1) ).
thf(2758,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(1271,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/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(8255,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)],[1271]) ).
thf(2232,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/sandbox2/benchmark/theBenchmark.p',cc2_tex_2) ).
thf(13034,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)],[2232]) ).
thf(305,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/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
thf(3618,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)],[305]) ).
thf(521,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/sandbox2/benchmark/theBenchmark.p',t64_mcart_1) ).
thf(4585,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)],[521]) ).
thf(1274,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/sandbox2/benchmark/theBenchmark.p',t24_partfun1) ).
thf(8270,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)],[1274]) ).
thf(1063,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/sandbox2/benchmark/theBenchmark.p',t82_finseq_2) ).
thf(7185,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)],[1063]) ).
thf(549,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/sandbox2/benchmark/theBenchmark.p',t48_funct_1) ).
thf(4725,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)],[549]) ).
thf(1249,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ ( k9_relat_1 @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_funct_1) ).
thf(8145,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ ( k2_relat_1 @ B ) @ ( k1_relat_1 @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ ( k5_relat_1 @ B @ C ) @ ( k9_relat_1 @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(1303,axiom,
! [A: $i] :
( ( k3_enumset1 @ A @ A @ A @ A @ A )
= ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_enumset1) ).
thf(8386,plain,
! [A: $i] :
( ( k3_enumset1 @ A @ A @ A @ A @ A )
= ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(63,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v2_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k4_card_3 @ A ) @ ( k4_card_3 @ 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 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_pua2mss1) ).
thf(2663,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v2_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k4_card_3 @ A ) @ ( k4_card_3 @ 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 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(115,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/sandbox2/benchmark/theBenchmark.p',t72_setwiseo) ).
thf(2826,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)],[115]) ).
thf(920,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/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
thf(6445,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)],[920]) ).
thf(2362,axiom,
! [A: $i,B: $i] :
( ( m1_eqrel_1 @ B @ A )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_eqrel_1) ).
thf(13568,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)],[2362]) ).
thf(1673,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/sandbox2/benchmark/theBenchmark.p',free_g1_lattices) ).
thf(10116,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)],[1673]) ).
thf(621,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
thf(5021,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(720,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/sandbox2/benchmark/theBenchmark.p',t40_mcart_1) ).
thf(5460,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)],[720]) ).
thf(1603,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/sandbox2/benchmark/theBenchmark.p',t33_domain_1) ).
thf(9758,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)],[1603]) ).
thf(514,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_6_0_domain_1) ).
thf(4553,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)],[514]) ).
thf(2242,axiom,
! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
thf(13070,plain,
! [A: $i] : ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2242]) ).
thf(333,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/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
thf(3718,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)],[333]) ).
thf(2317,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/sandbox2/benchmark/theBenchmark.p',idempotence_k1_relset_2) ).
thf(13359,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)],[2317]) ).
thf(693,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_relat_1) ).
thf(5341,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)],[693]) ).
thf(1500,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/sandbox2/benchmark/theBenchmark.p',t6_lattice2) ).
thf(9301,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)],[1500]) ).
thf(735,axiom,
m1_subset_1 @ k4_qc_lang1 @ ( k1_zfmisc_1 @ k1_qc_lang1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_qc_lang1) ).
thf(5551,plain,
m1_subset_1 @ k4_qc_lang1 @ ( k1_zfmisc_1 @ k1_qc_lang1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(1812,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/sandbox2/benchmark/theBenchmark.p',dt_k10_funcop_1) ).
thf(10794,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)],[1812]) ).
thf(189,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( v1_setfam_1 @ ( k2_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_funct_1) ).
thf(3144,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( v1_setfam_1 @ ( k2_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(484,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( v2_funct_1 @ ( k6_pralg_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_pralg_1) ).
thf(4402,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)],[484]) ).
thf(910,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/sandbox2/benchmark/theBenchmark.p',t57_funct_4) ).
thf(6392,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)],[910]) ).
thf(1429,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/sandbox2/benchmark/theBenchmark.p',t7_funct_4) ).
thf(8964,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)],[1429]) ).
thf(658,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/sandbox2/benchmark/theBenchmark.p',t10_card_fil) ).
thf(5201,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)],[658]) ).
thf(913,axiom,
! [A: $i,B: $i] :
( ( k4_enumset1 @ A @ A @ A @ A @ A @ B )
= ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_enumset1) ).
thf(6402,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)],[913]) ).
thf(2036,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/sandbox2/benchmark/theBenchmark.p',t157_relat_1) ).
thf(12095,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)],[2036]) ).
thf(969,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
( ( k10_relat_1 @ A @ ( k1_tarski @ B ) )
!= ( k1_tarski @ C ) ) )
<=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_funct_1) ).
thf(6666,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
( ( k10_relat_1 @ A @ ( k1_tarski @ B ) )
!= ( k1_tarski @ C ) ) )
=> ( v2_funct_1 @ A ) )
& ( ( v2_funct_1 @ A )
=> ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
& ! [C: $i] :
( ( k10_relat_1 @ A @ ( k1_tarski @ B ) )
!= ( k1_tarski @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(1948,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/sandbox2/benchmark/theBenchmark.p',dt_k4_setwiseo) ).
thf(11624,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)],[1948]) ).
thf(1279,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/sandbox2/benchmark/theBenchmark.p',d4_partfun1) ).
thf(8287,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)],[1279]) ).
thf(2332,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/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(13411,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)],[2332]) ).
thf(1620,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r2_hidden @ B @ C )
& ( r2_hidden @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(9868,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)],[1620]) ).
thf(315,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/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
thf(3647,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)],[315]) ).
thf(2221,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/sandbox2/benchmark/theBenchmark.p',t42_subset_1) ).
thf(12991,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)],[2221]) ).
thf(418,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/sandbox2/benchmark/theBenchmark.p',t2_multop_1) ).
thf(4080,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)],[418]) ).
thf(545,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/sandbox2/benchmark/theBenchmark.p',t36_funct_2) ).
thf(4680,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)],[545]) ).
thf(2293,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/sandbox2/benchmark/theBenchmark.p',s6_filter_1) ).
thf(13269,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)],[2293]) ).
thf(2240,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/sandbox2/benchmark/theBenchmark.p',rc4_tex_2) ).
thf(13063,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)],[2240]) ).
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 @ ( k15_funct_3 @ A @ B ) )
= ( k15_funct_3 @ ( k2_funct_1 @ A ) @ ( k2_funct_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_functor0) ).
thf(3799,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)],[353]) ).
thf(633,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/sandbox2/benchmark/theBenchmark.p',t166_funct_2) ).
thf(5066,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)],[633]) ).
thf(1253,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/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
thf(8155,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)],[1253]) ).
thf(665,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/sandbox2/benchmark/theBenchmark.p',d17_nattra_1) ).
thf(5221,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)],[665]) ).
thf(144,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( B
= ( k3_finseq_1 @ A ) )
<=> ( ( k2_finseq_1 @ B )
= ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_finseq_1) ).
thf(2946,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( ( B
= ( k3_finseq_1 @ A ) )
=> ( ( k2_finseq_1 @ B )
= ( k1_relat_1 @ A ) ) )
& ( ( ( k2_finseq_1 @ B )
= ( k1_relat_1 @ A ) )
=> ( B
= ( k3_finseq_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1811,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/sandbox2/benchmark/theBenchmark.p',d1_funcsdom) ).
thf(10791,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)],[1811]) ).
thf(2121,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/sandbox2/benchmark/theBenchmark.p',redefinition_k4_multop_1) ).
thf(12506,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)],[2121]) ).
thf(1135,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/sandbox2/benchmark/theBenchmark.p',d13_binop_1) ).
thf(7481,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)],[1135]) ).
thf(2087,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/sandbox2/benchmark/theBenchmark.p',t121_funct_2) ).
thf(12372,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)],[2087]) ).
thf(1884,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/sandbox2/benchmark/theBenchmark.p',t7_funct_2) ).
thf(11234,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)],[1884]) ).
thf(686,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/sandbox2/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(5313,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)],[686]) ).
thf(2170,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/sandbox2/benchmark/theBenchmark.p',t52_setfam_1) ).
thf(12760,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)],[2170]) ).
thf(986,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/sandbox2/benchmark/theBenchmark.p',t93_enumset1) ).
thf(6795,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)],[986]) ).
thf(1411,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/sandbox2/benchmark/theBenchmark.p',t17_binop_1) ).
thf(8895,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)],[1411]) ).
thf(2143,axiom,
! [A: $i] :
( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ A ) )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_sysrel) ).
thf(12645,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)],[2143]) ).
thf(1310,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/sandbox2/benchmark/theBenchmark.p',t9_funct_3) ).
thf(8462,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)],[1310]) ).
thf(2344,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/sandbox2/benchmark/theBenchmark.p',redefinition_k8_relset_2) ).
thf(13463,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)],[2344]) ).
thf(347,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( v2_funct_1 @ B ) )
=> ( r2_wellord2 @ A @ ( k9_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_card_1) ).
thf(3784,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
& ( v2_funct_1 @ B ) )
=> ( r2_wellord2 @ A @ ( k9_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(346,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/sandbox2/benchmark/theBenchmark.p',t51_finseq_2) ).
thf(3782,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)],[346]) ).
thf(380,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(3909,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)],[380]) ).
thf(1545,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/sandbox2/benchmark/theBenchmark.p',t44_subset_1) ).
thf(9493,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)],[1545]) ).
thf(1307,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/sandbox2/benchmark/theBenchmark.p',d10_binop_2) ).
thf(8446,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)],[1307]) ).
thf(2220,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/sandbox2/benchmark/theBenchmark.p',dt_k8_funcop_1) ).
thf(12987,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)],[2220]) ).
thf(2173,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/sandbox2/benchmark/theBenchmark.p',dt_k3_cantor_1) ).
thf(12769,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)],[2173]) ).
thf(897,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/sandbox2/benchmark/theBenchmark.p',t97_zfmisc_1) ).
thf(6324,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)],[897]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
thf(4957,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(1236,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/sandbox2/benchmark/theBenchmark.p',t6_funct_3) ).
thf(8068,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)],[1236]) ).
thf(1284,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/sandbox2/benchmark/theBenchmark.p',t51_funct_1) ).
thf(8314,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)],[1284]) ).
thf(1049,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/sandbox2/benchmark/theBenchmark.p',t24_filter_1) ).
thf(7142,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)],[1049]) ).
thf(358,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/sandbox2/benchmark/theBenchmark.p',t74_zfmisc_1) ).
thf(3831,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)],[358]) ).
thf(2367,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/sandbox2/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(13587,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)],[2367]) ).
thf(2280,axiom,
m1_subset_1 @ a_0_2_domain_1 @ ( k1_zfmisc_1 @ f3_s9_domain_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s9_domain_1) ).
thf(13222,plain,
m1_subset_1 @ a_0_2_domain_1 @ ( k1_zfmisc_1 @ f3_s9_domain_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2280]) ).
thf(2299,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_0_pre_circ) ).
thf(13297,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)],[2299]) ).
thf(620,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/sandbox2/benchmark/theBenchmark.p',t175_orders_1) ).
thf(5006,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)],[620]) ).
thf(1070,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k1_funct_2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_fraenkel) ).
thf(7205,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)],[1070]) ).
thf(668,axiom,
! [A: $i,B: $i,C: $i] :
( ( k5_enumset1 @ A @ A @ A @ A @ A @ B @ C )
= ( k1_enumset1 @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_enumset1) ).
thf(5238,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)],[668]) ).
thf(709,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_4) ).
thf(5423,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(366,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/sandbox2/benchmark/theBenchmark.p',t7_pua2mss1) ).
thf(3862,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)],[366]) ).
thf(929,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/sandbox2/benchmark/theBenchmark.p',redefinition_k10_cat_2) ).
thf(6477,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)],[929]) ).
thf(497,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/sandbox2/benchmark/theBenchmark.p',t15_functor0) ).
thf(4486,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)],[497]) ).
thf(511,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/sandbox2/benchmark/theBenchmark.p',t136_partfun1) ).
thf(4544,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)],[511]) ).
thf(1286,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/sandbox2/benchmark/theBenchmark.p',t13_binop_1) ).
thf(8319,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)],[1286]) ).
thf(1194,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(7838,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ A @ ( k3_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(579,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 @ ( k2_relat_1 @ ( k5_relat_1 @ B @ C ) ) )
& ( v2_funct_1 @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funct_3) ).
thf(4845,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 @ ( k2_relat_1 @ ( k5_relat_1 @ B @ C ) ) )
& ( v2_funct_1 @ C ) )
=> ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(711,axiom,
? [A: $i] :
~ ( v2_setfam_1 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_setfam_1) ).
thf(5428,plain,
? [A: $i] :
~ ( v2_setfam_1 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(1227,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/sandbox2/benchmark/theBenchmark.p',t1_waybel18) ).
thf(8014,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)],[1227]) ).
thf(1714,axiom,
~ ( v1_xboole_0 @ k1_numbers ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_numbers) ).
thf(10335,plain,
~ ( v1_xboole_0 @ k1_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1714]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_enumset1 @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_setwiseo) ).
thf(3963,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)],[392]) ).
thf(1407,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/sandbox2/benchmark/theBenchmark.p',t27_relat_1) ).
thf(8884,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)],[1407]) ).
thf(82,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_xboole_1) ).
thf(2726,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)],[82]) ).
thf(1928,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/sandbox2/benchmark/theBenchmark.p',t58_domain_1) ).
thf(11435,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)],[1928]) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',t28_finseq_2) ).
thf(2631,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)],[53]) ).
thf(2262,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/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(13163,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)],[2262]) ).
thf(1144,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/sandbox2/benchmark/theBenchmark.p',rc3_finseq_1) ).
thf(7593,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)],[1144]) ).
thf(1742,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/sandbox2/benchmark/theBenchmark.p',t20_finset_1) ).
thf(10445,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)],[1742]) ).
thf(1739,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/sandbox2/benchmark/theBenchmark.p',d4_binop_1) ).
thf(10434,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)],[1739]) ).
thf(799,axiom,
! [A: $i] :
( ( k12_funct_3 @ A )
= ( k13_funct_3 @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_funcop_1) ).
thf(5889,plain,
! [A: $i] :
( ( k12_funct_3 @ A )
= ( k13_funct_3 @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(1445,axiom,
( ( k1_funct_2 @ k1_xboole_0 @ k1_xboole_0 )
= ( k1_tarski @ ( k6_relat_1 @ k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_altcat_1) ).
thf(9063,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)],[1445]) ).
thf(1727,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/sandbox2/benchmark/theBenchmark.p',t7_closure2) ).
thf(10398,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)],[1727]) ).
thf(585,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/sandbox2/benchmark/theBenchmark.p',t73_funct_2) ).
thf(4883,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)],[585]) ).
thf(1861,axiom,
! [A: $i] :
( ( v1_fraenkel @ A )
<=> ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_fraenkel) ).
thf(11089,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)],[1861]) ).
thf(636,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/sandbox2/benchmark/theBenchmark.p',t138_partfun1) ).
thf(5081,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)],[636]) ).
thf(1391,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/sandbox2/benchmark/theBenchmark.p',redefinition_k10_relset_1) ).
thf(8800,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)],[1391]) ).
thf(2244,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/sandbox2/benchmark/theBenchmark.p',t25_funct_1) ).
thf(13074,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)],[2244]) ).
thf(400,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/sandbox2/benchmark/theBenchmark.p',d1_tex_2) ).
thf(4012,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)],[400]) ).
thf(382,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/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
thf(3916,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)],[382]) ).
thf(2314,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ A )
=> ? [C: $i] : ( m3_realset1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m3_realset1) ).
thf(13344,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)],[2314]) ).
thf(1351,axiom,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_subset_1 @ A ) )
& ( m1_subset_1 @ ( k1_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_subset_1) ).
thf(8662,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)],[1351]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
& ( v2_relat_1 @ ( k7_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k7_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pre_circ) ).
thf(2638,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k7_relat_1 @ A @ B ) )
& ( v2_relat_1 @ ( k7_relat_1 @ A @ B ) )
& ( v1_funct_1 @ ( k7_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1074,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(7222,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_finset_1 @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(423,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/sandbox2/benchmark/theBenchmark.p',existence_m1_nat_lat) ).
thf(4109,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)],[423]) ).
thf(2248,axiom,
! [A: $i] :
( ( v1_fraenkel @ A )
=> ! [B: $i] :
( ( v1_fraenkel @ B )
=> ! [C: $i] :
( ( ( v7_altcat_1 @ C )
& ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ B ) )
=> ( ( k1_binop_1 @ C @ D @ E )
= ( k5_relat_1 @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_altcat_1) ).
thf(13084,plain,
! [A: $i] :
( ( v1_fraenkel @ A )
=> ! [B: $i] :
( ( v1_fraenkel @ B )
=> ! [C: $i] :
( ( ( v7_altcat_1 @ C )
& ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ! [E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ B ) )
=> ( ( k1_binop_1 @ C @ D @ E )
= ( k5_relat_1 @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2248]) ).
thf(1396,axiom,
! [A: $i,B: $i] :
( ( B
= ( k1_tarski @ A ) )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(8815,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)],[1396]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k3_funct_5 @ B ) ) )
=> ( ( v1_relat_1 @ ( k1_funct_1 @ ( k3_funct_5 @ B ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k3_funct_5 @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funct_5) ).
thf(3205,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k3_funct_5 @ B ) ) )
=> ( ( v1_relat_1 @ ( k1_funct_1 @ ( k3_funct_5 @ B ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k3_funct_5 @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(728,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/sandbox2/benchmark/theBenchmark.p',t2_lattice2) ).
thf(5497,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)],[728]) ).
thf(814,axiom,
( ( k5_finsub_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finsub_1) ).
thf(5951,plain,
( ( k5_finsub_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(2215,axiom,
( ( ( v1_finset_1 @ f3_s22_fraenkel )
& ( v1_finset_1 @ f4_s22_fraenkel ) )
=> ( v1_finset_1 @ a_0_39_fraenkel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s22_fraenkel) ).
thf(12974,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)],[2215]) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(3060,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)],[166]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k3_partfun1 @ C @ A @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_partfun1) ).
thf(3176,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k3_partfun1 @ C @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(455,axiom,
! [A: $i] :
( ( k6_partfun1 @ A )
= ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(4263,plain,
! [A: $i] :
( ( k6_partfun1 @ A )
= ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(2339,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/sandbox2/benchmark/theBenchmark.p',dt_k14_domain_1) ).
thf(13434,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)],[2339]) ).
thf(1245,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_funct_4 @ A @ k1_xboole_0 )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_4) ).
thf(8105,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(2200,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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_multop_1) ).
thf(12906,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)],[2200]) ).
thf(1355,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k1_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
thf(8687,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k1_relat_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).
thf(1146,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/sandbox2/benchmark/theBenchmark.p',t73_funcop_1) ).
thf(7604,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)],[1146]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ A @ ( k3_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_xboole_1) ).
thf(3194,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)],[204]) ).
thf(1862,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/sandbox2/benchmark/theBenchmark.p',t1_ens_1) ).
thf(11097,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)],[1862]) ).
thf(439,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/sandbox2/benchmark/theBenchmark.p',t79_funct_2) ).
thf(4180,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)],[439]) ).
thf(1551,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/sandbox2/benchmark/theBenchmark.p',t9_realset1) ).
thf(9530,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)],[1551]) ).
thf(1388,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_partfun1) ).
thf(8792,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388]) ).
thf(1036,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/sandbox2/benchmark/theBenchmark.p',t189_relat_1) ).
thf(7101,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)],[1036]) ).
thf(465,axiom,
! [A: $i] :
( ( k7_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_relat_1) ).
thf(4320,plain,
! [A: $i] :
( ( k7_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(106,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/sandbox2/benchmark/theBenchmark.p',t39_sysrel) ).
thf(2798,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)],[106]) ).
thf(1033,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/sandbox2/benchmark/theBenchmark.p',t44_setwiseo) ).
thf(7091,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)],[1033]) ).
thf(238,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/sandbox2/benchmark/theBenchmark.p',t36_finseq_2) ).
thf(3311,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)],[238]) ).
thf(1670,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/sandbox2/benchmark/theBenchmark.p',t3_pua2mss1) ).
thf(10107,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)],[1670]) ).
thf(1397,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/sandbox2/benchmark/theBenchmark.p',d17_binop_1) ).
thf(8835,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)],[1397]) ).
thf(1064,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/sandbox2/benchmark/theBenchmark.p',t125_funct_1) ).
thf(7189,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)],[1064]) ).
thf(625,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/sandbox2/benchmark/theBenchmark.p',t16_finseq_1) ).
thf(5031,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)],[625]) ).
thf(1835,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/sandbox2/benchmark/theBenchmark.p',d2_filter_1) ).
thf(10946,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)],[1835]) ).
thf(520,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/sandbox2/benchmark/theBenchmark.p',t64_xboole_1) ).
thf(4582,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)],[520]) ).
thf(1401,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/sandbox2/benchmark/theBenchmark.p',dt_k5_domain_1) ).
thf(8864,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)],[1401]) ).
thf(2110,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/sandbox2/benchmark/theBenchmark.p',dt_k11_setwiseo) ).
thf(12449,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)],[2110]) ).
thf(199,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 ) )
=> ( ( v1_funct_1 @ ( k3_funct_5 @ D ) )
& ( v1_funct_2 @ ( k3_funct_5 @ D ) @ A @ ( k1_fraenkel @ B @ C ) )
& ( m2_relset_1 @ ( k3_funct_5 @ D ) @ A @ ( k1_fraenkel @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_cat_2) ).
thf(3179,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 ) )
=> ( ( v1_funct_1 @ ( k3_funct_5 @ D ) )
& ( v1_funct_2 @ ( k3_funct_5 @ D ) @ A @ ( k1_fraenkel @ B @ C ) )
& ( m2_relset_1 @ ( k3_funct_5 @ D ) @ A @ ( k1_fraenkel @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(1154,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/sandbox2/benchmark/theBenchmark.p',t32_relset_1) ).
thf(7631,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)],[1154]) ).
thf(2213,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/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(12967,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)],[2213]) ).
thf(612,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
=> ( r1_tarski @ A @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
thf(4983,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k1_relat_1 @ B ) )
=> ( r1_tarski @ A @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(1522,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/sandbox2/benchmark/theBenchmark.p',d1_funct_3) ).
thf(9397,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)],[1522]) ).
thf(1024,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ( m1_pboole @ ( k2_altcat_1 @ A @ B ) @ ( k3_zfmisc_1 @ A @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_altcat_1) ).
thf(7054,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ( m1_pboole @ ( k2_altcat_1 @ A @ B ) @ ( k3_zfmisc_1 @ A @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(1914,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/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).
thf(11364,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)],[1914]) ).
thf(1127,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/sandbox2/benchmark/theBenchmark.p',t1_isocat_1) ).
thf(7453,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)],[1127]) ).
thf(1580,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/sandbox2/benchmark/theBenchmark.p',cc4_tex_2) ).
thf(9662,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)],[1580]) ).
thf(254,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/sandbox2/benchmark/theBenchmark.p',t12_relset_2) ).
thf(3407,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)],[254]) ).
thf(1174,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/sandbox2/benchmark/theBenchmark.p',t168_partfun1) ).
thf(7717,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)],[1174]) ).
thf(1270,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/sandbox2/benchmark/theBenchmark.p',t30_filter_1) ).
thf(8251,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)],[1270]) ).
thf(1153,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/sandbox2/benchmark/theBenchmark.p',t45_yellow20) ).
thf(7629,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)],[1153]) ).
thf(1040,axiom,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(7111,plain,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(1519,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/sandbox2/benchmark/theBenchmark.p',t42_funcop_1) ).
thf(9387,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)],[1519]) ).
thf(821,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/sandbox2/benchmark/theBenchmark.p',t12_binop_1) ).
thf(5992,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)],[821]) ).
thf(781,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ k1_numbers )
=> ( ( k7_binop_2 @ ( k7_binop_2 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_binop_2) ).
thf(5791,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)],[781]) ).
thf(332,axiom,
! [A: $i,B: $i] :
( ( v1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ A @ B )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_partfun1) ).
thf(3714,plain,
! [A: $i,B: $i] :
( ( v1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ A @ B )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(1591,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/sandbox2/benchmark/theBenchmark.p',d1_realset1) ).
thf(9714,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)],[1591]) ).
thf(1225,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/sandbox2/benchmark/theBenchmark.p',t172_partfun1) ).
thf(8008,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)],[1225]) ).
thf(2165,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/sandbox2/benchmark/theBenchmark.p',t13_funct_5) ).
thf(12746,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)],[2165]) ).
thf(2194,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/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(12885,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)],[2194]) ).
thf(552,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/sandbox2/benchmark/theBenchmark.p',t12_borsuk_1) ).
thf(4750,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)],[552]) ).
thf(1568,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/sandbox2/benchmark/theBenchmark.p',redefinition_k11_domain_1) ).
thf(9609,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)],[1568]) ).
thf(1813,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/sandbox2/benchmark/theBenchmark.p',t57_funcop_1) ).
thf(10798,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)],[1813]) ).
thf(1953,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( r1_tarski @ ( k5_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ C ) @ A ) ) @ ( k9_relat_1 @ C @ ( k3_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relset_2) ).
thf(11642,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( r1_tarski @ ( k5_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ C ) @ A ) ) @ ( k9_relat_1 @ C @ ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1953]) ).
thf(1622,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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_nattra_1) ).
thf(9878,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)],[1622]) ).
thf(1540,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/sandbox2/benchmark/theBenchmark.p',t140_partfun1) ).
thf(9477,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)],[1540]) ).
thf(503,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/sandbox2/benchmark/theBenchmark.p',d3_pboole) ).
thf(4513,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)],[503]) ).
thf(742,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 ) )
=> ( ( r5_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 )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d19_binop_1) ).
thf(5588,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 ) )
=> ( ( ( r5_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 )
=> ( ( k2_binop_1 @ A @ A @ A @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ B @ 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 @ B @ ( k2_binop_1 @ A @ A @ A @ C @ D @ E ) @ F )
= ( k2_binop_1 @ A @ A @ A @ C @ ( k2_binop_1 @ A @ A @ A @ B @ D @ F ) @ ( k2_binop_1 @ A @ A @ A @ B @ E @ F ) ) ) ) ) )
=> ( r5_binop_1 @ A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(662,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/sandbox2/benchmark/theBenchmark.p',t37_setwiseo) ).
thf(5213,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)],[662]) ).
thf(1322,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finset_1) ).
thf(8499,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)],[1322]) ).
thf(879,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r1_tarski @ C @ B ) )
=> ( r1_tarski @ ( k3_tarski @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_zfmisc_1) ).
thf(6256,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)],[879]) ).
thf(1211,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/sandbox2/benchmark/theBenchmark.p',t60_setwiseo) ).
thf(7930,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)],[1211]) ).
thf(536,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/sandbox2/benchmark/theBenchmark.p',cc1_binop_1) ).
thf(4648,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)],[536]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( v1_funct_1 @ ( k9_funct_7 @ C @ B ) )
& ( v1_funct_2 @ ( k9_funct_7 @ C @ B ) @ A @ A )
& ( m2_relset_1 @ ( k9_funct_7 @ C @ B ) @ A @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_7) ).
thf(3428,plain,
! [A: $i,B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( v1_funct_2 @ C @ A @ A )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( v1_funct_1 @ ( k9_funct_7 @ C @ B ) )
& ( v1_funct_2 @ ( k9_funct_7 @ C @ B ) @ A @ A )
& ( m2_relset_1 @ ( k9_funct_7 @ C @ B ) @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(1765,axiom,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(10539,plain,
! [A: $i,B: $i] :
~ ( v1_xboole_0 @ ( k4_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1765]) ).
thf(1026,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/sandbox2/benchmark/theBenchmark.p',t29_mcart_1) ).
thf(7059,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)],[1026]) ).
thf(2267,axiom,
! [A: $i,B: $i] : ( m1_subset_1 @ ( k1_card_fil @ A @ B ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_card_fil) ).
thf(13184,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)],[2267]) ).
thf(1141,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/sandbox2/benchmark/theBenchmark.p',t91_funct_3) ).
thf(7577,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)],[1141]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_fraenkel @ C @ A @ B ) )
=> ? [D: $i] : ( m2_fraenkel @ D @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_fraenkel) ).
thf(3723,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_fraenkel @ C @ A @ B ) )
=> ? [D: $i] : ( m2_fraenkel @ D @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(314,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k3_funct_3 @ A ) )
& ( v1_funct_2 @ ( k3_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) )
& ( m2_relset_1 @ ( k3_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_funct_3) ).
thf(3643,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k3_funct_3 @ A ) )
& ( v1_funct_2 @ ( k3_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) )
& ( m2_relset_1 @ ( k3_funct_3 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ A ) ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(804,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_orders_1) ).
thf(5905,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( r2_hidden @ k1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
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/sandbox2/benchmark/theBenchmark.p',t74_funct_2) ).
thf(6541,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(292,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/sandbox2/benchmark/theBenchmark.p',t178_orders_1) ).
thf(3555,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)],[292]) ).
thf(1099,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/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(7313,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)],[1099]) ).
thf(884,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( v1_finset_1 @ ( k10_relat_1 @ B @ A ) ) )
=> ( v1_finset_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finset_1) ).
thf(6275,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
& ( v1_finset_1 @ ( k10_relat_1 @ B @ A ) ) )
=> ( v1_finset_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(883,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/sandbox2/benchmark/theBenchmark.p',redefinition_k3_cantor_1) ).
thf(6271,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)],[883]) ).
thf(2138,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/sandbox2/benchmark/theBenchmark.p',t8_funct_2) ).
thf(12622,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)],[2138]) ).
thf(1125,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_relat_1) ).
thf(7448,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ ( k2_relat_1 @ B ) )
=> ( ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(293,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/sandbox2/benchmark/theBenchmark.p',t14_sysrel) ).
thf(3573,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)],[293]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( v2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_partfun1) ).
thf(2781,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v2_funct_1 @ C )
=> ( v2_funct_1 @ ( k3_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(508,axiom,
! [A: $i,B: $i] :
( ( k1_enumset1 @ A @ A @ B )
= ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_enumset1) ).
thf(4530,plain,
! [A: $i,B: $i] :
( ( k1_enumset1 @ A @ A @ B )
= ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(1927,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/sandbox2/benchmark/theBenchmark.p',redefinition_k7_pboole) ).
thf(11432,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)],[1927]) ).
thf(2187,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/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(12859,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)],[2187]) ).
thf(724,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/sandbox2/benchmark/theBenchmark.p',t167_funct_2) ).
thf(5481,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)],[724]) ).
thf(1217,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/sandbox2/benchmark/theBenchmark.p',redefinition_k1_oppcat_1) ).
thf(7966,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)],[1217]) ).
thf(1625,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ~ ( v1_xboole_0 @ B ) )
=> ~ ( v1_xboole_0 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(9893,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)],[1625]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',d3_setwiseo) ).
thf(2505,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)],[34]) ).
thf(874,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/sandbox2/benchmark/theBenchmark.p',t78_funcop_1) ).
thf(6239,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)],[874]) ).
thf(2142,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/sandbox2/benchmark/theBenchmark.p',t58_funcop_1) ).
thf(12641,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)],[2142]) ).
thf(569,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t148_funct_1) ).
thf(4804,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( k9_relat_1 @ B @ ( k10_relat_1 @ B @ A ) )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ B @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(2247,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/sandbox2/benchmark/theBenchmark.p',redefinition_k12_domain_1) ).
thf(13081,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)],[2247]) ).
thf(1846,axiom,
r1_tarski @ a_0_32_fraenkel @ f2_s17_fraenkel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s17_fraenkel) ).
thf(11023,plain,
r1_tarski @ a_0_32_fraenkel @ f2_s17_fraenkel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1846]) ).
thf(304,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ B )
= k1_xboole_0 )
<=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(3611,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)],[304]) ).
thf(1148,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/sandbox2/benchmark/theBenchmark.p',dt_k7_relset_1) ).
thf(7609,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)],[1148]) ).
thf(317,axiom,
! [A: $i] :
( ( k1_orders_1 @ A )
= ( k4_xboole_0 @ ( k1_zfmisc_1 @ A ) @ ( k1_tarski @ k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_orders_1) ).
thf(3654,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)],[317]) ).
thf(2334,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_1_domain_1) ).
thf(13415,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)],[2334]) ).
thf(1210,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/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funcop_1) ).
thf(7927,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)],[1210]) ).
thf(2371,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/sandbox2/benchmark/theBenchmark.p',dt_k8_domain_1) ).
thf(13597,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)],[2371]) ).
thf(2094,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/sandbox2/benchmark/theBenchmark.p',t2_qc_lang1) ).
thf(12393,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)],[2094]) ).
thf(288,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/sandbox2/benchmark/theBenchmark.p',t6_closure2) ).
thf(3541,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)],[288]) ).
thf(2320,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/sandbox2/benchmark/theBenchmark.p',dt_k23_qc_lang1) ).
thf(13366,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)],[2320]) ).
thf(831,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/sandbox2/benchmark/theBenchmark.p',t6_tex_2) ).
thf(6033,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)],[831]) ).
thf(1131,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( r1_tarski @ A @ ( k2_zfmisc_1 @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(7463,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)],[1131]) ).
thf(117,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/sandbox2/benchmark/theBenchmark.p',dt_m3_pboole) ).
thf(2836,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)],[117]) ).
thf(2057,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/sandbox2/benchmark/theBenchmark.p',t49_setfam_1) ).
thf(12218,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)],[2057]) ).
thf(1017,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/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_partfun1) ).
thf(7014,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)],[1017]) ).
thf(2103,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/sandbox2/benchmark/theBenchmark.p',t17_yellow_9) ).
thf(12429,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)],[2103]) ).
thf(2376,axiom,
! [A: $i] : ( m1_subset_1 @ ( k1_pcomps_1 @ A ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pcomps_1) ).
thf(13607,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)],[2376]) ).
thf(1547,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/sandbox2/benchmark/theBenchmark.p',d1_funct_5) ).
thf(9498,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)],[1547]) ).
thf(983,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/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).
thf(6788,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)],[983]) ).
thf(1058,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( m1_subset_1 @ B @ A ) )
=> ( ( k2_setwiseo @ A @ B )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_setwiseo) ).
thf(7169,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)],[1058]) ).
thf(1831,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/sandbox2/benchmark/theBenchmark.p',rc2_lopclset) ).
thf(10904,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)],[1831]) ).
thf(2348,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/sandbox2/benchmark/theBenchmark.p',redefinition_k6_funct_3) ).
thf(13483,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)],[2348]) ).
thf(2019,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/sandbox2/benchmark/theBenchmark.p',free_g1_funcsdom) ).
thf(12004,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)],[2019]) ).
thf(37,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(2581,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k4_xboole_0 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1684,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/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(10158,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)],[1684]) ).
thf(1997,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/sandbox2/benchmark/theBenchmark.p',t113_funct_2) ).
thf(11888,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)],[1997]) ).
thf(867,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/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
thf(6211,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)],[867]) ).
thf(1759,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( r2_hidden @ D @ ( k8_relset_2 @ B @ A @ C @ E ) )
<=> ! [F: $i] :
( ( r2_hidden @ F @ C )
=> ( r2_hidden @ D @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_2) ).
thf(10518,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ B ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ A )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ B @ A ) ) )
=> ( ( ( r2_hidden @ D @ ( k8_relset_2 @ B @ A @ C @ E ) )
=> ! [F: $i] :
( ( r2_hidden @ F @ C )
=> ( r2_hidden @ D @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) ) )
& ( ! [F: $i] :
( ( r2_hidden @ F @ C )
=> ( r2_hidden @ D @ ( k9_relat_1 @ E @ ( k1_tarski @ F ) ) ) )
=> ( r2_hidden @ D @ ( k8_relset_2 @ B @ A @ C @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1759]) ).
thf(631,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/sandbox2/benchmark/theBenchmark.p',t53_zfmisc_1) ).
thf(5058,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)],[631]) ).
thf(1877,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/sandbox2/benchmark/theBenchmark.p',redefinition_k14_borsuk_1) ).
thf(11184,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)],[1877]) ).
thf(778,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/sandbox2/benchmark/theBenchmark.p',t82_funct_3) ).
thf(5776,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)],[778]) ).
thf(1111,axiom,
m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_numbers) ).
thf(7385,plain,
m1_subset_1 @ k5_numbers @ ( k1_zfmisc_1 @ k1_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(1020,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/sandbox2/benchmark/theBenchmark.p',t20_funct_2) ).
thf(7027,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)],[1020]) ).
thf(753,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/sandbox2/benchmark/theBenchmark.p',t46_funct_1) ).
thf(5683,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)],[753]) ).
thf(2184,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/sandbox2/benchmark/theBenchmark.p',existence_m2_subset_1) ).
thf(12838,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)],[2184]) ).
thf(2294,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(13277,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)],[2294]) ).
thf(2342,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_2_domain_1) ).
thf(13451,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)],[2342]) ).
thf(2303,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/sandbox2/benchmark/theBenchmark.p',redefinition_k6_relset_2) ).
thf(13316,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)],[2303]) ).
thf(1462,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/sandbox2/benchmark/theBenchmark.p',t6_funct_4) ).
thf(9144,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)],[1462]) ).
thf(309,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/sandbox2/benchmark/theBenchmark.p',involutiveness_k2_card_fil) ).
thf(3628,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)],[309]) ).
thf(1150,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/sandbox2/benchmark/theBenchmark.p',t159_funct_2) ).
thf(7614,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)],[1150]) ).
thf(921,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/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
thf(6450,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)],[921]) ).
thf(824,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/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
thf(6005,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)],[824]) ).
thf(2210,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_7_domain_1) ).
thf(12946,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)],[2210]) ).
thf(1005,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/sandbox2/benchmark/theBenchmark.p',d5_monoid_0) ).
thf(6908,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)],[1005]) ).
thf(926,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/sandbox2/benchmark/theBenchmark.p',t21_funct_5) ).
thf(6465,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)],[926]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( ( r2_hidden @ B @ A )
& ( v2_membered @ B ) )
=> ( v2_membered @ ( k1_setfam_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_membered) ).
thf(2862,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)],[123]) ).
thf(95,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k3_funct_3 @ A ) ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_3) ).
thf(2766,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k3_funct_3 @ A ) ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(1615,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/sandbox2/benchmark/theBenchmark.p',t4_funct_5) ).
thf(9846,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)],[1615]) ).
thf(1243,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/sandbox2/benchmark/theBenchmark.p',t3_lattice4) ).
thf(8090,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)],[1243]) ).
thf(1890,axiom,
r1_xboole_0 @ a_0_33_fraenkel @ f2_s18_fraenkel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s18_fraenkel) ).
thf(11261,plain,
r1_xboole_0 @ a_0_33_fraenkel @ f2_s18_fraenkel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1890]) ).
thf(1767,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/sandbox2/benchmark/theBenchmark.p',t5_funct_5) ).
thf(10550,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)],[1767]) ).
thf(1946,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/sandbox2/benchmark/theBenchmark.p',t51_subset_1) ).
thf(11610,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)],[1946]) ).
thf(981,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( m2_card_fil @ B @ A )
=> ( r2_hidden @ k1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_card_fil) ).
thf(6784,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)],[981]) ).
thf(2368,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/sandbox2/benchmark/theBenchmark.p',dt_k11_domain_1) ).
thf(13591,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)],[2368]) ).
thf(1757,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/sandbox2/benchmark/theBenchmark.p',t65_partfun1) ).
thf(10513,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)],[1757]) ).
thf(1628,axiom,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(9900,plain,
! [A: $i,B: $i] :
~ ( ( r2_hidden @ A @ B )
& ( r1_tarski @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1628]) ).
thf(1191,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ B )
= ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_relat_1) ).
thf(7826,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ B )
= ( k5_relat_1 @ B @ ( k6_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(858,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/sandbox2/benchmark/theBenchmark.p',t71_funct_1) ).
thf(6152,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)],[858]) ).
thf(548,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/sandbox2/benchmark/theBenchmark.p',d3_funct_4) ).
thf(4689,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)],[548]) ).
thf(623,axiom,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ( ~ ( v1_xboole_0 @ A )
& ~ ( v2_setfam_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_yellow21) ).
thf(5026,plain,
! [A: $i] :
( ~ ( v1_realset1 @ A )
=> ( ~ ( v1_xboole_0 @ A )
& ~ ( v2_setfam_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(1100,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/sandbox2/benchmark/theBenchmark.p',t35_setwiseo) ).
thf(7333,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)],[1100]) ).
thf(92,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/sandbox2/benchmark/theBenchmark.p',t27_funct_4) ).
thf(2756,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)],[92]) ).
thf(1841,axiom,
~ ( v1_xboole_0 @ k2_qc_lang1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_qc_lang1) ).
thf(11000,plain,
~ ( v1_xboole_0 @ k2_qc_lang1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1841]) ).
thf(194,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 @ ( k3_funct_5 @ C ) ) @ A )
& ( r1_tarski @ ( k1_relat_1 @ ( k5_funct_5 @ C ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_5) ).
thf(3162,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 @ ( k3_funct_5 @ C ) ) @ A )
& ( r1_tarski @ ( k1_relat_1 @ ( k5_funct_5 @ C ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(1060,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/sandbox2/benchmark/theBenchmark.p',t13_card_fil) ).
thf(7174,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)],[1060]) ).
thf(1699,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/sandbox2/benchmark/theBenchmark.p',dt_k5_metric_1) ).
thf(10252,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)],[1699]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( ( k1_relat_1 @ ( k3_funct_5 @ C ) )
= A )
& ( ( k1_relat_1 @ ( k5_funct_5 @ C ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funct_5) ).
thf(3215,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( ( k1_relat_1 @ ( k3_funct_5 @ C ) )
= A )
& ( ( k1_relat_1 @ ( k5_funct_5 @ C ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1447,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/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
thf(9068,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)],[1447]) ).
thf(2045,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(12138,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)],[2045]) ).
thf(1781,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/sandbox2/benchmark/theBenchmark.p',t3_mssubfam) ).
thf(10651,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)],[1781]) ).
thf(760,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/sandbox2/benchmark/theBenchmark.p',t33_funct_4) ).
thf(5711,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)],[760]) ).
thf(2330,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/sandbox2/benchmark/theBenchmark.p',dt_k15_domain_1) ).
thf(13404,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)],[2330]) ).
thf(1923,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/sandbox2/benchmark/theBenchmark.p',t8_pua2mss1) ).
thf(11407,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)],[1923]) ).
thf(790,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/sandbox2/benchmark/theBenchmark.p',t20_funct_3) ).
thf(5833,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)],[790]) ).
thf(1277,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/sandbox2/benchmark/theBenchmark.p',fc2_functor0) ).
thf(8279,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)],[1277]) ).
thf(2129,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/sandbox2/benchmark/theBenchmark.p',t79_funct_3) ).
thf(12553,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)],[2129]) ).
thf(397,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/sandbox2/benchmark/theBenchmark.p',t75_funct_4) ).
thf(4004,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)],[397]) ).
thf(616,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/sandbox2/benchmark/theBenchmark.p',t169_funct_2) ).
thf(4995,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)],[616]) ).
thf(513,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/sandbox2/benchmark/theBenchmark.p',t54_funcop_1) ).
thf(4550,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)],[513]) ).
thf(1679,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_relat_1) ).
thf(10143,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)],[1679]) ).
thf(269,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 ) )
=> ( ( k3_cat_2 @ A @ B @ C @ D )
= ( k5_funct_5 @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_cat_2) ).
thf(3454,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 ) )
=> ( ( k3_cat_2 @ A @ B @ C @ D )
= ( k5_funct_5 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(2198,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/sandbox2/benchmark/theBenchmark.p',t9_cantor_1) ).
thf(12902,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)],[2198]) ).
thf(1552,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/sandbox2/benchmark/theBenchmark.p',t3_zfrefle1) ).
thf(9534,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)],[1552]) ).
thf(433,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 )
<=> ( r4_binop_1 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_binop_1) ).
thf(4148,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 )
=> ( r4_binop_1 @ A @ C @ B ) )
& ( ( r4_binop_1 @ A @ C @ B )
=> ( r6_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(915,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/sandbox2/benchmark/theBenchmark.p',t5_funct_4) ).
thf(6409,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)],[915]) ).
thf(1019,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/sandbox2/benchmark/theBenchmark.p',t60_zfmisc_1) ).
thf(7020,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)],[1019]) ).
thf(1814,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/sandbox2/benchmark/theBenchmark.p',dt_k3_setwiseo) ).
thf(10802,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)],[1814]) ).
thf(2355,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_38_fraenkel) ).
thf(13507,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)],[2355]) ).
thf(354,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 ) )
=> ( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) )
= ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t161_funct_2) ).
thf(3802,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 ) )
=> ( ( k5_partfun1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) )
= ( k1_tarski @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(1452,axiom,
! [A: $i,B: $i] :
( ( k3_enumset1 @ A @ A @ A @ A @ B )
= ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_enumset1) ).
thf(9081,plain,
! [A: $i,B: $i] :
( ( k3_enumset1 @ A @ A @ A @ A @ B )
= ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452]) ).
thf(2340,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/sandbox2/benchmark/theBenchmark.p',s1_subset_1) ).
thf(13436,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)],[2340]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
=> ( ( ( k3_funct_5 @ ( k2_funcop_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
= ( k2_funcop_1 @ A @ ( k2_funcop_1 @ B @ C ) ) )
& ( ( k5_funct_5 @ ( k2_funcop_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
= ( k2_funcop_1 @ B @ ( k2_funcop_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_6) ).
thf(2926,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k2_zfmisc_1 @ A @ B )
!= k1_xboole_0 )
=> ( ( ( k3_funct_5 @ ( k2_funcop_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
= ( k2_funcop_1 @ A @ ( k2_funcop_1 @ B @ C ) ) )
& ( ( k5_funct_5 @ ( k2_funcop_1 @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
= ( k2_funcop_1 @ B @ ( k2_funcop_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(1184,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/sandbox2/benchmark/theBenchmark.p',t17_funcop_1) ).
thf(7770,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)],[1184]) ).
thf(1537,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/sandbox2/benchmark/theBenchmark.p',t4_funct_2) ).
thf(9468,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)],[1537]) ).
thf(2071,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/sandbox2/benchmark/theBenchmark.p',s13_funct_2) ).
thf(12305,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)],[2071]) ).
thf(1119,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/sandbox2/benchmark/theBenchmark.p',t89_mcart_1) ).
thf(7407,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)],[1119]) ).
thf(1776,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/sandbox2/benchmark/theBenchmark.p',t18_subset_1) ).
thf(10614,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)],[1776]) ).
thf(297,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_xboole_1) ).
thf(3587,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)],[297]) ).
thf(200,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/sandbox2/benchmark/theBenchmark.p',t53_relat_1) ).
thf(3183,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)],[200]) ).
thf(932,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/sandbox2/benchmark/theBenchmark.p',t76_funcop_1) ).
thf(6486,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)],[932]) ).
thf(2196,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/sandbox2/benchmark/theBenchmark.p',t8_multop_1) ).
thf(12889,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)],[2196]) ).
thf(1530,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/sandbox2/benchmark/theBenchmark.p',t49_relset_1) ).
thf(9436,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)],[1530]) ).
thf(197,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 ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ ( k1_relat_1 @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( ( k3_funct_5 @ C )
= ( k3_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_5) ).
thf(3173,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 ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ ( k1_relat_1 @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
& ( ( k3_funct_5 @ C )
= ( k3_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(1790,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/sandbox2/benchmark/theBenchmark.p',t39_subset_1) ).
thf(10689,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)],[1790]) ).
thf(2108,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/sandbox2/benchmark/theBenchmark.p',t12_funct_5) ).
thf(12442,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)],[2108]) ).
thf(886,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/sandbox2/benchmark/theBenchmark.p',t38_setwiseo) ).
thf(6279,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)],[886]) ).
thf(965,axiom,
! [A: $i] :
( ( k2_tarski @ A @ A )
= ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(6647,plain,
! [A: $i] :
( ( k2_tarski @ A @ A )
= ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(717,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/sandbox2/benchmark/theBenchmark.p',t174_partfun1) ).
thf(5447,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)],[717]) ).
thf(1456,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/sandbox2/benchmark/theBenchmark.p',t2_altcat_2) ).
thf(9104,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)],[1456]) ).
thf(15,axiom,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ~ ( r2_wellord2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_card_1) ).
thf(2440,plain,
! [A: $i] :
~ ( ( v1_finset_1 @ A )
& ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ~ ( r2_wellord2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1001,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/sandbox2/benchmark/theBenchmark.p',d6_setwiseo) ).
thf(6891,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)],[1001]) ).
thf(104,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v2_relat_1 @ B )
& ( m1_pboole @ B @ A ) )
=> ~ ( v1_xboole_0 @ ( k3_tarski @ ( k2_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_pre_circ) ).
thf(2793,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( ( v2_relat_1 @ B )
& ( m1_pboole @ B @ A ) )
=> ~ ( v1_xboole_0 @ ( k3_tarski @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1858,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/sandbox2/benchmark/theBenchmark.p',t4_ens_1) ).
thf(11065,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)],[1858]) ).
thf(1301,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k10_relat_1 @ B @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t168_relat_1) ).
thf(8378,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k10_relat_1 @ B @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).
thf(707,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/sandbox2/benchmark/theBenchmark.p',t12_funct_6) ).
thf(5417,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)],[707]) ).
thf(407,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/sandbox2/benchmark/theBenchmark.p',t47_funct_1) ).
thf(4036,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)],[407]) ).
thf(57,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( A
= ( k3_partfun1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_partfun1) ).
thf(2645,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( A
= ( k3_partfun1 @ A @ ( k1_relat_1 @ A ) @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(2180,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/sandbox2/benchmark/theBenchmark.p',t38_subset_1) ).
thf(12823,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)],[2180]) ).
thf(806,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/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(5909,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)],[806]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_xboole_0 @ A @ ( k4_xboole_0 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_xboole_1) ).
thf(3841,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)],[361]) ).
thf(680,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/sandbox2/benchmark/theBenchmark.p',t35_funcop_1) ).
thf(5295,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)],[680]) ).
thf(1460,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/sandbox2/benchmark/theBenchmark.p',dt_k1_partfun1) ).
thf(9137,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)],[1460]) ).
thf(672,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/sandbox2/benchmark/theBenchmark.p',d1_yellow18) ).
thf(5249,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)],[672]) ).
thf(793,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/sandbox2/benchmark/theBenchmark.p',t16_ens_1) ).
thf(5840,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)],[793]) ).
thf(1038,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t126_funct_1) ).
thf(7106,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k3_xboole_0 @ A @ ( k9_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( v1_funct_1 @ ( k9_funct_7 @ C @ B ) )
& ( m2_relset_1 @ ( k9_funct_7 @ C @ B ) @ A @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_funct_7) ).
thf(2423,plain,
! [A: $i,B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ! [C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ A ) )
=> ( ( v1_funct_1 @ ( k9_funct_7 @ C @ B ) )
& ( m2_relset_1 @ ( k9_funct_7 @ C @ B ) @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2307,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/sandbox2/benchmark/theBenchmark.p',commutativity_k7_subset_1) ).
thf(13326,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)],[2307]) ).
thf(1926,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_6_domain_1) ).
thf(11414,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)],[1926]) ).
thf(1650,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/sandbox2/benchmark/theBenchmark.p',dt_k8_setwiseo) ).
thf(9985,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)],[1650]) ).
thf(1046,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( ( k6_relat_1 @ A )
= ( k7_relat_1 @ ( k6_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_funct_3) ).
thf(7133,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)],[1046]) ).
thf(1363,axiom,
! [A: $i,B: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ B ) )
=> ? [C: $i] : ( m2_filter_1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_filter_1) ).
thf(8708,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)],[1363]) ).
thf(1007,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/sandbox2/benchmark/theBenchmark.p',d7_partfun1) ).
thf(6922,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)],[1007]) ).
thf(2060,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/sandbox2/benchmark/theBenchmark.p',s12_funct_2) ).
thf(12238,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)],[2060]) ).
thf(1966,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/sandbox2/benchmark/theBenchmark.p',t77_mcart_1) ).
thf(11705,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)],[1966]) ).
thf(1260,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/sandbox2/benchmark/theBenchmark.p',t185_partfun1) ).
thf(8195,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)],[1260]) ).
thf(1870,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/sandbox2/benchmark/theBenchmark.p',dt_k2_monoid_0) ).
thf(11148,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)],[1870]) ).
thf(762,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_relat_1) ).
thf(5715,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k1_tarski @ ( k4_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(1055,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_setfam_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_setfam_1) ).
thf(7160,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_setfam_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(2139,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/sandbox2/benchmark/theBenchmark.p',free_g1_metric_1) ).
thf(12628,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)],[2139]) ).
thf(597,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/sandbox2/benchmark/theBenchmark.p',t82_funct_1) ).
thf(4921,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)],[597]) ).
thf(1003,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_partfun1) ).
thf(6901,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ k1_xboole_0 @ A ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(1457,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/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(9107,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)],[1457]) ).
thf(1542,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/sandbox2/benchmark/theBenchmark.p',t30_subset_1) ).
thf(9484,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)],[1542]) ).
thf(2038,axiom,
! [A: $i,B: $i] :
( ( ( k4_zfmisc_1 @ A @ A @ A @ A )
= ( k4_zfmisc_1 @ B @ B @ B @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_mcart_1) ).
thf(12106,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)],[2038]) ).
thf(1254,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/sandbox2/benchmark/theBenchmark.p',t122_funct_1) ).
thf(8164,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)],[1254]) ).
thf(837,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/sandbox2/benchmark/theBenchmark.p',t44_funcop_1) ).
thf(6053,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)],[837]) ).
thf(1961,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/sandbox2/benchmark/theBenchmark.p',t7_altcat_1) ).
thf(11692,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)],[1961]) ).
thf(2186,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/sandbox2/benchmark/theBenchmark.p',t41_subset_1) ).
thf(12857,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)],[2186]) ).
thf(2291,axiom,
! [A: $i,B: $i,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 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k8_relset_2 @ A @ B @ D @ E ) @ ( k8_relset_2 @ A @ B @ C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_relset_2) ).
thf(13264,plain,
! [A: $i,B: $i,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 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k8_relset_2 @ A @ B @ D @ E ) @ ( k8_relset_2 @ A @ B @ C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2291]) ).
thf(1509,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( ( r1_tarski @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_xboole_1) ).
thf(9352,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)],[1509]) ).
thf(1848,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/sandbox2/benchmark/theBenchmark.p',t26_relset_1) ).
thf(11033,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)],[1848]) ).
thf(2374,axiom,
! [A: $i,B: $i] : ( m1_subset_1 @ ( k1_funct_7 @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_7) ).
thf(13603,plain,
! [A: $i,B: $i] : ( m1_subset_1 @ ( k1_funct_7 @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2374]) ).
thf(1687,axiom,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relset_1) ).
thf(10175,plain,
! [A: $i,B: $i] : ( m2_relset_1 @ k1_xboole_0 @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1687]) ).
thf(964,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/sandbox2/benchmark/theBenchmark.p',d5_setfam_1) ).
thf(6615,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)],[964]) ).
thf(528,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ( r1_tarski @ A @ k1_numbers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_membered) ).
thf(4613,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ( r1_tarski @ A @ k1_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(369,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 ) )
=> ( ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) )
<=> ( ( k4_finseq_1 @ A )
= ( k4_finseq_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_finseq_3) ).
thf(3871,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 ) )
=> ( ( ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) )
=> ( ( k4_finseq_1 @ A )
= ( k4_finseq_1 @ B ) ) )
& ( ( ( k4_finseq_1 @ A )
= ( k4_finseq_1 @ B ) )
=> ( ( k3_finseq_1 @ A )
= ( k3_finseq_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(699,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/sandbox2/benchmark/theBenchmark.p',t33_setwiseo) ).
thf(5359,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)],[699]) ).
thf(39,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_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t133_funct_2) ).
thf(2585,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_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(2059,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/sandbox2/benchmark/theBenchmark.p',t18_funct_2) ).
thf(12233,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)],[2059]) ).
thf(1693,axiom,
! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(10202,plain,
! [A: $i] : ( v1_relat_1 @ ( k6_relat_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1693]) ).
thf(375,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/sandbox2/benchmark/theBenchmark.p',t131_partfun1) ).
thf(3890,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)],[375]) ).
thf(1636,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/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(9939,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)],[1636]) ).
thf(1365,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( k2_relat_1 @ ( k2_funcop_1 @ A @ B ) )
= ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funcop_1) ).
thf(8713,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)],[1365]) ).
thf(1016,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/sandbox2/benchmark/theBenchmark.p',idempotence_k1_funct_4) ).
thf(7010,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)],[1016]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) )
& ( v2_relat_1 @ ( k5_relat_1 @ B @ A ) )
& ( v1_funct_1 @ ( k5_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_pre_circ) ).
thf(3491,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v1_relat_1 @ ( k5_relat_1 @ B @ A ) )
& ( v2_relat_1 @ ( k5_relat_1 @ B @ A ) )
& ( v1_funct_1 @ ( k5_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(2256,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/sandbox2/benchmark/theBenchmark.p',t27_borsuk_1) ).
thf(13135,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)],[2256]) ).
thf(1053,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 @ ( k10_relat_1 @ ( k1_funct_3 @ D ) @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_3) ).
thf(7155,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 @ ( k10_relat_1 @ ( k1_funct_3 @ D ) @ B ) @ ( k1_zfmisc_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(488,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/sandbox2/benchmark/theBenchmark.p',d5_card_3) ).
thf(4412,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)],[488]) ).
thf(2345,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_0_group_5) ).
thf(13466,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)],[2345]) ).
thf(1905,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/sandbox2/benchmark/theBenchmark.p',t55_domain_1) ).
thf(11332,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)],[1905]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ A @ C ) @ ( k3_partfun1 @ D @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_partfun1) ).
thf(2941,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ A @ C ) @ ( k3_partfun1 @ D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1662,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/sandbox2/benchmark/theBenchmark.p',t4_relset_1) ).
thf(10079,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)],[1662]) ).
thf(954,axiom,
! [A: $i,B: $i] : ( v1_fraenkel @ ( k1_funct_2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_fraenkel) ).
thf(6578,plain,
! [A: $i,B: $i] : ( v1_fraenkel @ ( k1_funct_2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(1181,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/sandbox2/benchmark/theBenchmark.p',t186_partfun1) ).
thf(7753,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)],[1181]) ).
thf(1473,axiom,
~ ( v1_xboole_0 @ k4_qc_lang1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_qc_lang1) ).
thf(9181,plain,
~ ( v1_xboole_0 @ k4_qc_lang1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473]) ).
thf(1706,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( m1_subset_1 @ ( a_4_1_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relset_2) ).
thf(10289,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ! [D: $i] :
( ( m2_relset_1 @ D @ A @ B )
=> ( m1_subset_1 @ ( a_4_1_relset_2 @ A @ B @ C @ D ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1706]) ).
thf(1021,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/sandbox2/benchmark/theBenchmark.p',t76_funct_4) ).
thf(7031,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)],[1021]) ).
thf(2323,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/sandbox2/benchmark/theBenchmark.p',free_g2_struct_0) ).
thf(13372,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)],[2323]) ).
thf(1137,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/sandbox2/benchmark/theBenchmark.p',t38_funct_1) ).
thf(7491,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)],[1137]) ).
thf(231,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/sandbox2/benchmark/theBenchmark.p',d8_ens_1) ).
thf(3289,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)],[231]) ).
thf(501,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/sandbox2/benchmark/theBenchmark.p',redefinition_r6_pboole) ).
thf(4503,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)],[501]) ).
thf(1703,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/sandbox2/benchmark/theBenchmark.p',t27_relset_1) ).
thf(10274,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)],[1703]) ).
thf(1857,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/sandbox2/benchmark/theBenchmark.p',dt_k19_pralg_1) ).
thf(11063,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)],[1857]) ).
thf(1207,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/sandbox2/benchmark/theBenchmark.p',t4_pre_circ) ).
thf(7920,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)],[1207]) ).
thf(947,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_fraenkel @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_fraenkel) ).
thf(6546,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_fraenkel @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(872,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_0_ens_1) ).
thf(6228,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)],[872]) ).
thf(179,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/sandbox2/benchmark/theBenchmark.p',t54_relat_1) ).
thf(3111,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)],[179]) ).
thf(1940,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/sandbox2/benchmark/theBenchmark.p',fc2_card_fil) ).
thf(11561,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)],[1940]) ).
thf(473,axiom,
! [A: $i,B: $i] :
( ( v2_membered @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v2_membered @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_membered) ).
thf(4365,plain,
! [A: $i,B: $i] :
( ( v2_membered @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v2_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(1844,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( r2_hidden @ C @ A )
<=> ( r2_hidden @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(11011,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)],[1844]) ).
thf(2231,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/sandbox2/benchmark/theBenchmark.p',t54_setfam_1) ).
thf(13031,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)],[2231]) ).
thf(251,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/sandbox2/benchmark/theBenchmark.p',t40_sysrel) ).
thf(3396,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)],[251]) ).
thf(2003,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/sandbox2/benchmark/theBenchmark.p',t7_relset_2) ).
thf(11920,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)],[2003]) ).
thf(669,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/sandbox2/benchmark/theBenchmark.p',t45_funcop_1) ).
thf(5241,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)],[669]) ).
thf(1393,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/sandbox2/benchmark/theBenchmark.p',t86_enumset1) ).
thf(8807,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)],[1393]) ).
thf(247,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/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
thf(3343,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)],[247]) ).
thf(193,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 @ A @ ( k1_relat_1 @ ( k3_funct_5 @ C ) ) )
& ( v1_relat_1 @ ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_funct_5) ).
thf(3158,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 @ A @ ( k1_relat_1 @ ( k3_funct_5 @ C ) ) )
& ( v1_relat_1 @ ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k3_funct_5 @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(150,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/sandbox2/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(2970,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)],[150]) ).
thf(1989,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/sandbox2/benchmark/theBenchmark.p',t2_card_fil) ).
thf(11836,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)],[1989]) ).
thf(103,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/sandbox2/benchmark/theBenchmark.p',d3_pua2mss1) ).
thf(2789,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)],[103]) ).
thf(2239,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/sandbox2/benchmark/theBenchmark.p',t21_yellow_9) ).
thf(13060,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)],[2239]) ).
thf(1749,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/sandbox2/benchmark/theBenchmark.p',t8_card_fil) ).
thf(10480,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)],[1749]) ).
thf(2127,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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_cat_5) ).
thf(12541,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)],[2127]) ).
thf(961,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k6_relat_1 @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
thf(6606,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)],[961]) ).
thf(210,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ ( k1_relat_1 @ A ) )
=> ( m1_eqrel_1 @ ( a_2_1_pua2mss1 @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pua2mss1) ).
thf(3213,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( m1_eqrel_1 @ B @ ( k1_relat_1 @ A ) )
=> ( m1_eqrel_1 @ ( a_2_1_pua2mss1 @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(286,axiom,
! [A: $i] : ( r3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k1_setwiseo @ A ) @ ( k9_setwiseo @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_setwiseo) ).
thf(3536,plain,
! [A: $i] : ( r3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k1_setwiseo @ A ) @ ( k9_setwiseo @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(563,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/sandbox2/benchmark/theBenchmark.p',t17_ens_1) ).
thf(4786,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)],[563]) ).
thf(1149,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) )
& ( v2_funct_1 @ B ) )
=> ( ( k3_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ B ) @ A ) )
= ( k9_relat_1 @ B @ ( k3_tarski @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_funct_3) ).
thf(7611,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) )
& ( v2_funct_1 @ B ) )
=> ( ( k3_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ B ) @ A ) )
= ( k9_relat_1 @ B @ ( k3_tarski @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(2021,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/sandbox2/benchmark/theBenchmark.p',t58_setfam_1) ).
thf(12028,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)],[2021]) ).
thf(1171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ D @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_funct_2) ).
thf(7709,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_funct_1 @ D )
& ( m2_relset_1 @ D @ A @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ D @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(248,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/sandbox2/benchmark/theBenchmark.p',t9_setfam_1) ).
thf(3372,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)],[248]) ).
thf(1660,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/sandbox2/benchmark/theBenchmark.p',t111_zfmisc_1) ).
thf(10068,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)],[1660]) ).
thf(1736,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/sandbox2/benchmark/theBenchmark.p',t55_funct_4) ).
thf(10425,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)],[1736]) ).
thf(202,axiom,
! [A: $i,B: $i] : ( r1_xboole_0 @ ( k4_xboole_0 @ A @ B ) @ ( k4_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_xboole_1) ).
thf(3187,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)],[202]) ).
thf(1957,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/sandbox2/benchmark/theBenchmark.p',t72_funcop_1) ).
thf(11682,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)],[1957]) ).
thf(1683,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/sandbox2/benchmark/theBenchmark.p',t60_funcop_1) ).
thf(10155,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)],[1683]) ).
thf(1173,axiom,
! [A: $i,B: $i,C: $i] :
( ( k1_enumset1 @ A @ B @ C )
= ( k1_enumset1 @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_enumset1) ).
thf(7714,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)],[1173]) ).
thf(457,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 )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ D ) )
& ( C
= ( k5_funcop_1 @ D @ A @ B ) ) )
=> ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_finseq_2) ).
thf(4268,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 )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( ( r1_tarski @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_relat_1 @ B ) ) @ ( k1_relat_1 @ D ) )
& ( C
= ( k5_funcop_1 @ D @ A @ B ) ) )
=> ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(168,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/sandbox2/benchmark/theBenchmark.p',t11_functor0) ).
thf(3070,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)],[168]) ).
thf(1690,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k5_finsub_1 @ A ) @ ( k5_finsub_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).
thf(10194,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)],[1690]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ ( k3_funct_5 @ C ) ) @ ( k1_funct_2 @ B @ ( k2_relat_1 @ C ) ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k5_funct_5 @ C ) ) @ ( k1_funct_2 @ A @ ( k2_relat_1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_funct_5) ).
thf(3636,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_zfmisc_1 @ A @ B ) )
=> ( ( r1_tarski @ ( k2_relat_1 @ ( k3_funct_5 @ C ) ) @ ( k1_funct_2 @ B @ ( k2_relat_1 @ C ) ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k5_funct_5 @ C ) ) @ ( k1_funct_2 @ A @ ( k2_relat_1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(216,axiom,
! [A: $i,B: $i] : ( r2_wellord2 @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_wellord2) ).
thf(3234,plain,
! [A: $i] : ( r2_wellord2 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ A @ ( k4_relset_1 @ B @ C @ ( k3_partfun1 @ D @ B @ C ) ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_partfun1) ).
thf(2859,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ A @ ( k4_relset_1 @ B @ C @ ( k3_partfun1 @ D @ B @ C ) ) )
=> ( ( k1_funct_1 @ ( k3_partfun1 @ D @ B @ C ) @ A )
= ( k1_funct_1 @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(141,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_relat_1 @ ( k5_funct_5 @ A ) )
= ( k2_funct_5 @ ( k1_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_funct_5) ).
thf(2938,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( k1_relat_1 @ ( k5_funct_5 @ A ) )
= ( k2_funct_5 @ ( k1_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(1379,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/sandbox2/benchmark/theBenchmark.p',d1_lattice2) ).
thf(8762,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)],[1379]) ).
thf(2321,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/sandbox2/benchmark/theBenchmark.p',commutativity_k1_relset_2) ).
thf(13368,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)],[2321]) ).
thf(998,axiom,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(6881,plain,
( ( k3_tarski @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(219,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k7_funct_6 @ A ) )
& ( v1_funct_1 @ ( k7_funct_6 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_funct_6) ).
thf(3240,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k7_funct_6 @ A ) )
& ( v1_funct_1 @ ( k7_funct_6 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(1567,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( k5_setfam_1 @ A @ B )
= k1_xboole_0 )
<=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relset_2) ).
thf(9602,plain,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ A ) ) )
=> ( ( ( ( k5_setfam_1 @ A @ B )
= k1_xboole_0 )
=> ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = k1_xboole_0 ) ) )
& ( ! [C: $i] :
( ( r2_hidden @ C @ B )
=> ( C = k1_xboole_0 ) )
=> ( ( k5_setfam_1 @ A @ B )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567]) ).
thf(61,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/sandbox2/benchmark/theBenchmark.p',t62_setwiseo) ).
thf(2657,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)],[61]) ).
thf(1077,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_funct_1) ).
thf(7233,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k10_relat_1 @ ( k7_relat_1 @ C @ A ) @ B )
= ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(1596,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_fraenkel @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_closure2) ).
thf(9733,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_fraenkel @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1596]) ).
thf(1313,axiom,
! [A: $i] :
? [B: $i] :
( ( v1_relat_1 @ B )
& ( r2_wellord1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_wellord2) ).
thf(8470,plain,
! [A: $i] :
? [B: $i] :
( ( v1_relat_1 @ B )
& ( r2_wellord1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(1965,axiom,
! [A: $i] :
? [B: $i] : ( m1_pboole @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_pboole) ).
thf(11703,plain,
! [A: $i] :
? [B: $i] : ( m1_pboole @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1965]) ).
thf(171,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ( ( ( ( k3_finseq_1 @ B )
= A )
& ( ( k3_finseq_1 @ C )
= A )
& ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( r2_hidden @ D @ ( k2_finseq_1 @ A ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finseq_2) ).
thf(3081,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( v1_finseq_1 @ B ) )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ( ( ( ( k3_finseq_1 @ B )
= A )
& ( ( k3_finseq_1 @ C )
= A )
& ! [D: $i] :
( ( m2_subset_1 @ D @ k1_numbers @ k5_numbers )
=> ( ( r2_hidden @ D @ ( k2_finseq_1 @ A ) )
=> ( ( k1_funct_1 @ B @ D )
= ( k1_funct_1 @ C @ D ) ) ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(388,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/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
thf(3945,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)],[388]) ).
thf(598,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/sandbox2/benchmark/theBenchmark.p',t17_funct_3) ).
thf(4926,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)],[598]) ).
thf(544,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/sandbox2/benchmark/theBenchmark.p',t92_funct_3) ).
thf(4677,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)],[544]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_funct_3) ).
thf(3266,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',t14_functor0) ).
thf(2674,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)],[67]) ).
thf(1354,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/sandbox2/benchmark/theBenchmark.p',d7_realset1) ).
thf(8684,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)],[1354]) ).
thf(789,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/sandbox2/benchmark/theBenchmark.p',t69_partfun1) ).
thf(5831,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)],[789]) ).
thf(1498,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k7_relat_1 @ A @ ( k1_relat_1 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_relat_1) ).
thf(9295,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k7_relat_1 @ A @ ( k1_relat_1 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498]) ).
thf(1792,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/sandbox2/benchmark/theBenchmark.p',dt_k6_relset_2) ).
thf(10700,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)],[1792]) ).
thf(1669,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r2_relat_2 @ A @ B )
<=> ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ ( k4_tarski @ C @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_2) ).
thf(10100,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( r2_relat_2 @ A @ B )
=> ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ ( k4_tarski @ C @ C ) @ A ) ) )
& ( ! [C: $i] :
~ ( ( r2_hidden @ C @ B )
& ( r2_hidden @ ( k4_tarski @ C @ C ) @ A ) )
=> ( r2_relat_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1669]) ).
thf(2188,axiom,
~ ( v1_xboole_0 @ k3_qc_lang1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_qc_lang1) ).
thf(12862,plain,
~ ( v1_xboole_0 @ k3_qc_lang1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2188]) ).
thf(1359,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 @ ( k2_relat_1 @ C ) )
& ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k2_relat_1 @ B ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_funct_3) ).
thf(8697,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 @ ( k2_relat_1 @ C ) )
& ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k2_relat_1 @ B ) ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ ( k5_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).
thf(490,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/sandbox2/benchmark/theBenchmark.p',t37_funcop_1) ).
thf(4465,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)],[490]) ).
thf(2185,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/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
thf(12840,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)],[2185]) ).
thf(526,axiom,
( ( ( k1_relat_1 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
thf(4605,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)],[526]) ).
thf(641,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
<=> ( ( k3_xboole_0 @ A @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(5099,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)],[641]) ).
thf(1383,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/sandbox2/benchmark/theBenchmark.p',fc3_funcop_1) ).
thf(8777,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)],[1383]) ).
thf(2201,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/sandbox2/benchmark/theBenchmark.p',t55_partfun1) ).
thf(12909,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)],[2201]) ).
thf(1170,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
<=> ( ( k10_relat_1 @ B @ ( k1_tarski @ A ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_1) ).
thf(7704,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( r2_hidden @ A @ ( k2_relat_1 @ B ) )
=> ( ( k10_relat_1 @ B @ ( k1_tarski @ A ) )
!= k1_xboole_0 ) )
& ( ( ( k10_relat_1 @ B @ ( k1_tarski @ A ) )
!= k1_xboole_0 )
=> ( r2_hidden @ A @ ( k2_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(2318,axiom,
m1_subset_1 @ a_0_1_domain_1 @ ( k1_zfmisc_1 @ f2_s8_domain_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_domain_1) ).
thf(13363,plain,
m1_subset_1 @ a_0_1_domain_1 @ ( k1_zfmisc_1 @ f2_s8_domain_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2318]) ).
thf(1289,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/sandbox2/benchmark/theBenchmark.p',fc1_rfinseq) ).
thf(8332,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)],[1289]) ).
thf(640,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( r2_wellord1 @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r2_wellord1 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t187_orders_1) ).
thf(5097,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( r2_wellord1 @ A @ B )
& ( r1_tarski @ C @ B ) )
=> ( r2_wellord1 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(1255,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/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
thf(8167,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)],[1255]) ).
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/sandbox2/benchmark/theBenchmark.p',dt_k6_setwiseo) ).
thf(2398,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(468,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/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).
thf(4328,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)],[468]) ).
thf(1216,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ ( k2_relat_1 @ A ) )
= ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t169_relat_1) ).
thf(7963,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k10_relat_1 @ A @ ( k2_relat_1 @ A ) )
= ( k1_relat_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(78,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 ) )
& ( ( k3_funct_5 @ C )
= ( k3_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_funct_5) ).
thf(2716,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 ) )
& ( ( k3_funct_5 @ C )
= ( k3_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(478,axiom,
! [A: $i] :
( ( ( k1_relat_1 @ ( k6_relat_1 @ A ) )
= A )
& ( ( k2_relat_1 @ ( k6_relat_1 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
thf(4381,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)],[478]) ).
thf(676,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/sandbox2/benchmark/theBenchmark.p',t16_yellow20) ).
thf(5271,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)],[676]) ).
thf(696,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v1_xboole_0 @ ( k1_tarski @ A ) )
& ( v1_setfam_1 @ ( k1_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_setfam_1) ).
thf(5350,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)],[696]) ).
thf(522,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/sandbox2/benchmark/theBenchmark.p',t4_funct_7) ).
thf(4590,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)],[522]) ).
thf(610,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ ( k2_funcop_1 @ A @ B ) )
& ( v1_funct_1 @ ( k2_funcop_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funcop_1) ).
thf(4975,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)],[610]) ).
thf(1506,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/sandbox2/benchmark/theBenchmark.p',t118_funct_1) ).
thf(9339,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)],[1506]) ).
thf(253,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/sandbox2/benchmark/theBenchmark.p',t124_funct_1) ).
thf(3404,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)],[253]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C )
& ( r2_wellord2 @ A @ C ) )
=> ( ( r2_wellord2 @ A @ B )
& ( r2_wellord2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_card_1) ).
thf(3868,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C )
& ( r2_wellord2 @ A @ C ) )
=> ( ( r2_wellord2 @ A @ B )
& ( r2_wellord2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(554,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/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
thf(4758,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)],[554]) ).
thf(784,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/sandbox2/benchmark/theBenchmark.p',t34_funct_2) ).
thf(5799,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)],[784]) ).
thf(1608,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/sandbox2/benchmark/theBenchmark.p',t79_relat_1) ).
thf(9820,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)],[1608]) ).
thf(602,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/sandbox2/benchmark/theBenchmark.p',cc17_membered) ).
thf(4946,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)],[602]) ).
thf(1641,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/sandbox2/benchmark/theBenchmark.p',t32_domain_1) ).
thf(9952,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)],[1641]) ).
thf(2393,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ? [C: $i] : ( m2_realset1 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_realset1) ).
thf(13685,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)],[2393]) ).
thf(1968,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_5_domain_1) ).
thf(11714,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)],[1968]) ).
thf(2212,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/sandbox2/benchmark/theBenchmark.p',t15_relset_2) ).
thf(12964,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)],[2212]) ).
thf(300,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_relat_1 @ A )
=> ( v1_setfam_1 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_pboole) ).
thf(3599,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_relat_1 @ A )
=> ( v1_setfam_1 @ ( k2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(2304,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/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(13319,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)],[2304]) ).
thf(1350,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/sandbox2/benchmark/theBenchmark.p',d8_binop_1) ).
thf(8656,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)],[1350]) ).
thf(1885,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/sandbox2/benchmark/theBenchmark.p',t108_zfmisc_1) ).
thf(11237,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)],[1885]) ).
thf(1773,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/sandbox2/benchmark/theBenchmark.p',t63_mcart_1) ).
thf(10596,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)],[1773]) ).
thf(172,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/sandbox2/benchmark/theBenchmark.p',dt_k9_binop_2) ).
thf(3091,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)],[172]) ).
thf(1646,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/sandbox2/benchmark/theBenchmark.p',dt_k2_nattra_1) ).
thf(9967,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)],[1646]) ).
thf(1520,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/sandbox2/benchmark/theBenchmark.p',t78_funct_4) ).
thf(9390,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)],[1520]) ).
thf(1302,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/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
thf(8381,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)],[1302]) ).
thf(451,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/sandbox2/benchmark/theBenchmark.p',t28_funct_2) ).
thf(4251,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)],[451]) ).
thf(2273,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/sandbox2/benchmark/theBenchmark.p',t8_subset_1) ).
thf(13197,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)],[2273]) ).
thf(352,axiom,
! [A: $i] :
( ( r2_hidden @ k1_xboole_0 @ A )
=> ( ( k1_setfam_1 @ A )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_setfam_1) ).
thf(3796,plain,
! [A: $i] :
( ( r2_hidden @ k1_xboole_0 @ A )
=> ( ( k1_setfam_1 @ A )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(653,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 ) )
=> ( ( k2_yellow_3 @ A @ B @ C @ D @ E @ F )
= ( k1_yellow_3 @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_yellow_3) ).
thf(5185,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 ) )
=> ( ( k2_yellow_3 @ A @ B @ C @ D @ E @ F )
= ( k1_yellow_3 @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(2385,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_18_fraenkel) ).
thf(13633,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)],[2385]) ).
thf(429,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/sandbox2/benchmark/theBenchmark.p',t3_lattice5) ).
thf(4127,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)],[429]) ).
thf(1065,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/sandbox2/benchmark/theBenchmark.p',t28_zfmisc_1) ).
thf(7191,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)],[1065]) ).
thf(907,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_funct_1) ).
thf(6385,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_tarski @ ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(1992,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A ) )
=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( k1_eqrel_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_toler_1) ).
thf(11846,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_hidden @ B @ A )
& ( r2_hidden @ C @ A ) )
=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( k1_eqrel_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1992]) ).
thf(2277,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/sandbox2/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(13217,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)],[2277]) ).
thf(1089,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/sandbox2/benchmark/theBenchmark.p',d9_binop_2) ).
thf(7270,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)],[1089]) ).
thf(535,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/sandbox2/benchmark/theBenchmark.p',t29_funcop_1) ).
thf(4645,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)],[535]) ).
thf(1252,axiom,
! [A: $i] :
( ( k5_relset_1 @ A @ A @ ( k1_eqrel_1 @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_toler_1) ).
thf(8152,plain,
! [A: $i] :
( ( k5_relset_1 @ A @ A @ ( k1_eqrel_1 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(2032,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/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(12067,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)],[2032]) ).
thf(1664,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/sandbox2/benchmark/theBenchmark.p',fc16_finset_1) ).
thf(10083,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)],[1664]) ).
thf(2027,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/sandbox2/benchmark/theBenchmark.p',t33_partfun1) ).
thf(12053,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)],[2027]) ).
thf(1856,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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_monoid_0) ).
thf(11060,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)],[1856]) ).
thf(1398,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/sandbox2/benchmark/theBenchmark.p',t20_funct_1) ).
thf(8841,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)],[1398]) ).
thf(2354,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_33_fraenkel) ).
thf(13497,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)],[2354]) ).
thf(1344,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/sandbox2/benchmark/theBenchmark.p',t102_relat_1) ).
thf(8629,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)],[1344]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_funct_1) ).
thf(3695,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) )
= ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(1329,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/sandbox2/benchmark/theBenchmark.p',t42_funct_1) ).
thf(8566,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)],[1329]) ).
thf(243,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ k5_numbers @ B )
& ( m2_relset_1 @ D @ k5_numbers @ B ) )
=> ( ( C
= ( k2_partfun1 @ k5_numbers @ B @ D @ ( k2_finseq_1 @ A ) ) )
=> ( ( k3_finseq_1 @ C )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_finseq_2) ).
thf(3330,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( ( v1_funct_1 @ D )
& ( v1_funct_2 @ D @ k5_numbers @ B )
& ( m2_relset_1 @ D @ k5_numbers @ B ) )
=> ( ( C
= ( k2_partfun1 @ k5_numbers @ B @ D @ ( k2_finseq_1 @ A ) ) )
=> ( ( k3_finseq_1 @ C )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(209,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/sandbox2/benchmark/theBenchmark.p',t56_funct_1) ).
thf(3208,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)],[209]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_relat_1) ).
thf(5331,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(1472,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/sandbox2/benchmark/theBenchmark.p',t16_funct_4) ).
thf(9178,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)],[1472]) ).
thf(140,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k4_relat_1 @ A ) )
& ( v1_relat_1 @ ( k4_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(2935,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)],[140]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k1_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( r2_hidden @ ( k3_funct_5 @ D ) @ ( k1_funct_2 @ A @ ( k1_funct_2 @ B @ C ) ) )
& ( r2_hidden @ ( k5_funct_5 @ D ) @ ( k1_funct_2 @ B @ ( k1_funct_2 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_6) ).
thf(3002,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r2_hidden @ D @ ( k1_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ C ) )
=> ( ( ( k2_zfmisc_1 @ A @ B )
= k1_xboole_0 )
| ( ( r2_hidden @ ( k3_funct_5 @ D ) @ ( k1_funct_2 @ A @ ( k1_funct_2 @ B @ C ) ) )
& ( r2_hidden @ ( k5_funct_5 @ D ) @ ( k1_funct_2 @ B @ ( k1_funct_2 @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(2325,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_0_card_fil) ).
thf(13380,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)],[2325]) ).
thf(575,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/sandbox2/benchmark/theBenchmark.p',t54_funct_4) ).
thf(4822,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)],[575]) ).
thf(1716,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/sandbox2/benchmark/theBenchmark.p',dt_k3_funct_2) ).
thf(10348,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)],[1716]) ).
thf(1295,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/sandbox2/benchmark/theBenchmark.p',t7_funct_5) ).
thf(8359,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)],[1295]) ).
thf(1343,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/sandbox2/benchmark/theBenchmark.p',t11_finseq_2) ).
thf(8624,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)],[1343]) ).
thf(1039,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 ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ ( k7_relat_1 @ ( k8_relat_1 @ A @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_funct_4) ).
thf(7109,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 ) )
=> ( ( r1_tarski @ C @ D )
=> ( r1_tarski @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ ( k7_relat_1 @ ( k8_relat_1 @ A @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(2381,axiom,
m1_subset_1 @ k2_zfrefle1 @ ( k1_zfmisc_1 @ k9_zf_lang ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfrefle1) ).
thf(13621,plain,
m1_subset_1 @ k2_zfrefle1 @ ( k1_zfmisc_1 @ k9_zf_lang ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2381]) ).
thf(517,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/sandbox2/benchmark/theBenchmark.p',t67_relat_1) ).
thf(4573,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)],[517]) ).
thf(638,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_1_pua2mss1) ).
thf(5086,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)],[638]) ).
thf(2005,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_finset_1) ).
thf(11924,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)],[2005]) ).
thf(2012,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/sandbox2/benchmark/theBenchmark.p',d1_borsuk_1) ).
thf(11968,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)],[2012]) ).
thf(556,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/sandbox2/benchmark/theBenchmark.p',redefinition_k5_domain_1) ).
thf(4764,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)],[556]) ).
thf(1034,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_relat_1 @ A @ B ) @ ( k8_relat_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_relat_1) ).
thf(7094,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_relat_1 @ A @ B ) @ ( k8_relat_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(1209,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/sandbox2/benchmark/theBenchmark.p',redefinition_k1_nattra_1) ).
thf(7924,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)],[1209]) ).
thf(655,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/sandbox2/benchmark/theBenchmark.p',t18_functor0) ).
thf(5190,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)],[655]) ).
thf(660,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/sandbox2/benchmark/theBenchmark.p',t41_funct_4) ).
thf(5207,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)],[660]) ).
thf(1291,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/sandbox2/benchmark/theBenchmark.p',t91_relat_1) ).
thf(8344,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)],[1291]) ).
thf(1557,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/sandbox2/benchmark/theBenchmark.p',free_g1_group_1) ).
thf(9555,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)],[1557]) ).
thf(1546,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ C ) )
=> ( r1_tarski @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(9496,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)],[1546]) ).
thf(1132,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_relat_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(7465,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)],[1132]) ).
thf(1128,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k5_relat_1 @ ( k6_relat_1 @ ( k1_relat_1 @ A ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_relat_1) ).
thf(7455,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)],[1128]) ).
thf(295,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k3_pralg_3 @ A @ B ) )
& ( v1_funct_1 @ ( k3_pralg_3 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_pralg_3) ).
thf(3579,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_relat_1 @ ( k3_pralg_3 @ A @ B ) )
& ( v1_funct_1 @ ( k3_pralg_3 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(582,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/sandbox2/benchmark/theBenchmark.p',d5_functor0) ).
thf(4854,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)],[582]) ).
thf(1321,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ ( k3_tarski @ A ) @ B )
& ( r2_hidden @ C @ A ) )
=> ( r1_tarski @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_setfam_1) ).
thf(8497,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)],[1321]) ).
thf(313,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/sandbox2/benchmark/theBenchmark.p',dt_k12_binop_2) ).
thf(3641,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)],[313]) ).
thf(1510,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/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
thf(9354,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)],[1510]) ).
thf(1978,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/sandbox2/benchmark/theBenchmark.p',fc5_subset_1) ).
thf(11765,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)],[1978]) ).
thf(235,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/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(3302,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)],[235]) ).
thf(586,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/sandbox2/benchmark/theBenchmark.p',t73_enumset1) ).
thf(4887,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)],[586]) ).
thf(1114,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_partfun1 @ k1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t141_partfun1) ).
thf(7394,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)],[1114]) ).
thf(2122,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/sandbox2/benchmark/theBenchmark.p',t31_sysrel) ).
thf(12509,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)],[2122]) ).
thf(1850,axiom,
! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
thf(11038,plain,
! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1850]) ).
thf(1180,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/sandbox2/benchmark/theBenchmark.p',t16_funct_5) ).
thf(7746,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)],[1180]) ).
thf(828,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/sandbox2/benchmark/theBenchmark.p',d1_orders_1) ).
thf(6016,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)],[828]) ).
thf(2190,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r2_wellord1 @ B @ A )
=> ! [C: $i] :
~ ( ( r1_tarski @ C @ A )
& ( C != k1_xboole_0 )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ C )
& ! [E: $i] :
( ( r2_hidden @ E @ C )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_wellord1) ).
thf(12867,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( r2_wellord1 @ B @ A )
=> ! [C: $i] :
~ ( ( r1_tarski @ C @ A )
& ( C != k1_xboole_0 )
& ! [D: $i] :
~ ( ( r2_hidden @ D @ C )
& ! [E: $i] :
( ( r2_hidden @ E @ C )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2190]) ).
thf(1531,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( m1_pboole @ ( k18_pralg_1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k18_pralg_1) ).
thf(9439,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( m1_pboole @ ( k18_pralg_1 @ A @ B @ C ) @ ( k2_zfmisc_1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1531]) ).
thf(840,axiom,
! [A: $i] :
( ( k1_funct_2 @ k1_xboole_0 @ A )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_5) ).
thf(6061,plain,
! [A: $i] :
( ( k1_funct_2 @ k1_xboole_0 @ A )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(1770,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/sandbox2/benchmark/theBenchmark.p',t7_cqc_lang) ).
thf(10565,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)],[1770]) ).
thf(901,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_realset1) ).
thf(6340,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ A )
=> ( v1_relat_1 @ ( k1_realset1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(960,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/sandbox2/benchmark/theBenchmark.p',t73_funct_1) ).
thf(6604,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)],[960]) ).
thf(479,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/sandbox2/benchmark/theBenchmark.p',redefinition_k7_filter_1) ).
thf(4388,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)],[479]) ).
thf(1228,axiom,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
& ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_zfmisc_1) ).
thf(8042,plain,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
& ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(2022,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/sandbox2/benchmark/theBenchmark.p',dt_k9_domain_1) ).
thf(12032,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)],[2022]) ).
thf(1558,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/sandbox2/benchmark/theBenchmark.p',t18_binop_1) ).
thf(9560,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)],[1558]) ).
thf(1819,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/sandbox2/benchmark/theBenchmark.p',dt_k18_group_2) ).
thf(10842,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)],[1819]) ).
thf(80,axiom,
! [A: $i] :
? [B: $i] : ( m2_finseq_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_finseq_1) ).
thf(2721,plain,
! [A: $i] :
? [B: $i] : ( m2_finseq_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(2377,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( C = k1_xboole_0 )
=> ( ( k8_relset_2 @ A @ B @ C @ D )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_relset_2) ).
thf(13609,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( C = k1_xboole_0 )
=> ( ( k8_relset_2 @ A @ B @ C @ D )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2377]) ).
thf(1720,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/sandbox2/benchmark/theBenchmark.p',t53_funct_3) ).
thf(10370,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)],[1720]) ).
thf(1276,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/sandbox2/benchmark/theBenchmark.p',fc3_ens_1) ).
thf(8276,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)],[1276]) ).
thf(839,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/sandbox2/benchmark/theBenchmark.p',symmetry_r6_pboole) ).
thf(6059,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)],[839]) ).
thf(1959,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/sandbox2/benchmark/theBenchmark.p',t47_relset_1) ).
thf(11686,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)],[1959]) ).
thf(599,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/sandbox2/benchmark/theBenchmark.p',t3_realset1) ).
thf(4929,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)],[599]) ).
thf(1763,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/sandbox2/benchmark/theBenchmark.p',t158_funct_2) ).
thf(10532,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)],[1763]) ).
thf(1242,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/sandbox2/benchmark/theBenchmark.p',t8_funct_4) ).
thf(8088,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)],[1242]) ).
thf(1212,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/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
thf(7933,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)],[1212]) ).
thf(310,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m1_orders_1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_orders_1) ).
thf(3631,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m1_orders_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(1842,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/sandbox2/benchmark/theBenchmark.p',t48_funct_2) ).
thf(11002,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)],[1842]) ).
thf(895,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/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
thf(6308,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)],[895]) ).
thf(222,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/sandbox2/benchmark/theBenchmark.p',t70_zfmisc_1) ).
thf(3251,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)],[222]) ).
thf(1508,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/sandbox2/benchmark/theBenchmark.p',t39_funcop_1) ).
thf(9349,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)],[1508]) ).
thf(1867,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/sandbox2/benchmark/theBenchmark.p',t73_relat_1) ).
thf(11127,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)],[1867]) ).
thf(1865,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/sandbox2/benchmark/theBenchmark.p',t18_finset_1) ).
thf(11117,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)],[1865]) ).
thf(356,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/sandbox2/benchmark/theBenchmark.p',t3_monoid_0) ).
thf(3815,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)],[356]) ).
thf(1565,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/sandbox2/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(9592,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)],[1565]) ).
thf(730,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/sandbox2/benchmark/theBenchmark.p',t13_borsuk_1) ).
thf(5506,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)],[730]) ).
thf(1006,axiom,
~ ( v1_finset_1 @ k5_numbers ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_card_4) ).
thf(6920,plain,
~ ( v1_finset_1 @ k5_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(218,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/sandbox2/benchmark/theBenchmark.p',t15_relat_1) ).
thf(3238,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)],[218]) ).
thf(670,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ A @ ( k5_relat_1 @ B @ C ) )
= ( k5_relat_1 @ B @ ( k8_relat_1 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_relat_1) ).
thf(5244,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ A @ ( k5_relat_1 @ B @ C ) )
= ( k5_relat_1 @ B @ ( k8_relat_1 @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(1029,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 @ C )
= ( k2_relat_1 @ B ) )
& ( v2_funct_1 @ B )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( r2_wellord2 @ ( k1_funct_1 @ A @ D ) @ ( k1_funct_1 @ C @ ( k1_funct_1 @ B @ D ) ) ) ) )
=> ( r2_wellord2 @ ( k4_card_3 @ A ) @ ( k4_card_3 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_6) ).
thf(7077,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 @ C )
= ( k2_relat_1 @ B ) )
& ( v2_funct_1 @ B )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ B ) )
=> ( r2_wellord2 @ ( k1_funct_1 @ A @ D ) @ ( k1_funct_1 @ C @ ( k1_funct_1 @ B @ D ) ) ) ) )
=> ( r2_wellord2 @ ( k4_card_3 @ A ) @ ( k4_card_3 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',commutativity_k9_binop_2) ).
thf(2415,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)],[6]) ).
thf(2008,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/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
thf(11932,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)],[2008]) ).
thf(1694,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/sandbox2/benchmark/theBenchmark.p',redefinition_m1_triang_1) ).
thf(10204,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)],[1694]) ).
thf(1516,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( ( k10_relat_1 @ B @ ( k1_tarski @ C ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_funct_1) ).
thf(9377,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( ( k10_relat_1 @ B @ ( k1_tarski @ C ) )
= k1_xboole_0 ) )
=> ( r1_tarski @ A @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516]) ).
thf(1629,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/sandbox2/benchmark/theBenchmark.p',t14_cantor_1) ).
thf(9903,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)],[1629]) ).
thf(462,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/sandbox2/benchmark/theBenchmark.p',t10_relset_1) ).
thf(4305,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)],[462]) ).
thf(1204,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/sandbox2/benchmark/theBenchmark.p',t71_partfun1) ).
thf(7907,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)],[1204]) ).
thf(1431,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( k10_relat_1 @ A @ B ) )
<=> ! [D: $i] :
( ( r2_hidden @ D @ C )
<=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
thf(8970,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i,C: $i] :
( ( ( C
= ( k10_relat_1 @ A @ B ) )
=> ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( r2_hidden @ D @ C )
=> ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) ) )
& ( ? [E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ A )
& ( r2_hidden @ E @ B ) )
=> ( r2_hidden @ D @ C ) ) )
=> ( C
= ( k10_relat_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431]) ).
thf(1787,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/sandbox2/benchmark/theBenchmark.p',dt_m3_realset1) ).
thf(10677,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)],[1787]) ).
thf(856,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(6147,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( v1_relat_1 @ ( k8_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ B )
= ( k4_xboole_0 @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(2774,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)],[98]) ).
thf(869,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/sandbox2/benchmark/theBenchmark.p',t35_sysrel) ).
thf(6217,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)],[869]) ).
thf(2023,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/sandbox2/benchmark/theBenchmark.p',t29_borsuk_1) ).
thf(12034,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)],[2023]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k3_partfun1 @ A @ B @ C ) )
& ( m2_relset_1 @ ( k3_partfun1 @ A @ B @ C ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_partfun1) ).
thf(3683,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v1_funct_1 @ ( k3_partfun1 @ A @ B @ C ) )
& ( m2_relset_1 @ ( k3_partfun1 @ A @ B @ C ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(577,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/sandbox2/benchmark/theBenchmark.p',t25_funct_2) ).
thf(4828,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)],[577]) ).
thf(345,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/sandbox2/benchmark/theBenchmark.p',d9_funct_1) ).
thf(3779,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)],[345]) ).
thf(1147,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( v1_fraenkel @ ( k4_card_3 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_card_3) ).
thf(7607,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)],[1147]) ).
thf(683,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/sandbox2/benchmark/theBenchmark.p',dt_m1_card_fil) ).
thf(5303,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)],[683]) ).
thf(1123,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/sandbox2/benchmark/theBenchmark.p',t10_lattice2) ).
thf(7438,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)],[1123]) ).
thf(1829,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/sandbox2/benchmark/theBenchmark.p',cc6_tex_2) ).
thf(10898,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)],[1829]) ).
thf(1970,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/sandbox2/benchmark/theBenchmark.p',t33_subset_1) ).
thf(11735,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)],[1970]) ).
thf(2100,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/sandbox2/benchmark/theBenchmark.p',d2_binop_1) ).
thf(12413,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)],[2100]) ).
thf(803,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(5901,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v2_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(2083,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/sandbox2/benchmark/theBenchmark.p',dt_k6_funcop_1) ).
thf(12354,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)],[2083]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( r2_wellord2 @ A @ B )
=> ( r2_wellord2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r2_wellord2) ).
thf(3106,plain,
! [A: $i,B: $i] :
( ( r2_wellord2 @ A @ B )
=> ( r2_wellord2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(798,axiom,
! [A: $i] :
( ( v1_realset1 @ A )
<=> ~ ( ~ ( v1_xboole_0 @ A )
& ! [B: $i] :
( A
!= ( k1_tarski @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_realset1) ).
thf(5880,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)],[798]) ).
thf(1911,axiom,
! [A: $i] :
( ( v1_fraenkel @ A )
=> ! [B: $i] :
( ( r1_tarski @ B @ A )
=> ( v1_fraenkel @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_fraenkel) ).
thf(11355,plain,
! [A: $i] :
( ( v1_fraenkel @ A )
=> ! [B: $i] :
( ( r1_tarski @ B @ A )
=> ( v1_fraenkel @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1911]) ).
thf(1633,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/sandbox2/benchmark/theBenchmark.p',t32_partfun1) ).
thf(9920,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)],[1633]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(5054,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_tarski @ A )
= ( k2_tarski @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(1894,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k5_relset_2 @ A @ C ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relset_2) ).
thf(11268,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( r1_tarski @ ( k2_relat_1 @ ( k5_relset_2 @ A @ C ) ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1894]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k9_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t155_funct_1) ).
thf(2669,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k10_relat_1 @ B @ A )
= ( k9_relat_1 @ ( k2_funct_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(1229,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/sandbox2/benchmark/theBenchmark.p',t96_funct_3) ).
thf(8047,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)],[1229]) ).
thf(2064,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/sandbox2/benchmark/theBenchmark.p',t53_relset_1) ).
thf(12263,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)],[2064]) ).
thf(432,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/sandbox2/benchmark/theBenchmark.p',t34_zfmisc_1) ).
thf(4139,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)],[432]) ).
thf(2145,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/sandbox2/benchmark/theBenchmark.p',t60_domain_1) ).
thf(12656,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)],[2145]) ).
thf(1561,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/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
thf(9570,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)],[1561]) ).
thf(143,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/sandbox2/benchmark/theBenchmark.p',t123_funct_1) ).
thf(2943,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)],[143]) ).
thf(2226,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/sandbox2/benchmark/theBenchmark.p',rc1_closure2) ).
thf(13005,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)],[2226]) ).
thf(1907,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/sandbox2/benchmark/theBenchmark.p',t25_subset_1) ).
thf(11338,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)],[1907]) ).
thf(1087,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/sandbox2/benchmark/theBenchmark.p',t103_relat_1) ).
thf(7265,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)],[1087]) ).
thf(2310,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/sandbox2/benchmark/theBenchmark.p',redefinition_k9_relset_2) ).
thf(13334,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)],[2310]) ).
thf(417,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/sandbox2/benchmark/theBenchmark.p',t24_relat_1) ).
thf(4073,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)],[417]) ).
thf(2179,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( C
= ( k1_yellow_3 @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
<=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( D
= ( k4_tarski @ F @ G ) )
& ( E
= ( k4_tarski @ H @ I ) )
& ( r2_hidden @ ( k4_tarski @ F @ H ) @ A )
& ( r2_hidden @ ( k4_tarski @ G @ I ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_yellow_3) ).
thf(12791,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( C
= ( k1_yellow_3 @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( D
= ( k4_tarski @ F @ G ) )
& ( E
= ( k4_tarski @ H @ I ) )
& ( r2_hidden @ ( k4_tarski @ F @ H ) @ A )
& ( r2_hidden @ ( k4_tarski @ G @ I ) @ B ) ) )
& ( ? [F: $i,G: $i,H: $i,I: $i] :
( ( D
= ( k4_tarski @ F @ G ) )
& ( E
= ( k4_tarski @ H @ I ) )
& ( r2_hidden @ ( k4_tarski @ F @ H ) @ A )
& ( r2_hidden @ ( k4_tarski @ G @ I ) @ B ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( r2_hidden @ ( k4_tarski @ D @ E ) @ C )
=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( D
= ( k4_tarski @ F @ G ) )
& ( E
= ( k4_tarski @ H @ I ) )
& ( r2_hidden @ ( k4_tarski @ F @ H ) @ A )
& ( r2_hidden @ ( k4_tarski @ G @ I ) @ B ) ) )
& ( ? [F: $i,G: $i,H: $i,I: $i] :
( ( D
= ( k4_tarski @ F @ G ) )
& ( E
= ( k4_tarski @ H @ I ) )
& ( r2_hidden @ ( k4_tarski @ F @ H ) @ A )
& ( r2_hidden @ ( k4_tarski @ G @ I ) @ B ) )
=> ( r2_hidden @ ( k4_tarski @ D @ E ) @ C ) ) )
=> ( C
= ( k1_yellow_3 @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2179]) ).
thf(2279,axiom,
m1_subset_1 @ k2_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_urysohn1) ).
thf(13221,plain,
m1_subset_1 @ k2_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2279]) ).
thf(205,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 ) )
=> ( ( k8_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ C @ F @ ( k1_domain_1 @ A @ B @ D @ E ) )
= ( k8_funct_2 @ B @ C @ ( k1_cat_2 @ A @ B @ C @ ( k1_fraenkel @ B @ C ) @ ( k2_cat_2 @ A @ B @ C @ F ) @ D ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_cat_2) ).
thf(3197,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 ) )
=> ( ( k8_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ C @ F @ ( k1_domain_1 @ A @ B @ D @ E ) )
= ( k8_funct_2 @ B @ C @ ( k1_cat_2 @ A @ B @ C @ ( k1_fraenkel @ B @ C ) @ ( k2_cat_2 @ A @ B @ C @ F ) @ D ) @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1317,axiom,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v1_membered @ B ) )
=> ( v1_membered @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_membered) ).
thf(8485,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)],[1317]) ).
thf(1709,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(10296,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1709]) ).
thf(541,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/sandbox2/benchmark/theBenchmark.p',t101_relat_1) ).
thf(4667,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)],[541]) ).
thf(1804,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(10766,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_finset_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1804]) ).
thf(1422,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( r1_xboole_0 @ A @ ( k3_xboole_0 @ B @ C ) )
& ( r1_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_xboole_1) ).
thf(8937,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)],[1422]) ).
thf(1323,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/sandbox2/benchmark/theBenchmark.p',t23_filter_1) ).
thf(8502,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)],[1323]) ).
thf(861,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/sandbox2/benchmark/theBenchmark.p',t34_setwiseo) ).
thf(6184,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)],[861]) ).
thf(2316,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_39_fraenkel) ).
thf(13348,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)],[2316]) ).
thf(819,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k10_relat_1 @ C @ B ) )
<=> ? [D: $i] :
( ( r2_hidden @ D @ ( k2_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ A @ D ) @ C )
& ( r2_hidden @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t166_relat_1) ).
thf(5972,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k10_relat_1 @ C @ B ) )
=> ? [D: $i] :
( ( r2_hidden @ D @ ( k2_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ A @ D ) @ C )
& ( r2_hidden @ D @ B ) ) )
& ( ? [D: $i] :
( ( r2_hidden @ D @ ( k2_relat_1 @ C ) )
& ( r2_hidden @ ( k4_tarski @ A @ D ) @ C )
& ( r2_hidden @ D @ B ) )
=> ( r2_hidden @ A @ ( k10_relat_1 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(1389,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/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).
thf(8794,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)],[1389]) ).
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 ) )
=> ( ( r1_tarski @ ( k3_subset_1 @ A @ B ) @ C )
=> ( r1_tarski @ ( k3_subset_1 @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_subset_1) ).
thf(9491,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)],[1544]) ).
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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_1_ens_1) ).
thf(11438,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(2014,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ! [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_lopclset) ).
thf(11979,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)],[2014]) ).
thf(127,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_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k4_finseq_1 @ A ) @ ( k4_finseq_1 @ A ) )
& ( m2_relset_1 @ C @ ( k4_finseq_1 @ A ) @ ( k4_finseq_1 @ A ) ) )
=> ( ( ( ( k2_relat_1 @ C )
= ( k4_finseq_1 @ A ) )
& ( B
= ( k5_relat_1 @ C @ A ) ) )
=> ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_finseq_2) ).
thf(2871,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_funct_1 @ C )
& ( v1_funct_2 @ C @ ( k4_finseq_1 @ A ) @ ( k4_finseq_1 @ A ) )
& ( m2_relset_1 @ C @ ( k4_finseq_1 @ A ) @ ( k4_finseq_1 @ A ) ) )
=> ( ( ( ( k2_relat_1 @ C )
= ( k4_finseq_1 @ A ) )
& ( B
= ( k5_relat_1 @ C @ A ) ) )
=> ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(502,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/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
thf(4509,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)],[502]) ).
thf(925,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/sandbox2/benchmark/theBenchmark.p',fc3_binop_2) ).
thf(6460,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)],[925]) ).
thf(1097,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/sandbox2/benchmark/theBenchmark.p',t150_pboole) ).
thf(7307,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)],[1097]) ).
thf(494,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/sandbox2/benchmark/theBenchmark.p',t63_setwiseo) ).
thf(4477,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)],[494]) ).
thf(2086,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/sandbox2/benchmark/theBenchmark.p',t40_funct_4) ).
thf(12369,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)],[2086]) ).
thf(1079,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ ( k8_relat_1 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_partfun1) ).
thf(7238,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_partfun1 @ ( k8_relat_1 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(2061,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/sandbox2/benchmark/theBenchmark.p',redefinition_k4_funct_2) ).
thf(12246,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)],[2061]) ).
thf(1427,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/sandbox2/benchmark/theBenchmark.p',t63_zfmisc_1) ).
thf(8958,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)],[1427]) ).
thf(399,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(4009,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( r1_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(714,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/sandbox2/benchmark/theBenchmark.p',t79_funcop_1) ).
thf(5439,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)],[714]) ).
thf(613,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/sandbox2/benchmark/theBenchmark.p',fc2_fraenkel) ).
thf(4985,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)],[613]) ).
thf(2168,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ k2_qc_lang1 )
=> ( ( k23_qc_lang1 @ A )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k23_qc_lang1) ).
thf(12755,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)],[2168]) ).
thf(2357,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/sandbox2/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(13518,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)],[2357]) ).
thf(23,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 ) )
& ( ( k5_funct_5 @ C )
= ( k5_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_5) ).
thf(2461,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 ) )
& ( ( k5_funct_5 @ C )
= ( k5_funct_5 @ D ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1860,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/sandbox2/benchmark/theBenchmark.p',t11_funct_5) ).
thf(11078,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)],[1860]) ).
thf(736,axiom,
! [A: $i] :
( ( k3_pua2mss1 @ A )
= ( k8_eqrel_1 @ A @ ( k6_partfun1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_pua2mss1) ).
thf(5552,plain,
! [A: $i] :
( ( k3_pua2mss1 @ A )
= ( k8_eqrel_1 @ A @ ( k6_partfun1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(114,axiom,
( ( k10_funct_6 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_funct_6) ).
thf(2824,plain,
( ( k10_funct_6 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(1780,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/sandbox2/benchmark/theBenchmark.p',d6_binop_1) ).
thf(10645,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)],[1780]) ).
thf(731,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/sandbox2/benchmark/theBenchmark.p',redefinition_k9_cat_2) ).
thf(5511,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)],[731]) ).
thf(1370,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k8_relat_1 @ A @ C ) ) )
=> ( ( k1_funct_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_funct_1) ).
thf(8735,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k8_relat_1 @ A @ C ) ) )
=> ( ( k1_funct_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k1_funct_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).
thf(1339,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/sandbox2/benchmark/theBenchmark.p',t23_borsuk_1) ).
thf(8605,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)],[1339]) ).
thf(1618,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/sandbox2/benchmark/theBenchmark.p',t1_waybel14) ).
thf(9857,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)],[1618]) ).
thf(1259,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/sandbox2/benchmark/theBenchmark.p',t53_funcop_1) ).
thf(8192,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)],[1259]) ).
thf(510,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/sandbox2/benchmark/theBenchmark.p',t143_funct_2) ).
thf(4541,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)],[510]) ).
thf(1837,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/sandbox2/benchmark/theBenchmark.p',t7_card_fil) ).
thf(10957,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)],[1837]) ).
thf(48,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 ) )
=> ? [F: $i] :
( ( m2_fraenkel @ F @ B @ A @ ( k1_fraenkel @ B @ A ) )
& ( ( k7_relat_1 @ F @ C )
= E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_fraenkel) ).
thf(2610,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 ) )
=> ? [F: $i] :
( ( m2_fraenkel @ F @ B @ A @ ( k1_fraenkel @ B @ A ) )
& ( ( k7_relat_1 @ F @ C )
= E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( r2_wellord2 @ A @ B )
<=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v2_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k2_relat_1 @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord2) ).
thf(3027,plain,
! [A: $i,B: $i] :
( ( ( r2_wellord2 @ A @ B )
=> ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v2_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k2_relat_1 @ C )
= B ) ) )
& ( ? [C: $i] :
( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v2_funct_1 @ C )
& ( ( k1_relat_1 @ C )
= A )
& ( ( k2_relat_1 @ C )
= B ) )
=> ( r2_wellord2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(1043,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/sandbox2/benchmark/theBenchmark.p',t61_setwiseo) ).
thf(7119,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)],[1043]) ).
thf(2040,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/sandbox2/benchmark/theBenchmark.p',t77_relat_1) ).
thf(12114,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)],[2040]) ).
thf(766,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/sandbox2/benchmark/theBenchmark.p',t43_funct_4) ).
thf(5730,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)],[766]) ).
thf(801,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_funct_1) ).
thf(5894,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ ( k9_relat_1 @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(2105,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/sandbox2/benchmark/theBenchmark.p',fc1_setfam_1) ).
thf(12433,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)],[2105]) ).
thf(489,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/sandbox2/benchmark/theBenchmark.p',t80_enumset1) ).
thf(4462,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)],[489]) ).
thf(2306,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/sandbox2/benchmark/theBenchmark.p',t52_domain_1) ).
thf(13323,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)],[2306]) ).
thf(169,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/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(3073,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)],[169]) ).
thf(1998,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/sandbox2/benchmark/theBenchmark.p',t15_relset_1) ).
thf(11893,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)],[1998]) ).
thf(1612,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/sandbox2/benchmark/theBenchmark.p',t2_t_0topsp) ).
thf(9830,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)],[1612]) ).
thf(1014,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/sandbox2/benchmark/theBenchmark.p',redefinition_m1_nat_lat) ).
thf(6989,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)],[1014]) ).
thf(1576,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/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_1) ).
thf(9642,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)],[1576]) ).
thf(1587,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/sandbox2/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(9691,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)],[1587]) ).
thf(195,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ~ ( v1_xboole_0 @ ( k4_card_3 @ A ) )
& ( v1_fraenkel @ ( k4_card_3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_card_3) ).
thf(3165,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ~ ( v1_xboole_0 @ ( k4_card_3 @ A ) )
& ( v1_fraenkel @ ( k4_card_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(1807,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/sandbox2/benchmark/theBenchmark.p',t7_subset_1) ).
thf(10778,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)],[1807]) ).
thf(1543,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/sandbox2/benchmark/theBenchmark.p',dt_k14_funct_3) ).
thf(9487,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)],[1543]) ).
thf(2389,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/sandbox2/benchmark/theBenchmark.p',s24_fraenkel) ).
thf(13653,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)],[2389]) ).
thf(1942,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/sandbox2/benchmark/theBenchmark.p',t19_borsuk_1) ).
thf(11569,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)],[1942]) ).
thf(1495,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/sandbox2/benchmark/theBenchmark.p',t20_xboole_1) ).
thf(9280,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)],[1495]) ).
thf(41,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/sandbox2/benchmark/theBenchmark.p',t5_altcat_2) ).
thf(2593,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)],[41]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_relat_1 @ F )
& ( v1_funct_1 @ F ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ F ) @ ( k2_zfmisc_1 @ D @ E ) )
=> ( ( ~ ( r2_hidden @ ( k3_funct_5 @ F ) @ ( k1_funct_2 @ A @ ( k1_funct_2 @ B @ C ) ) )
& ~ ( r2_hidden @ ( k5_funct_5 @ F ) @ ( k1_funct_2 @ B @ ( k1_funct_2 @ A @ C ) ) ) )
| ( r2_hidden @ F @ ( k1_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_6) ).
thf(3451,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( v1_relat_1 @ F )
& ( v1_funct_1 @ F ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ F ) @ ( k2_zfmisc_1 @ D @ E ) )
=> ( ( ~ ( r2_hidden @ ( k3_funct_5 @ F ) @ ( k1_funct_2 @ A @ ( k1_funct_2 @ B @ C ) ) )
& ~ ( r2_hidden @ ( k5_funct_5 @ F ) @ ( k1_funct_2 @ B @ ( k1_funct_2 @ A @ C ) ) ) )
| ( r2_hidden @ F @ ( k1_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(1186,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finseq_1) ).
thf(7778,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finseq_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(1158,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/sandbox2/benchmark/theBenchmark.p',t112_relat_1) ).
thf(7654,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)],[1158]) ).
thf(687,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/sandbox2/benchmark/theBenchmark.p',t84_funct_1) ).
thf(5318,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)],[687]) ).
thf(1299,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_realset1) ).
thf(8372,plain,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_realset1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(2131,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/sandbox2/benchmark/theBenchmark.p',t29_subset_1) ).
thf(12562,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)],[2131]) ).
thf(1952,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/sandbox2/benchmark/theBenchmark.p',cc1_triang_1) ).
thf(11640,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)],[1952]) ).
thf(1384,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 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t133_relat_1) ).
thf(8782,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 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).
thf(1732,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/sandbox2/benchmark/theBenchmark.p',d4_zfmisc_1) ).
thf(10412,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)],[1732]) ).
thf(1630,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/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(9905,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)],[1630]) ).
thf(1314,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/sandbox2/benchmark/theBenchmark.p',t14_funct_1) ).
thf(8473,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)],[1314]) ).
thf(1984,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/sandbox2/benchmark/theBenchmark.p',t142_funct_2) ).
thf(11814,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)],[1984]) ).
thf(2135,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/sandbox2/benchmark/theBenchmark.p',d2_funct_5) ).
thf(12587,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)],[2135]) ).
thf(1550,axiom,
( ( r2_hidden @ f2_s1_card_fil @ a_0_0_card_fil )
=> ( p1_s1_card_fil @ f2_s1_card_fil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_card_fil) ).
thf(9528,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)],[1550]) ).
thf(1979,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/sandbox2/benchmark/theBenchmark.p',t17_domain_1) ).
thf(11767,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)],[1979]) ).
thf(1083,axiom,
! [A: $i,B: $i,C: $i] :
( ( k1_enumset1 @ A @ B @ C )
= ( k1_enumset1 @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_enumset1) ).
thf(7250,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)],[1083]) ).
thf(1449,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/sandbox2/benchmark/theBenchmark.p',t52_relat_1) ).
thf(9074,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)],[1449]) ).
thf(1724,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/sandbox2/benchmark/theBenchmark.p',t22_funct_3) ).
thf(10380,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)],[1724]) ).
thf(950,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/sandbox2/benchmark/theBenchmark.p',t2_ens_1) ).
thf(6553,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)],[950]) ).
thf(1455,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_domain_1) ).
thf(9101,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( A
= ( a_1_0_domain_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455]) ).
thf(1977,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/sandbox2/benchmark/theBenchmark.p',dt_k6_pralg_1) ).
thf(11761,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)],[1977]) ).
thf(546,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ A @ B ) )
= ( k8_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_relat_1) ).
thf(4684,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ A @ B ) )
= ( k8_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(2349,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/sandbox2/benchmark/theBenchmark.p',s1_filter_1) ).
thf(13486,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)],[2349]) ).
thf(792,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( r1_zfrefle1 @ A @ ( k1_subset_1 @ k9_zf_lang ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfrefle1) ).
thf(5838,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( r1_zfrefle1 @ A @ ( k1_subset_1 @ k9_zf_lang ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1503,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k9_relat_1 @ B @ A ) @ ( k2_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
thf(9327,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)],[1503]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( k1_setfam_1 @ ( k2_tarski @ A @ B ) )
= ( k3_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_setfam_1) ).
thf(2578,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)],[36]) ).
thf(2153,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/sandbox2/benchmark/theBenchmark.p',rc7_tex_2) ).
thf(12680,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)],[2153]) ).
thf(1240,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/sandbox2/benchmark/theBenchmark.p',t19_funct_4) ).
thf(8084,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)],[1240]) ).
thf(2130,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/sandbox2/benchmark/theBenchmark.p',d2_fraenkel) ).
thf(12556,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)],[2130]) ).
thf(628,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/sandbox2/benchmark/theBenchmark.p',t61_card_3) ).
thf(5042,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)],[628]) ).
thf(1945,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/sandbox2/benchmark/theBenchmark.p',t53_domain_1) ).
thf(11607,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)],[1945]) ).
thf(1794,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/sandbox2/benchmark/theBenchmark.p',t52_relset_1) ).
thf(10707,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)],[1794]) ).
thf(1464,axiom,
! [A: $i] : ( m1_eqrel_1 @ ( k3_pua2mss1 @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_pua2mss1) ).
thf(9150,plain,
! [A: $i] : ( m1_eqrel_1 @ ( k3_pua2mss1 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).
thf(97,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/sandbox2/benchmark/theBenchmark.p',dt_m1_orders_1) ).
thf(2770,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)],[97]) ).
thf(2035,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/sandbox2/benchmark/theBenchmark.p',t6_orders_1) ).
thf(12092,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)],[2035]) ).
thf(1681,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/sandbox2/benchmark/theBenchmark.p',d10_setfam_1) ).
thf(10147,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)],[1681]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ A )
=> ( v1_finset_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_finset_1) ).
thf(2418,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)],[7]) ).
thf(600,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( C
= ( k5_relset_2 @ A @ B ) )
<=> ( ( ( k1_relat_1 @ C )
= ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r1_tarski @ D @ A )
=> ( ( k1_funct_1 @ C @ D )
= ( k9_relat_1 @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relset_2) ).
thf(4933,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( C
= ( k5_relset_2 @ A @ B ) )
=> ( ( ( k1_relat_1 @ C )
= ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r1_tarski @ D @ A )
=> ( ( k1_funct_1 @ C @ D )
= ( k9_relat_1 @ B @ D ) ) ) ) )
& ( ( ( ( k1_relat_1 @ C )
= ( k1_zfmisc_1 @ A ) )
& ! [D: $i] :
( ( r1_tarski @ D @ A )
=> ( ( k1_funct_1 @ C @ D )
= ( k9_relat_1 @ B @ D ) ) ) )
=> ( C
= ( k5_relset_2 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(2113,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
<=> ! [C: $i] :
( ( r2_hidden @ C @ A )
=> ( r2_hidden @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(12460,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)],[2113]) ).
thf(958,axiom,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(6589,plain,
! [A: $i] : ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k3_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(2369,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/sandbox2/benchmark/theBenchmark.p',dt_k13_domain_1) ).
thf(13593,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)],[2369]) ).
thf(770,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/sandbox2/benchmark/theBenchmark.p',t20_finseq_1) ).
thf(5742,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)],[770]) ).
thf(1601,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/sandbox2/benchmark/theBenchmark.p',dt_k3_realset1) ).
thf(9751,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)],[1601]) ).
thf(1909,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/sandbox2/benchmark/theBenchmark.p',t59_funcop_1) ).
thf(11348,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)],[1909]) ).
thf(1570,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/sandbox2/benchmark/theBenchmark.p',t2_binop_1) ).
thf(9619,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)],[1570]) ).
thf(2384,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(13630,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)],[2384]) ).
thf(2224,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/sandbox2/benchmark/theBenchmark.p',t156_relat_1) ).
thf(13000,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)],[2224]) ).
thf(715,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k7_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_relat_1) ).
thf(5442,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)],[715]) ).
thf(2104,axiom,
r1_tarski @ a_0_18_fraenkel @ f1_s10_fraenkel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s10_fraenkel) ).
thf(12432,plain,
r1_tarski @ a_0_18_fraenkel @ f1_s10_fraenkel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2104]) ).
thf(1308,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/sandbox2/benchmark/theBenchmark.p',t96_relat_1) ).
thf(8456,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)],[1308]) ).
thf(973,axiom,
! [A: $i,B: $i,C: $i] : ( v1_finset_1 @ ( k1_enumset1 @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_finset_1) ).
thf(6687,plain,
! [A: $i,B: $i,C: $i] : ( v1_finset_1 @ ( k1_enumset1 @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(663,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/sandbox2/benchmark/theBenchmark.p',t29_finset_1) ).
thf(5216,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)],[663]) ).
thf(962,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/sandbox2/benchmark/theBenchmark.p',t36_setwiseo) ).
thf(6609,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)],[962]) ).
thf(338,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/sandbox2/benchmark/theBenchmark.p',t39_relat_1) ).
thf(3759,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)],[338]) ).
thf(360,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/sandbox2/benchmark/theBenchmark.p',t56_classes2) ).
thf(3838,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)],[360]) ).
thf(1134,axiom,
! [A: $i] : ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_finsub_1) ).
thf(7479,plain,
! [A: $i] : ( v4_finsub_1 @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(1331,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_funct_1 @ A @ B ) ) )
=> ( ~ ( r1_xboole_0 @ ( k10_relat_1 @ ( k3_pralg_3 @ A @ B ) @ ( k1_tarski @ C ) ) @ ( k10_relat_1 @ ( k3_pralg_3 @ A @ B ) @ D ) )
=> ( r2_hidden @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_yellow17) ).
thf(8573,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i,D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_funct_1 @ A @ B ) ) )
=> ( ~ ( r1_xboole_0 @ ( k10_relat_1 @ ( k3_pralg_3 @ A @ B ) @ ( k1_tarski @ C ) ) @ ( k10_relat_1 @ ( k3_pralg_3 @ A @ B ) @ D ) )
=> ( r2_hidden @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(1851,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/sandbox2/benchmark/theBenchmark.p',t1_nattra_1) ).
thf(11041,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)],[1851]) ).
thf(639,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/sandbox2/benchmark/theBenchmark.p',t98_funct_3) ).
thf(5094,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)],[639]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k2_partfun1 @ A @ B @ ( k3_partfun1 @ D @ A @ B ) @ C )
= ( k3_partfun1 @ D @ ( k3_xboole_0 @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_partfun1) ).
thf(3423,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( k2_partfun1 @ A @ B @ ( k3_partfun1 @ D @ A @ B ) @ C )
= ( k3_partfun1 @ D @ ( k3_xboole_0 @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(1891,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/sandbox2/benchmark/theBenchmark.p',fc3_cantor_1) ).
thf(11262,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)],[1891]) ).
thf(1822,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/sandbox2/benchmark/theBenchmark.p',dt_k31_binop_2) ).
thf(10852,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)],[1822]) ).
thf(2044,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/sandbox2/benchmark/theBenchmark.p',t31_partfun1) ).
thf(12135,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)],[2044]) ).
thf(1964,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/sandbox2/benchmark/theBenchmark.p',dt_k1_domain_1) ).
thf(11701,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)],[1964]) ).
thf(2150,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/sandbox2/benchmark/theBenchmark.p',t8_cantor_1) ).
thf(12672,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)],[2150]) ).
thf(1808,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(10782,plain,
! [A: $i,B: $i] :
? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1808]) ).
thf(1661,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/sandbox2/benchmark/theBenchmark.p',t56_setwiseo) ).
thf(10076,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)],[1661]) ).
thf(2312,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/sandbox2/benchmark/theBenchmark.p',dt_k2_relset_2) ).
thf(13339,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)],[2312]) ).
thf(2391,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/sandbox2/benchmark/theBenchmark.p',dt_k1_relset_2) ).
thf(13666,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)],[2391]) ).
thf(1613,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/sandbox2/benchmark/theBenchmark.p',fc15_finset_1) ).
thf(9841,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)],[1613]) ).
thf(1486,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/sandbox2/benchmark/theBenchmark.p',cc1_finseq_1) ).
thf(9249,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)],[1486]) ).
thf(889,axiom,
! [A: $i,B: $i] :
( ( k4_tarski @ A @ B )
= ( k2_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(6288,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)],[889]) ).
thf(2084,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/sandbox2/benchmark/theBenchmark.p',t21_finset_1) ).
thf(12358,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)],[2084]) ).
thf(1918,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/sandbox2/benchmark/theBenchmark.p',free_g3_vectsp_1) ).
thf(11380,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)],[1918]) ).
thf(1514,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/sandbox2/benchmark/theBenchmark.p',t176_partfun1) ).
thf(9371,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)],[1514]) ).
thf(1215,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/sandbox2/benchmark/theBenchmark.p',t73_funct_3) ).
thf(7960,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)],[1215]) ).
thf(323,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/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).
thf(3674,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)],[323]) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(3016,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)],[155]) ).
thf(1730,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/sandbox2/benchmark/theBenchmark.p',t21_funct_2) ).
thf(10407,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)],[1730]) ).
thf(596,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/sandbox2/benchmark/theBenchmark.p',t77_funct_4) ).
thf(4918,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)],[596]) ).
thf(1512,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/sandbox2/benchmark/theBenchmark.p',t104_relat_1) ).
thf(9366,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)],[1512]) ).
thf(1944,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(11605,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)],[1944]) ).
thf(1621,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/sandbox2/benchmark/theBenchmark.p',t70_setwiseo) ).
thf(9871,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)],[1621]) ).
thf(1868,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/sandbox2/benchmark/theBenchmark.p',t17_subset_1) ).
thf(11130,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)],[1868]) ).
thf(2099,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/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(12409,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)],[2099]) ).
thf(54,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/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(2633,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)],[54]) ).
thf(1068,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k7_relat_1 @ B @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
thf(7200,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)],[1068]) ).
thf(188,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 @ ( k2_zfmisc_1 @ C @ D ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_relset_1 @ E @ ( k2_zfmisc_1 @ C @ D ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_subset_1 @ F @ ( k2_zfmisc_1 @ C @ D ) ) )
=> ( m2_fraenkel @ ( k2_funcsdom @ A @ B @ C @ D @ E @ F ) @ A @ B @ ( k1_fraenkel @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funcsdom) ).
thf(3142,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 @ ( k2_zfmisc_1 @ C @ D ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_relset_1 @ E @ ( k2_zfmisc_1 @ C @ D ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_subset_1 @ F @ ( k2_zfmisc_1 @ C @ D ) ) )
=> ( m2_fraenkel @ ( k2_funcsdom @ A @ B @ C @ D @ E @ F ) @ A @ B @ ( k1_fraenkel @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(604,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/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
thf(4954,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)],[604]) ).
thf(149,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/sandbox2/benchmark/theBenchmark.p',t42_setwiseo) ).
thf(2967,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)],[149]) ).
thf(1107,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/sandbox2/benchmark/theBenchmark.p',t40_funct_1) ).
thf(7366,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)],[1107]) ).
thf(2052,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ! [C: $i] :
( ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ A ) )
=> ! [D: $i] :
( ( m1_pboole @ D @ ( k3_zfmisc_1 @ A @ A @ A ) )
=> ( ( D
= ( k3_altcat_1 @ A @ B @ C ) )
<=> ! [E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ A )
& ( r2_hidden @ G @ A ) )
=> ( ( k1_multop_1 @ D @ E @ F @ G )
= ( k2_zfmisc_1 @ ( k1_binop_1 @ C @ F @ G ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_altcat_1) ).
thf(12178,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ! [C: $i] :
( ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ A ) )
=> ! [D: $i] :
( ( m1_pboole @ D @ ( k3_zfmisc_1 @ A @ A @ A ) )
=> ( ( ( D
= ( k3_altcat_1 @ A @ B @ C ) )
=> ! [E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ A )
& ( r2_hidden @ G @ A ) )
=> ( ( k1_multop_1 @ D @ E @ F @ G )
= ( k2_zfmisc_1 @ ( k1_binop_1 @ C @ F @ G ) @ ( k1_binop_1 @ B @ E @ F ) ) ) ) )
& ( ! [E: $i,F: $i,G: $i] :
( ( ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ A )
& ( r2_hidden @ G @ A ) )
=> ( ( k1_multop_1 @ D @ E @ F @ G )
= ( k2_zfmisc_1 @ ( k1_binop_1 @ C @ F @ G ) @ ( k1_binop_1 @ B @ E @ F ) ) ) )
=> ( D
= ( k3_altcat_1 @ A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2052]) ).
thf(446,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/sandbox2/benchmark/theBenchmark.p',t9_relset_1) ).
thf(4196,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)],[446]) ).
thf(1102,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/sandbox2/benchmark/theBenchmark.p',t171_partfun1) ).
thf(7339,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)],[1102]) ).
thf(282,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/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
thf(3512,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)],[282]) ).
thf(2080,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/sandbox2/benchmark/theBenchmark.p',t30_finset_1) ).
thf(12341,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)],[2080]) ).
thf(756,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/sandbox2/benchmark/theBenchmark.p',t2_funct_4) ).
thf(5693,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)],[756]) ).
thf(2378,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/sandbox2/benchmark/theBenchmark.p',dt_k8_setfam_1) ).
thf(13613,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)],[2378]) ).
thf(2276,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/sandbox2/benchmark/theBenchmark.p',redefinition_k14_mcart_1) ).
thf(13214,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)],[2276]) ).
thf(727,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_funct_2 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_fraenkel) ).
thf(5495,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)],[727]) ).
thf(587,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_funct_1) ).
thf(4890,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ ( k1_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k1_relat_1 @ B ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(2274,axiom,
! [A: $i,B: $i] :
( ( ( k2_zfmisc_1 @ A @ A )
= ( k2_zfmisc_1 @ B @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(13208,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)],[2274]) ).
thf(370,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/sandbox2/benchmark/theBenchmark.p',t67_classes2) ).
thf(3876,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)],[370]) ).
thf(608,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/sandbox2/benchmark/theBenchmark.p',t17_finseq_1) ).
thf(4965,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)],[608]) ).
thf(1129,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( v2_funct_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_partfun1) ).
thf(7458,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)],[1129]) ).
thf(1936,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/sandbox2/benchmark/theBenchmark.p',t12_funct_2) ).
thf(11535,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)],[1936]) ).
thf(1753,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/sandbox2/benchmark/theBenchmark.p',t5_mssubfam) ).
thf(10499,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)],[1753]) ).
thf(1913,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/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_2) ).
thf(11361,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)],[1913]) ).
thf(435,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/sandbox2/benchmark/theBenchmark.p',t41_mcart_1) ).
thf(4158,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)],[435]) ).
thf(1563,axiom,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_relat_1) ).
thf(9582,plain,
! [A: $i,B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1563]) ).
thf(125,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/sandbox2/benchmark/theBenchmark.p',existence_m3_pboole) ).
thf(2867,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)],[125]) ).
thf(1698,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/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
thf(10226,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)],[1698]) ).
thf(2054,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/sandbox2/benchmark/theBenchmark.p',t31_domain_1) ).
thf(12192,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)],[2054]) ).
thf(1356,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_mcart_1 @ A @ B @ C )
= ( k4_tarski @ ( k4_tarski @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_mcart_1) ).
thf(8689,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)],[1356]) ).
thf(1059,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/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(7172,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)],[1059]) ).
thf(1642,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/sandbox2/benchmark/theBenchmark.p',t3_ens_1) ).
thf(9958,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)],[1642]) ).
thf(1426,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/sandbox2/benchmark/theBenchmark.p',dt_k3_metric_1) ).
thf(8954,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)],[1426]) ).
thf(1012,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k5_relat_1 @ A @ ( k6_relat_1 @ ( k2_relat_1 @ A ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_relat_1) ).
thf(6977,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)],[1012]) ).
thf(1042,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/sandbox2/benchmark/theBenchmark.p',symmetry_r1_partfun1) ).
thf(7117,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)],[1042]) ).
thf(294,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/sandbox2/benchmark/theBenchmark.p',t7_realset1) ).
thf(3576,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)],[294]) ).
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/sandbox2/benchmark/theBenchmark.p',d6_eqrel_1) ).
thf(10920,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(413,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 ) )
=> ( ( ( r5_binop_1 @ A @ C @ D )
& ( r5_binop_1 @ B @ E @ F ) )
<=> ( r5_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_filter_1) ).
thf(4052,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 ) )
=> ( ( ( ( r5_binop_1 @ A @ C @ D )
& ( r5_binop_1 @ B @ E @ F ) )
=> ( r5_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) ) )
& ( ( r5_binop_1 @ ( k2_zfmisc_1 @ A @ B ) @ ( k7_filter_1 @ A @ B @ C @ E ) @ ( k7_filter_1 @ A @ B @ D @ F ) )
=> ( ( r5_binop_1 @ A @ C @ D )
& ( r5_binop_1 @ B @ E @ F ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(1346,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_funct_1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) )
& ( m2_relset_1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_partfun1) ).
thf(8637,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_funct_1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) )
& ( m2_relset_1 @ ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).
thf(2254,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_1_domain_1) ).
thf(13117,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)],[2254]) ).
thf(1028,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/sandbox2/benchmark/theBenchmark.p',t45_setwiseo) ).
thf(7070,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)],[1028]) ).
thf(721,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/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(5463,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)],[721]) ).
thf(1744,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/sandbox2/benchmark/theBenchmark.p',dt_m2_realset1) ).
thf(10456,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)],[1744]) ).
thf(469,axiom,
! [A: $i] :
( ( k1_zfmisc_1 @ ( k1_tarski @ A ) )
= ( k2_tarski @ k1_xboole_0 @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(4331,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)],[469]) ).
thf(153,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/sandbox2/benchmark/theBenchmark.p',commutativity_k11_binop_2) ).
thf(3009,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)],[153]) ).
thf(1454,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/sandbox2/benchmark/theBenchmark.p',t82_relat_1) ).
thf(9097,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)],[1454]) ).
thf(450,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/sandbox2/benchmark/theBenchmark.p',d3_enumset1) ).
thf(4207,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)],[450]) ).
thf(265,axiom,
! [A: $i] : ( m2_finseq_1 @ k1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_finseq_1) ).
thf(3444,plain,
! [A: $i] : ( m2_finseq_1 @ k1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(2056,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice5) ).
thf(12207,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)],[2056]) ).
thf(145,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_relat_1 @ A )
<=> ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15_funct_1) ).
thf(2952,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_relat_1 @ A )
=> ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) ) )
& ( ! [B: $i] :
~ ( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
& ( v1_xboole_0 @ ( k1_funct_1 @ A @ B ) ) )
=> ( v2_relat_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(2322,axiom,
m1_subset_1 @ k4_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_urysohn1) ).
thf(13371,plain,
m1_subset_1 @ k4_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2322]) ).
thf(481,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/sandbox2/benchmark/theBenchmark.p',t26_subset_1) ).
thf(4394,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)],[481]) ).
thf(1470,axiom,
! [A: $i,B: $i] :
~ ( ~ ( r1_xboole_0 @ A @ B )
& ( r1_xboole_0 @ ( k3_xboole_0 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_xboole_1) ).
thf(9170,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)],[1470]) ).
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 ) ) )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k8_setfam_1 @ A @ C ) @ ( k8_setfam_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_setfam_1) ).
thf(12941,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)],[2208]) ).
thf(917,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/sandbox2/benchmark/theBenchmark.p',t9_lattice2) ).
thf(6417,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)],[917]) ).
thf(1479,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/sandbox2/benchmark/theBenchmark.p',t24_finsub_1) ).
thf(9227,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)],[1479]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_xboole_1) ).
thf(4260,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)],[454]) ).
thf(871,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/sandbox2/benchmark/theBenchmark.p',d1_relset_2) ).
thf(6225,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)],[871]) ).
thf(1157,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 )
<=> ( ( r4_binop_1 @ A @ B @ C )
& ( r5_binop_1 @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_binop_1) ).
thf(7650,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 )
=> ( ( r4_binop_1 @ A @ B @ C )
& ( r5_binop_1 @ A @ B @ C ) ) )
& ( ( ( r4_binop_1 @ A @ B @ C )
& ( r5_binop_1 @ A @ B @ C ) )
=> ( r6_binop_1 @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(1702,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_relset_1 @ C @ A @ B )
<=> ( r1_tarski @ C @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
thf(10269,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)],[1702]) ).
thf(1165,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/sandbox2/benchmark/theBenchmark.p',t36_zfmisc_1) ).
thf(7681,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)],[1165]) ).
thf(1559,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/sandbox2/benchmark/theBenchmark.p',dt_k7_pboole) ).
thf(9563,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)],[1559]) ).
thf(1489,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/sandbox2/benchmark/theBenchmark.p',t6_yellow21) ).
thf(9259,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)],[1489]) ).
thf(59,axiom,
! [A: $i] :
~ ( r2_wellord2 @ A @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_card_1) ).
thf(2652,plain,
! [A: $i] :
~ ( r2_wellord2 @ A @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(1528,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/sandbox2/benchmark/theBenchmark.p',t28_funcop_1) ).
thf(9430,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)],[1528]) ).
thf(1094,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/sandbox2/benchmark/theBenchmark.p',t42_funct_4) ).
thf(7298,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)],[1094]) ).
thf(1392,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/sandbox2/benchmark/theBenchmark.p',t160_relat_1) ).
thf(8804,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)],[1392]) ).
thf(322,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_relat_1 @ B ) )
=> ( v1_relat_1 @ ( k4_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(3672,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)],[322]) ).
thf(1610,axiom,
m1_subset_1 @ k2_qc_lang1 @ ( k1_zfmisc_1 @ k1_qc_lang1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_qc_lang1) ).
thf(9826,plain,
m1_subset_1 @ k2_qc_lang1 @ ( k1_zfmisc_1 @ k1_qc_lang1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1610]) ).
thf(1577,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 @ ( k1_fraenkel @ A @ B ) @ ( k1_fraenkel @ A @ B ) ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ ( k1_fraenkel @ A @ B ) @ ( k1_fraenkel @ A @ B ) ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_subset_1 @ D @ ( k1_fraenkel @ A @ B ) )
& ( m1_subset_1 @ E @ ( k1_fraenkel @ A @ B ) ) )
=> ( ( k1_funcsdom @ A @ B @ C @ D @ E )
= ( k1_binop_1 @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_funcsdom) ).
thf(9646,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 @ ( k1_fraenkel @ A @ B ) @ ( k1_fraenkel @ A @ B ) ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ ( k1_fraenkel @ A @ B ) @ ( k1_fraenkel @ A @ B ) ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_subset_1 @ D @ ( k1_fraenkel @ A @ B ) )
& ( m1_subset_1 @ E @ ( k1_fraenkel @ A @ B ) ) )
=> ( ( k1_funcsdom @ A @ B @ C @ D @ E )
= ( k1_binop_1 @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1577]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_partfun1) ).
thf(3146,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1201,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/sandbox2/benchmark/theBenchmark.p',t58_setwiseo) ).
thf(7897,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)],[1201]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) ) @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k3_partfun1 @ C @ A @ B ) ) @ ( k2_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t77_partfun1) ).
thf(2449,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r1_tarski @ ( k4_relset_1 @ A @ B @ ( k3_partfun1 @ C @ A @ B ) ) @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ ( k3_partfun1 @ C @ A @ B ) ) @ ( k2_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1523,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/sandbox2/benchmark/theBenchmark.p',fc7_finset_1) ).
thf(9408,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)],[1523]) ).
thf(838,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k8_relat_1 @ A @ ( k7_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_relat_1) ).
thf(6056,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k7_relat_1 @ ( k8_relat_1 @ A @ C ) @ B )
= ( k8_relat_1 @ A @ ( k7_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(1676,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/sandbox2/benchmark/theBenchmark.p',dt_m1_realset1) ).
thf(10132,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)],[1676]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i] :
( ( k3_enumset1 @ A @ A @ A @ B @ C )
= ( k1_enumset1 @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t78_enumset1) ).
thf(4177,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)],[438]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_wellord2 @ A @ B )
& ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ B ) )
=> ( r2_wellord2 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ B @ ( k1_tarski @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_card_1) ).
thf(2629,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( r2_wellord2 @ A @ B )
& ( r2_hidden @ C @ A )
& ( r2_hidden @ D @ B ) )
=> ( r2_wellord2 @ ( k4_xboole_0 @ A @ ( k1_tarski @ C ) ) @ ( k4_xboole_0 @ B @ ( k1_tarski @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1575,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/sandbox2/benchmark/theBenchmark.p',t63_domain_1) ).
thf(9639,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)],[1575]) ).
thf(515,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/sandbox2/benchmark/theBenchmark.p',t95_relat_1) ).
thf(4566,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)],[515]) ).
thf(1164,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/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
thf(7679,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)],[1164]) ).
thf(842,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/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
thf(6076,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)],[842]) ).
thf(1817,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/sandbox2/benchmark/theBenchmark.p',t118_funct_2) ).
thf(10829,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)],[1817]) ).
thf(1120,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/sandbox2/benchmark/theBenchmark.p',dt_k10_relset_1) ).
thf(7420,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)],[1120]) ).
thf(1044,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(7122,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',t8_setfam_1) ).
thf(2597,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)],[43]) ).
thf(1810,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/sandbox2/benchmark/theBenchmark.p',redefinition_k13_domain_1) ).
thf(10788,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)],[1810]) ).
thf(1919,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k6_relat_1 @ A ) @ ( k6_relat_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_sysrel) ).
thf(11391,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)],[1919]) ).
thf(232,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 ) )
=> ( ( k8_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ C @ F @ ( k1_domain_1 @ A @ B @ D @ E ) )
= ( k8_funct_2 @ A @ C @ ( k1_cat_2 @ B @ A @ C @ ( k1_fraenkel @ A @ C ) @ ( k3_cat_2 @ A @ B @ C @ F ) @ E ) @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_cat_2) ).
thf(3292,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 ) )
=> ( ( k8_funct_2 @ ( k2_zfmisc_1 @ A @ B ) @ C @ F @ ( k1_domain_1 @ A @ B @ D @ E ) )
= ( k8_funct_2 @ A @ C @ ( k1_cat_2 @ B @ A @ C @ ( k1_fraenkel @ A @ C ) @ ( k3_cat_2 @ A @ B @ C @ F ) @ E ) @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1981,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/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
thf(11795,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)],[1981]) ).
thf(1976,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k9_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).
thf(11758,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)],[1976]) ).
thf(2230,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/sandbox2/benchmark/theBenchmark.p',t74_relat_1) ).
thf(13027,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)],[2230]) ).
thf(572,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/sandbox2/benchmark/theBenchmark.p',t168_funct_2) ).
thf(4812,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)],[572]) ).
thf(1010,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k1_relat_1 @ ( k7_relat_1 @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_relat_1) ).
thf(6973,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)],[1010]) ).
thf(471,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/sandbox2/benchmark/theBenchmark.p',t82_funct_2) ).
thf(4336,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)],[471]) ).
thf(1949,axiom,
! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(11626,plain,
! [A: $i] : ( r1_tarski @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1949]) ).
thf(706,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/sandbox2/benchmark/theBenchmark.p',t30_relset_1) ).
thf(5414,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)],[706]) ).
thf(1785,axiom,
! [A: $i,B: $i,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 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( r1_tarski @ ( k4_subset_1 @ B @ ( k8_relset_2 @ A @ B @ C @ E ) @ ( k8_relset_2 @ A @ B @ D @ E ) ) @ ( k8_relset_2 @ A @ B @ ( k5_subset_1 @ A @ C @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_relset_2) ).
thf(10672,plain,
! [A: $i,B: $i,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 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( r1_tarski @ ( k4_subset_1 @ B @ ( k8_relset_2 @ A @ B @ C @ E ) @ ( k8_relset_2 @ A @ B @ D @ E ) ) @ ( k8_relset_2 @ A @ B @ ( k5_subset_1 @ A @ C @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1785]) ).
thf(786,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/sandbox2/benchmark/theBenchmark.p',redefinition_k4_domain_1) ).
thf(5822,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)],[786]) ).
thf(1248,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/sandbox2/benchmark/theBenchmark.p',t16_card_fil) ).
thf(8143,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)],[1248]) ).
thf(2346,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_finsub_1) ).
thf(13477,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)],[2346]) ).
thf(796,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 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t180_relat_1) ).
thf(5871,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 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(458,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( k18_pralg_1 @ A @ B @ C )
= ( k2_funct_4 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k18_pralg_1) ).
thf(4272,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) )
=> ( ( k18_pralg_1 @ A @ B @ C )
= ( k2_funct_4 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(2066,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/sandbox2/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(12271,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)],[2066]) ).
thf(1337,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/sandbox2/benchmark/theBenchmark.p',t5_altcat_1) ).
thf(8598,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)],[1337]) ).
thf(319,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_pboole @ B @ A )
& ( v1_relat_1 @ B )
& ( v2_relat_1 @ B )
& ( v1_funct_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_pboole) ).
thf(3659,plain,
! [A: $i] :
? [B: $i] :
( ( m1_pboole @ B @ A )
& ( v1_relat_1 @ B )
& ( v2_relat_1 @ B )
& ( v1_funct_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_partfun1) ).
thf(3129,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ k1_xboole_0 @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t177_relat_1) ).
thf(3786,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k4_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) @ ( k10_relat_1 @ C @ ( k4_xboole_0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(1573,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/sandbox2/benchmark/theBenchmark.p',rc6_tex_2) ).
thf(9631,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)],[1573]) ).
thf(1971,axiom,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(11738,plain,
! [A: $i] :
( ( r1_tarski @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1971]) ).
thf(1145,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 @ ( k1_fraenkel @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k1_fraenkel @ B @ C ) ) )
=> ( ( v1_funct_1 @ ( k1_isocat_2 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k1_isocat_2 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ ( k1_isocat_2 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_isocat_2) ).
thf(7600,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 @ ( k1_fraenkel @ B @ C ) )
& ( m1_relset_1 @ D @ A @ ( k1_fraenkel @ B @ C ) ) )
=> ( ( v1_funct_1 @ ( k1_isocat_2 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k1_isocat_2 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) @ C )
& ( m2_relset_1 @ ( k1_isocat_2 @ A @ B @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(718,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 ) )
=> ( ( k10_relat_1 @ ( k15_funct_3 @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
= ( k2_zfmisc_1 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_funct_3) ).
thf(5452,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 ) )
=> ( ( k10_relat_1 @ ( k15_funct_3 @ C @ D ) @ ( k2_zfmisc_1 @ A @ B ) )
= ( k2_zfmisc_1 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(1336,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 )
<=> ( r1_xboole_0 @ ( k2_relat_1 @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t173_relat_1) ).
thf(8593,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 )
=> ( r1_xboole_0 @ ( k2_relat_1 @ B ) @ A ) )
& ( ( r1_xboole_0 @ ( k2_relat_1 @ B ) @ A )
=> ( ( k10_relat_1 @ B @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(1223,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t150_funct_1) ).
thf(8003,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ C @ ( k3_xboole_0 @ A @ ( k10_relat_1 @ C @ B ) ) )
= ( k3_xboole_0 @ ( k9_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(1031,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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_functor0) ).
thf(7085,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)],[1031]) ).
thf(2116,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/sandbox2/benchmark/theBenchmark.p',d3_binop_1) ).
thf(12487,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)],[2116]) ).
thf(1691,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/sandbox2/benchmark/theBenchmark.p',t83_funcop_1) ).
thf(10196,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)],[1691]) ).
thf(1057,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/sandbox2/benchmark/theBenchmark.p',dt_k15_funct_3) ).
thf(7166,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)],[1057]) ).
thf(1381,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/sandbox2/benchmark/theBenchmark.p',t10_fraenkel) ).
thf(8772,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)],[1381]) ).
thf(2119,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/sandbox2/benchmark/theBenchmark.p',dt_k4_multop_1) ).
thf(12502,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)],[2119]) ).
thf(1155,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/sandbox2/benchmark/theBenchmark.p',t15_funcop_1) ).
thf(7635,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)],[1155]) ).
thf(1904,axiom,
? [A: $i] :
( ~ ( v1_xboole_0 @ A )
& ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc7_finseq_1) ).
thf(11327,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)],[1904]) ).
thf(1789,axiom,
( ~ ( v1_xboole_0 @ k5_urysohn1 )
& ( v1_membered @ k5_urysohn1 )
& ( v2_membered @ k5_urysohn1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_urysohn1) ).
thf(10685,plain,
( ~ ( v1_xboole_0 @ k5_urysohn1 )
& ( v1_membered @ k5_urysohn1 )
& ( v2_membered @ k5_urysohn1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1789]) ).
thf(922,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/sandbox2/benchmark/theBenchmark.p',t10_functor0) ).
thf(6453,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)],[922]) ).
thf(810,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/sandbox2/benchmark/theBenchmark.p',t46_yellow20) ).
thf(5927,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)],[810]) ).
thf(732,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/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(5514,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)],[732]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_funct_5 @ B ) ) )
=> ( ( v1_relat_1 @ ( k1_funct_1 @ ( k5_funct_5 @ B ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k5_funct_5 @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_5) ).
thf(3507,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k5_funct_5 @ B ) ) )
=> ( ( v1_relat_1 @ ( k1_funct_1 @ ( k5_funct_5 @ B ) @ A ) )
& ( v1_funct_1 @ ( k1_funct_1 @ ( k5_funct_5 @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1487,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/sandbox2/benchmark/theBenchmark.p',t7_tex_2) ).
thf(9253,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)],[1487]) ).
thf(912,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/sandbox2/benchmark/theBenchmark.p',t57_subset_1) ).
thf(6399,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)],[912]) ).
thf(2236,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/sandbox2/benchmark/theBenchmark.p',t19_yellow_9) ).
thf(13047,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)],[2236]) ).
thf(2072,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/sandbox2/benchmark/theBenchmark.p',existence_m1_realset1) ).
thf(12313,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)],[2072]) ).
thf(1983,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/sandbox2/benchmark/theBenchmark.p',t2_grcat_1) ).
thf(11808,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)],[1983]) ).
thf(1823,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/sandbox2/benchmark/theBenchmark.p',t61_funcop_1) ).
thf(10856,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)],[1823]) ).
thf(2093,axiom,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(12390,plain,
( ( v1_xboole_0 @ k1_xboole_0 )
& ( v1_relat_1 @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2093]) ).
thf(2028,axiom,
( ( k6_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_relat_1) ).
thf(12056,plain,
( ( k6_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2028]) ).
thf(2144,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/sandbox2/benchmark/theBenchmark.p',d7_binop_2) ).
thf(12648,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)],[2144]) ).
thf(378,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/sandbox2/benchmark/theBenchmark.p',t37_funct_2) ).
thf(3904,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)],[378]) ).
thf(990,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_8_0_domain_1) ).
thf(6826,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)],[990]) ).
thf(2297,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/sandbox2/benchmark/theBenchmark.p',dt_k13_mcart_1) ).
thf(13285,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)],[2297]) ).
thf(635,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/sandbox2/benchmark/theBenchmark.p',t39_setwiseo) ).
thf(5074,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)],[635]) ).
thf(1768,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/sandbox2/benchmark/theBenchmark.p',s1_binop_2) ).
thf(10553,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)],[1768]) ).
thf(1783,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/sandbox2/benchmark/theBenchmark.p',t36_partfun1) ).
thf(10667,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)],[1783]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_3) ).
thf(2678,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1793,axiom,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
thf(10704,plain,
! [A: $i] :
( ( k2_subset_1 @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1793]) ).
thf(2174,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/sandbox2/benchmark/theBenchmark.p',t6_card_fil) ).
thf(12772,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)],[2174]) ).
thf(764,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( k1_tarski @ B ) )
& ( A != k1_xboole_0 )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ A )
& ( C != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(5721,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)],[764]) ).
thf(1413,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_relat_1) ).
thf(8904,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ ( k3_xboole_0 @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413]) ).
thf(2191,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/sandbox2/benchmark/theBenchmark.p',t70_funct_2) ).
thf(12873,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)],[2191]) ).
thf(461,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/sandbox2/benchmark/theBenchmark.p',t27_wellord2) ).
thf(4287,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)],[461]) ).
thf(113,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/sandbox2/benchmark/theBenchmark.p',t5_realset1) ).
thf(2821,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)],[113]) ).
thf(1435,axiom,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_enumset1 @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_setwiseo) ).
thf(9005,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)],[1435]) ).
thf(1293,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k10_relat_1 @ A @ ( k1_relat_1 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t182_relat_1) ).
thf(8350,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k1_relat_1 @ ( k5_relat_1 @ A @ B ) )
= ( k10_relat_1 @ A @ ( k1_relat_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(532,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/sandbox2/benchmark/theBenchmark.p',t11_funct_7) ).
thf(4630,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)],[532]) ).
thf(1296,axiom,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(8364,plain,
! [A: $i,B: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(1281,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/sandbox2/benchmark/theBenchmark.p',redefinition_v1_yellow18) ).
thf(8295,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)],[1281]) ).
thf(303,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/sandbox2/benchmark/theBenchmark.p',t66_funct_1) ).
thf(3608,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)],[303]) ).
thf(1395,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/sandbox2/benchmark/theBenchmark.p',t186_relat_1) ).
thf(8813,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)],[1395]) ).
thf(2353,axiom,
m1_subset_1 @ a_0_0_group_5 @ ( k1_zfmisc_1 @ f2_s1_group_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_group_5) ).
thf(13496,plain,
m1_subset_1 @ a_0_0_group_5 @ ( k1_zfmisc_1 @ f2_s1_group_5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2353]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(2850,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)],[120]) ).
thf(1492,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/sandbox2/benchmark/theBenchmark.p',dt_k6_domain_1) ).
thf(9270,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)],[1492]) ).
thf(1726,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/sandbox2/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(10392,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)],[1726]) ).
thf(2017,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/sandbox2/benchmark/theBenchmark.p',t4_mssubfam) ).
thf(11988,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)],[2017]) ).
thf(2284,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/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(13229,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)],[2284]) ).
thf(1373,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 @ ( k1_fraenkel @ A @ B ) @ ( k1_fraenkel @ A @ B ) ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ ( k1_fraenkel @ A @ B ) @ ( k1_fraenkel @ A @ B ) ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_subset_1 @ D @ ( k1_fraenkel @ A @ B ) )
& ( m1_subset_1 @ E @ ( k1_fraenkel @ A @ B ) ) )
=> ( m2_fraenkel @ ( k1_funcsdom @ A @ B @ C @ D @ E ) @ A @ B @ ( k1_fraenkel @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funcsdom) ).
thf(8744,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 @ ( k1_fraenkel @ A @ B ) @ ( k1_fraenkel @ A @ B ) ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_relset_1 @ C @ ( k2_zfmisc_1 @ ( k1_fraenkel @ A @ B ) @ ( k1_fraenkel @ A @ B ) ) @ ( k1_fraenkel @ A @ B ) )
& ( m1_subset_1 @ D @ ( k1_fraenkel @ A @ B ) )
& ( m1_subset_1 @ E @ ( k1_fraenkel @ A @ B ) ) )
=> ( m2_fraenkel @ ( k1_funcsdom @ A @ B @ C @ D @ E ) @ A @ B @ ( k1_fraenkel @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373]) ).
thf(2146,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/sandbox2/benchmark/theBenchmark.p',redefinition_k3_pre_circ) ).
thf(12659,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)],[2146]) ).
thf(1956,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/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(11650,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)],[1956]) ).
thf(2123,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/sandbox2/benchmark/theBenchmark.p',t54_mcart_1) ).
thf(12514,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)],[2123]) ).
thf(2167,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/sandbox2/benchmark/theBenchmark.p',d1_binop_1) ).
thf(12752,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)],[2167]) ).
thf(1888,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/sandbox2/benchmark/theBenchmark.p',t17_finset_1) ).
thf(11257,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)],[1888]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_partfun1) ).
thf(3769,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ( ( r1_tarski @ A @ B )
=> ( r1_tarski @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ D @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(2265,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/sandbox2/benchmark/theBenchmark.p',redefinition_k12_mcart_1) ).
thf(13172,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)],[2265]) ).
thf(1162,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/sandbox2/benchmark/theBenchmark.p',t31_filter_1) ).
thf(7672,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)],[1162]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( k4_relat_1 @ ( k2_zfmisc_1 @ A @ B ) )
= ( k2_zfmisc_1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_sysrel) ).
thf(3019,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)],[156]) ).
thf(89,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/sandbox2/benchmark/theBenchmark.p',t64_funct_1) ).
thf(2747,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)],[89]) ).
thf(487,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( ( k3_xboole_0 @ B @ ( k1_tarski @ A ) )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_zfmisc_1) ).
thf(4409,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)],[487]) ).
thf(1816,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/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
thf(10820,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)],[1816]) ).
thf(1833,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/sandbox2/benchmark/theBenchmark.p',redefinition_m2_subset_1) ).
thf(10915,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)],[1833]) ).
thf(505,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/sandbox2/benchmark/theBenchmark.p',t5_funct_7) ).
thf(4522,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)],[505]) ).
thf(673,axiom,
( ~ ( v1_xboole_0 @ k1_numbers )
& ( v1_membered @ k1_numbers )
& ( v2_membered @ k1_numbers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_membered) ).
thf(5262,plain,
( ~ ( v1_xboole_0 @ k1_numbers )
& ( v1_membered @ k1_numbers )
& ( v2_membered @ k1_numbers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(1233,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ k1_numbers )
=> ( m1_subset_1 @ ( k8_binop_2 @ A ) @ k1_numbers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_binop_2) ).
thf(8060,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)],[1233]) ).
thf(667,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(5235,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(1306,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/sandbox2/benchmark/theBenchmark.p',d4_enumset1) ).
thf(8396,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)],[1306]) ).
thf(1986,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/sandbox2/benchmark/theBenchmark.p',dt_k9_funct_3) ).
thf(11823,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)],[1986]) ).
thf(2207,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/sandbox2/benchmark/theBenchmark.p',dt_k33_binop_2) ).
thf(12937,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)],[2207]) ).
thf(712,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/sandbox2/benchmark/theBenchmark.p',t62_partfun1) ).
thf(5431,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)],[712]) ).
thf(1754,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/sandbox2/benchmark/theBenchmark.p',symmetry_r4_nattra_1) ).
thf(10504,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)],[1754]) ).
thf(1653,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/sandbox2/benchmark/theBenchmark.p',t151_funct_2) ).
thf(9991,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)],[1653]) ).
thf(1247,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/sandbox2/benchmark/theBenchmark.p',d1_enumset1) ).
thf(8111,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)],[1247]) ).
thf(2034,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/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).
thf(12071,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)],[2034]) ).
thf(420,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/sandbox2/benchmark/theBenchmark.p',t5_funct_2) ).
thf(4092,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)],[420]) ).
thf(591,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/sandbox2/benchmark/theBenchmark.p',t36_funct_4) ).
thf(4905,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)],[591]) ).
thf(708,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/sandbox2/benchmark/theBenchmark.p',t60_subset_1) ).
thf(5420,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)],[708]) ).
thf(1990,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/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(11842,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)],[1990]) ).
thf(1138,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/sandbox2/benchmark/theBenchmark.p',d6_enumset1) ).
thf(7494,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)],[1138]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( r2_wellord2 @ A @ B )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_card_1) ).
thf(2454,plain,
! [A: $i,B: $i] :
( ( ( r2_wellord2 @ A @ B )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(236,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( r2_wellord2 @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_finseq_1) ).
thf(3305,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( r2_wellord2 @ ( k2_finseq_1 @ A ) @ ( k2_finseq_1 @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(443,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( r2_hidden @ A @ ( k1_orders_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_orders_1) ).
thf(4190,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( r2_hidden @ A @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(326,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/sandbox2/benchmark/theBenchmark.p',t14_finseq_2) ).
thf(3691,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)],[326]) ).
thf(180,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/sandbox2/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(3114,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)],[180]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_partfun1 @ E @ A @ C ) @ ( k3_partfun1 @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_partfun1) ).
thf(3273,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( v1_relat_1 @ E )
& ( v1_funct_1 @ E ) )
=> ( ( ( r1_tarski @ A @ B )
& ( r1_tarski @ C @ D ) )
=> ( r1_tarski @ ( k3_partfun1 @ E @ A @ C ) @ ( k3_partfun1 @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(244,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/sandbox2/benchmark/theBenchmark.p',fc3_funct_1) ).
thf(3334,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)],[244]) ).
thf(350,axiom,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(3791,plain,
! [A: $i] :
( ( k4_xboole_0 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(1168,axiom,
! [A: $i] :
( ( k5_enumset1 @ A @ A @ A @ A @ A @ A @ A )
= ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_enumset1) ).
thf(7693,plain,
! [A: $i] :
( ( k5_enumset1 @ A @ A @ A @ A @ A @ A @ A )
= ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(1446,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/sandbox2/benchmark/theBenchmark.p',t53_funct_4) ).
thf(9065,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)],[1446]) ).
thf(833,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k3_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc28_membered) ).
thf(6037,plain,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k3_xboole_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(1566,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/sandbox2/benchmark/theBenchmark.p',t37_partfun1) ).
thf(9599,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)],[1566]) ).
thf(1578,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/sandbox2/benchmark/theBenchmark.p',rc4_triang_1) ).
thf(9649,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)],[1578]) ).
thf(1081,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/sandbox2/benchmark/theBenchmark.p',t6_ens_1) ).
thf(7243,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)],[1081]) ).
thf(2380,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/sandbox2/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(13617,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)],[2380]) ).
thf(772,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/sandbox2/benchmark/theBenchmark.p',t46_mcart_1) ).
thf(5753,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)],[772]) ).
thf(1899,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/sandbox2/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
thf(11295,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)],[1899]) ).
thf(737,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/sandbox2/benchmark/theBenchmark.p',t3_funct_2) ).
thf(5555,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)],[737]) ).
thf(207,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( r2_wellord2 @ A @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_card_1) ).
thf(3202,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ! [B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( r2_wellord2 @ A @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(1548,axiom,
v1_finset_1 @ a_0_0_pre_circ,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_pre_circ) ).
thf(9518,plain,
v1_finset_1 @ a_0_0_pre_circ,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1548]) ).
thf(1824,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/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
thf(10861,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)],[1824]) ).
thf(1696,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/sandbox2/benchmark/theBenchmark.p',t10_subset_1) ).
thf(10211,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)],[1696]) ).
thf(1555,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/sandbox2/benchmark/theBenchmark.p',t107_zfmisc_1) ).
thf(9550,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)],[1555]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( m2_pua2mss1 @ B @ A )
=> ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_pua2mss1) ).
thf(2429,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)],[11]) ).
thf(2164,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/sandbox2/benchmark/theBenchmark.p',t35_mcart_1) ).
thf(12733,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)],[2164]) ).
thf(1161,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/sandbox2/benchmark/theBenchmark.p',d4_setwiseo) ).
thf(7662,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)],[1161]) ).
thf(813,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/sandbox2/benchmark/theBenchmark.p',t13_lattice2) ).
thf(5948,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)],[813]) ).
thf(1051,axiom,
! [A: $i,B: $i] :
( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ ( k1_tarski @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funcop_1) ).
thf(7149,plain,
! [A: $i,B: $i] :
( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ ( k1_tarski @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(2260,axiom,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ! [C: $i] :
( ( m1_pboole @ C @ ( k3_zfmisc_1 @ A @ A @ A ) )
=> ( ( C
= ( k2_altcat_1 @ A @ B ) )
<=> ! [D: $i,E: $i,F: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ A ) )
=> ( ( k1_multop_1 @ C @ D @ E @ F )
= ( k1_binop_1 @ B @ D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_altcat_1) ).
thf(13149,plain,
! [A: $i,B: $i] :
( ( m1_pboole @ B @ ( k2_zfmisc_1 @ A @ A ) )
=> ! [C: $i] :
( ( m1_pboole @ C @ ( k3_zfmisc_1 @ A @ A @ A ) )
=> ( ( ( C
= ( k2_altcat_1 @ A @ B ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ A ) )
=> ( ( k1_multop_1 @ C @ D @ E @ F )
= ( k1_binop_1 @ B @ D @ F ) ) ) )
& ( ! [D: $i,E: $i,F: $i] :
( ( ( r2_hidden @ D @ A )
& ( r2_hidden @ E @ A )
& ( r2_hidden @ F @ A ) )
=> ( ( k1_multop_1 @ C @ D @ E @ F )
= ( k1_binop_1 @ B @ D @ F ) ) )
=> ( C
= ( k2_altcat_1 @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2260]) ).
thf(1418,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/sandbox2/benchmark/theBenchmark.p',t50_funct_1) ).
thf(8917,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)],[1418]) ).
thf(1607,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/sandbox2/benchmark/theBenchmark.p',t45_relset_1) ).
thf(9815,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)],[1607]) ).
thf(2055,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/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(12202,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)],[2055]) ).
thf(1008,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( m1_subset_1 @ ( k1_tarski @ A ) @ ( k1_zfmisc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_subset_1) ).
thf(6966,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)],[1008]) ).
thf(2098,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/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
thf(12405,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)],[2098]) ).
thf(343,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( ( k9_funct_7 @ k1_xboole_0 @ A )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_funct_7) ).
thf(3774,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( ( k9_funct_7 @ k1_xboole_0 @ A )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(1719,axiom,
( ( ( k1_funct_5 @ k1_xboole_0 )
= k1_xboole_0 )
& ( ( k2_funct_5 @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_funct_5) ).
thf(10365,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)],[1719]) ).
thf(646,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/sandbox2/benchmark/theBenchmark.p',t54_partfun1) ).
thf(5152,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)],[646]) ).
thf(1305,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/sandbox2/benchmark/theBenchmark.p',t23_funct_2) ).
thf(8391,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)],[1305]) ).
thf(1288,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k4_card_fil @ A ) )
<=> ( m1_card_fil @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_card_fil) ).
thf(8327,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)],[1288]) ).
thf(1143,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/sandbox2/benchmark/theBenchmark.p',t2_filter_2) ).
thf(7583,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)],[1143]) ).
thf(1269,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/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(8248,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)],[1269]) ).
thf(134,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/sandbox2/benchmark/theBenchmark.p',t28_relat_1) ).
thf(2903,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)],[134]) ).
thf(1880,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/sandbox2/benchmark/theBenchmark.p',t11_pua2mss1) ).
thf(11198,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)],[1880]) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',dt_k10_binop_2) ).
thf(2599,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)],[44]) ).
thf(1525,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/sandbox2/benchmark/theBenchmark.p',t24_binop_1) ).
thf(9413,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)],[1525]) ).
thf(363,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/sandbox2/benchmark/theBenchmark.p',t65_setwiseo) ).
thf(3847,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)],[363]) ).
thf(567,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/sandbox2/benchmark/theBenchmark.p',cc1_setfam_1) ).
thf(4800,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)],[567]) ).
thf(307,axiom,
( ( k1_setfam_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_setfam_1) ).
thf(3623,plain,
( ( k1_setfam_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(256,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_classes2 @ A ) )
=> ( r2_hidden @ k1_xboole_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_classes2) ).
thf(3412,plain,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_classes2 @ A ) )
=> ( r2_hidden @ k1_xboole_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1015,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 @ ( k3_funct_5 @ B ) ) )
& ( C
= ( k1_funct_1 @ ( k3_funct_5 @ B ) @ A ) ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_funct_5 @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_funct_5 @ ( k1_relat_1 @ B ) ) ) ) ) )
& ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_funct_5 @ ( k1_relat_1 @ B ) ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k2_relat_1 @ B ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ ( k4_tarski @ A @ D ) ) )
& ( r2_hidden @ ( k4_tarski @ A @ D ) @ ( k1_relat_1 @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funct_5) ).
thf(6994,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 @ ( k3_funct_5 @ B ) ) )
& ( C
= ( k1_funct_1 @ ( k3_funct_5 @ B ) @ A ) ) )
=> ( ( ( k1_relat_1 @ C )
= ( k2_funct_5 @ ( k3_xboole_0 @ ( k1_relat_1 @ B ) @ ( k2_zfmisc_1 @ ( k1_tarski @ A ) @ ( k2_funct_5 @ ( k1_relat_1 @ B ) ) ) ) ) )
& ( r1_tarski @ ( k1_relat_1 @ C ) @ ( k2_funct_5 @ ( k1_relat_1 @ B ) ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ ( k2_relat_1 @ B ) )
& ! [D: $i] :
( ( r2_hidden @ D @ ( k1_relat_1 @ C ) )
=> ( ( ( k1_funct_1 @ C @ D )
= ( k1_funct_1 @ B @ ( k4_tarski @ A @ D ) ) )
& ( r2_hidden @ ( k4_tarski @ A @ D ) @ ( k1_relat_1 @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(2049,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/sandbox2/benchmark/theBenchmark.p',t7_mssubfam) ).
thf(12163,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)],[2049]) ).
thf(1821,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/sandbox2/benchmark/theBenchmark.p',d1_filter_1) ).
thf(10846,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)],[1821]) ).
thf(2218,axiom,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(12983,plain,
! [A: $i] :
? [B: $i] : ( m1_eqrel_1 @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2218]) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',t65_funct_1) ).
thf(3041,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)],[161]) ).
thf(642,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/sandbox2/benchmark/theBenchmark.p',d12_binop_2) ).
thf(5106,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)],[642]) ).
thf(568,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m2_card_fil @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_card_fil) ).
thf(4802,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ? [B: $i] : ( m2_card_fil @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k3_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) ) @ ( k10_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_funct_3) ).
thf(3652,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k3_tarski @ ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A ) ) @ ( k10_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1071,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/sandbox2/benchmark/theBenchmark.p',t31_borsuk_1) ).
thf(7207,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)],[1071]) ).
thf(1987,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/sandbox2/benchmark/theBenchmark.p',dt_m2_filter_1) ).
thf(11830,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)],[1987]) ).
thf(498,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ k1_numbers )
=> ( ( k8_binop_2 @ ( k8_binop_2 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k8_binop_2) ).
thf(4488,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)],[498]) ).
thf(1649,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/sandbox2/benchmark/theBenchmark.p',t51_setfam_1) ).
thf(9983,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)],[1649]) ).
thf(754,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/sandbox2/benchmark/theBenchmark.p',t19_funct_1) ).
thf(5685,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)],[754]) ).
thf(1246,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/sandbox2/benchmark/theBenchmark.p',t62_subset_1) ).
thf(8108,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)],[1246]) ).
thf(763,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_funct_1 @ ( k3_cat_2 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k3_cat_2 @ A @ B @ C @ D ) @ B @ ( k1_fraenkel @ A @ C ) )
& ( m2_relset_1 @ ( k3_cat_2 @ A @ B @ C @ D ) @ B @ ( k1_fraenkel @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_cat_2) ).
thf(5717,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_funct_1 @ ( k3_cat_2 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k3_cat_2 @ A @ B @ C @ D ) @ B @ ( k1_fraenkel @ A @ C ) )
& ( m2_relset_1 @ ( k3_cat_2 @ A @ B @ C @ D ) @ B @ ( k1_fraenkel @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(743,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/sandbox2/benchmark/theBenchmark.p',t80_finseq_2) ).
thf(5596,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)],[743]) ).
thf(985,axiom,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_partfun1) ).
thf(6793,plain,
( ( k2_relat_1 @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(2102,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/sandbox2/benchmark/theBenchmark.p',t18_setwiseo) ).
thf(12424,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)],[2102]) ).
thf(2360,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/sandbox2/benchmark/theBenchmark.p',dt_k8_relset_2) ).
thf(13545,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)],[2360]) ).
thf(645,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/sandbox2/benchmark/theBenchmark.p',t26_partfun1) ).
thf(5147,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)],[645]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_funcop_1) ).
thf(6457,plain,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(1675,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/sandbox2/benchmark/theBenchmark.p',t40_subset_1) ).
thf(10129,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)],[1675]) ).
thf(966,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) ) )
=> ( r1_tarski @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_1) ).
thf(6650,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) ) )
=> ( r1_tarski @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(975,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ B )
=> ( v1_finset_1 @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(6701,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)],[975]) ).
thf(274,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/sandbox2/benchmark/theBenchmark.p',dt_k3_card_fil) ).
thf(3488,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)],[274]) ).
thf(2075,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/sandbox2/benchmark/theBenchmark.p',redefinition_k14_domain_1) ).
thf(12328,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)],[2075]) ).
thf(1198,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/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(7876,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)],[1198]) ).
thf(2343,axiom,
! [A: $i] :
( ( v1_fraenkel @ A )
=> ! [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
=> ( v1_fraenkel @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_altcat_1) ).
thf(13461,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)],[2343]) ).
thf(2363,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/sandbox2/benchmark/theBenchmark.p',dt_k1_cat_5) ).
thf(13570,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)],[2363]) ).
thf(1764,axiom,
! [A: $i,B: $i] :
( ( ( r1_tarski @ A @ B )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
thf(10536,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)],[1764]) ).
thf(606,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/sandbox2/benchmark/theBenchmark.p',t31_setwiseo) ).
thf(4959,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)],[606]) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(2838,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)],[118]) ).
thf(394,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/sandbox2/benchmark/theBenchmark.p',t65_funct_2) ).
thf(3970,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)],[394]) ).
thf(768,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/sandbox2/benchmark/theBenchmark.p',redefinition_k14_funct_3) ).
thf(5736,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)],[768]) ).
thf(1002,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/sandbox2/benchmark/theBenchmark.p',t156_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 )
=> ( r2_hidden @ C @ ( k5_partfun1 @ A @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(1656,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/sandbox2/benchmark/theBenchmark.p',t55_mcart_1) ).
thf(10023,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)],[1656]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',t109_relat_1) ).
thf(2426,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)],[10]) ).
thf(431,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/sandbox2/benchmark/theBenchmark.p',t116_funct_2) ).
thf(4133,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)],[431]) ).
thf(2366,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/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(13585,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)],[2366]) ).
thf(1142,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/sandbox2/benchmark/theBenchmark.p',t16_lattice2) ).
thf(7580,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)],[1142]) ).
thf(1708,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/sandbox2/benchmark/theBenchmark.p',t28_subset_1) ).
thf(10293,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)],[1708]) ).
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/sandbox2/benchmark/theBenchmark.p',t24_funct_2) ).
thf(6775,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(822,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/sandbox2/benchmark/theBenchmark.p',t188_relat_1) ).
thf(5998,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)],[822]) ).
thf(747,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/sandbox2/benchmark/theBenchmark.p',d5_enumset1) ).
thf(5613,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)],[747]) ).
thf(2375,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/sandbox2/benchmark/theBenchmark.p',dt_k14_mcart_1) ).
thf(13605,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)],[2375]) ).
thf(1733,axiom,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( ( k5_finsub_1 @ A )
= ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finsub_1) ).
thf(10415,plain,
! [A: $i] :
( ( v1_finset_1 @ A )
=> ( ( k5_finsub_1 @ A )
= ( k1_zfmisc_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1733]) ).
thf(1027,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/sandbox2/benchmark/theBenchmark.p',t61_subset_1) ).
thf(7067,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)],[1027]) ).
thf(1113,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/sandbox2/benchmark/theBenchmark.p',t12_funct_7) ).
thf(7391,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)],[1113]) ).
thf(2266,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_0_0_altcat_2) ).
thf(13175,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)],[2266]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v2_relat_1 @ B )
& ( m1_pboole @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_funct_1 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pboole) ).
thf(2711,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v2_relat_1 @ B )
& ( m1_pboole @ B @ A )
& ( m1_subset_1 @ C @ A ) )
=> ~ ( v1_xboole_0 @ ( k1_funct_1 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(1639,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/sandbox2/benchmark/theBenchmark.p',t59_funct_2) ).
thf(9947,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)],[1639]) ).
thf(615,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/sandbox2/benchmark/theBenchmark.p',t131_funct_2) ).
thf(4991,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)],[615]) ).
thf(864,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/sandbox2/benchmark/theBenchmark.p',t6_mcart_1) ).
thf(6193,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)],[864]) ).
thf(1285,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/sandbox2/benchmark/theBenchmark.p',t8_relset_2) ).
thf(8317,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)],[1285]) ).
thf(1338,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ B )
= ( k3_xboole_0 @ B @ ( k2_zfmisc_1 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_relat_1) ).
thf(8602,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( k8_relat_1 @ A @ B )
= ( k3_xboole_0 @ B @ ( k2_zfmisc_1 @ ( k1_relat_1 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).
thf(1056,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/sandbox2/benchmark/theBenchmark.p',t80_funcop_1) ).
thf(7163,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)],[1056]) ).
thf(1484,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/sandbox2/benchmark/theBenchmark.p',t89_funct_3) ).
thf(9242,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)],[1484]) ).
thf(213,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/sandbox2/benchmark/theBenchmark.p',t41_relat_1) ).
thf(3224,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)],[213]) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',t13_finseq_2) ).
thf(2728,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)],[83]) ).
thf(1069,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/sandbox2/benchmark/theBenchmark.p',t29_partfun1) ).
thf(7202,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)],[1069]) ).
thf(391,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_2) ).
thf(3961,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)],[391]) ).
thf(723,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/sandbox2/benchmark/theBenchmark.p',t77_funct_2) ).
thf(5472,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)],[723]) ).
thf(1494,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/sandbox2/benchmark/theBenchmark.p',fc12_binop_2) ).
thf(9274,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)],[1494]) ).
thf(637,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/sandbox2/benchmark/theBenchmark.p',t5_orders_1) ).
thf(5083,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)],[637]) ).
thf(876,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ B @ ( k2_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t170_relat_1) ).
thf(6245,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ B @ ( k2_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(2097,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/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
thf(12402,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)],[2097]) ).
thf(192,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/sandbox2/benchmark/theBenchmark.p',t59_classes2) ).
thf(3156,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)],[192]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k3_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ B ) @ A ) ) @ ( k9_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_funct_3) ).
thf(2807,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k3_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ B ) @ A ) ) @ ( k9_relat_1 @ B @ ( k3_tarski @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1515,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/sandbox2/benchmark/theBenchmark.p',t81_enumset1) ).
thf(9374,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)],[1515]) ).
thf(2245,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/sandbox2/benchmark/theBenchmark.p',t48_relat_1) ).
thf(13076,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)],[2245]) ).
thf(1400,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/sandbox2/benchmark/theBenchmark.p',t61_funct_4) ).
thf(8861,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)],[1400]) ).
thf(1175,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/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
thf(7720,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)],[1175]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_partfun1) ).
thf(3007,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( r1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1805,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/sandbox2/benchmark/theBenchmark.p',t57_domain_1) ).
thf(10769,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)],[1805]) ).
thf(1167,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k3_xboole_0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc27_membered) ).
thf(7690,plain,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( k3_xboole_0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(1136,axiom,
! [A: $i,B: $i] :
( ( k2_funcop_1 @ A @ B )
= ( k2_zfmisc_1 @ A @ ( k1_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_funcop_1) ).
thf(7488,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)],[1136]) ).
thf(453,axiom,
! [A: $i,B: $i] :
( ( k3_tarski @ ( k3_setfam_1 @ A @ B ) )
= ( k3_xboole_0 @ ( k3_tarski @ A ) @ ( k3_tarski @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_setfam_1) ).
thf(4257,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)],[453]) ).
thf(2370,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/sandbox2/benchmark/theBenchmark.p',t16_relset_2) ).
thf(13595,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)],[2370]) ).
thf(1786,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/sandbox2/benchmark/theBenchmark.p',t59_domain_1) ).
thf(10674,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)],[1786]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i] :
( ( r2_hidden @ B @ A )
=> ( ( k1_funct_1 @ ( k2_funcop_1 @ A @ C ) @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_funcop_1) ).
thf(4111,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)],[424]) ).
thf(1011,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t179_relat_1) ).
thf(6975,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ B @ C )
=> ( r1_tarski @ ( k10_relat_1 @ B @ A ) @ ( k10_relat_1 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(2181,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/sandbox2/benchmark/theBenchmark.p',t43_funct_2) ).
thf(12829,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)],[2181]) ).
thf(870,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ B )
<=> ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(6220,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)],[870]) ).
thf(918,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/sandbox2/benchmark/theBenchmark.p',t18_funct_1) ).
thf(6420,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)],[918]) ).
thf(1163,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/sandbox2/benchmark/theBenchmark.p',t30_funcop_1) ).
thf(7676,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)],[1163]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_xboole_0 @ A @ B )
=> ( r1_xboole_0 @ A @ ( k4_xboole_0 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t80_xboole_1) ).
thf(3401,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)],[252]) ).
thf(1761,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/sandbox2/benchmark/theBenchmark.p',dt_k6_funct_3) ).
thf(10526,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)],[1761]) ).
thf(1333,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/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(8579,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)],[1333]) ).
thf(634,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/sandbox2/benchmark/theBenchmark.p',t155_funct_2) ).
thf(5068,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)],[634]) ).
thf(124,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/sandbox2/benchmark/theBenchmark.p',t63_classes2) ).
thf(2865,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)],[124]) ).
thf(1353,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/sandbox2/benchmark/theBenchmark.p',t63_funcop_1) ).
thf(8681,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)],[1353]) ).
thf(128,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/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).
thf(2875,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)],[128]) ).
thf(196,axiom,
! [A: $i] :
( ( v1_xboole_0 @ ( k1_setwiseo @ A ) )
& ( m1_subset_1 @ ( k1_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_setwiseo) ).
thf(3168,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)],[196]) ).
thf(2046,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/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(12145,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)],[2046]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ A @ ( k1_relat_1 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_partfun1) ).
thf(2435,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B )
=> ( r1_tarski @ A @ ( k1_relat_1 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1795,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/sandbox2/benchmark/theBenchmark.p',t38_funct_2) ).
thf(10712,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)],[1795]) ).
thf(94,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/sandbox2/benchmark/theBenchmark.p',d2_finseq_1) ).
thf(2760,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)],[94]) ).
thf(1701,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/sandbox2/benchmark/theBenchmark.p',rc3_closure2) ).
thf(10261,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)],[1701]) ).
thf(888,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/sandbox2/benchmark/theBenchmark.p',t5_isocat_2) ).
thf(6286,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)],[888]) ).
thf(2233,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_finsub_1) ).
thf(13036,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)],[2233]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) @ ( k10_relat_1 @ ( k4_relat_1 @ B ) @ ( k10_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t183_relat_1) ).
thf(2924,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ B ) @ A ) @ ( k10_relat_1 @ ( k4_relat_1 @ B ) @ ( k10_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(2227,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/sandbox2/benchmark/theBenchmark.p',t51_relset_1) ).
thf(13012,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)],[2227]) ).
thf(1160,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/sandbox2/benchmark/theBenchmark.p',t55_funcop_1) ).
thf(7659,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)],[1160]) ).
thf(460,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/sandbox2/benchmark/theBenchmark.p',t23_relset_1) ).
thf(4278,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)],[460]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( ( r2_hidden @ B @ A )
& ( v1_membered @ B ) )
=> ( v1_membered @ ( k1_setfam_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_membered) ).
thf(3584,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)],[296]) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A )
= ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_3) ).
thf(3139,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( ( k9_relat_1 @ ( k3_funct_3 @ B ) @ A )
= ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(1994,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/sandbox2/benchmark/theBenchmark.p',t109_zfmisc_1) ).
thf(11862,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)],[1994]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k19_pralg_1 @ A @ B @ C )
= ( k3_funct_5 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k19_pralg_1) ).
thf(3620,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k19_pralg_1 @ A @ B @ C )
= ( k3_funct_5 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(797,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/sandbox2/benchmark/theBenchmark.p',t72_mcart_1) ).
thf(5873,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)],[797]) ).
thf(1050,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ~ ( v1_xboole_0 @ ( k1_ens_1 @ A ) )
& ( v1_fraenkel @ ( k1_ens_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ens_1) ).
thf(7146,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)],[1050]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_relat_1) ).
thf(3457,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( k8_relat_1 @ ( k4_xboole_0 @ A @ B ) @ C )
= ( k4_xboole_0 @ ( k8_relat_1 @ A @ C ) @ ( k8_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(1866,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/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(11123,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)],[1866]) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ A @ ( k4_xboole_0 @ B @ A ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(3589,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)],[298]) ).
thf(2331,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/sandbox2/benchmark/theBenchmark.p',free_g1_pre_topc) ).
thf(13406,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)],[2331]) ).
thf(2085,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/sandbox2/benchmark/theBenchmark.p',t3_multop_1) ).
thf(12360,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)],[2085]) ).
thf(112,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k3_partfun1 @ A @ B @ C )
= ( k7_relat_1 @ ( k8_relat_1 @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_partfun1) ).
thf(2818,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i,C: $i] :
( ( k3_partfun1 @ A @ B @ C )
= ( k7_relat_1 @ ( k8_relat_1 @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(167,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v2_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k4_card_3 @ A )
= ( k4_card_3 @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_pua2mss1) ).
thf(3067,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v2_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( k4_card_3 @ A )
= ( k4_card_3 @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1920,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/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(11393,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)],[1920]) ).
thf(558,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/sandbox2/benchmark/theBenchmark.p',t31_relset_1) ).
thf(4770,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)],[558]) ).
thf(2114,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/sandbox2/benchmark/theBenchmark.p',t12_cantor_1) ).
thf(12467,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)],[2114]) ).
thf(1581,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/sandbox2/benchmark/theBenchmark.p',t32_subset_1) ).
thf(9665,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)],[1581]) ).
thf(1672,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(10114,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1672]) ).
thf(2249,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/sandbox2/benchmark/theBenchmark.p',dt_k12_funct_3) ).
thf(13087,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)],[2249]) ).
thf(72,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/sandbox2/benchmark/theBenchmark.p',dt_k5_setwiseo) ).
thf(2696,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)],[72]) ).
thf(1572,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/sandbox2/benchmark/theBenchmark.p',dt_k1_oppcat_1) ).
thf(9628,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)],[1572]) ).
thf(1203,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/sandbox2/benchmark/theBenchmark.p',t37_funct_4) ).
thf(7904,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)],[1203]) ).
thf(1980,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/sandbox2/benchmark/theBenchmark.p',t18_funct_5) ).
thf(11789,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)],[1980]) ).
thf(827,axiom,
! [A: $i] :
( ( k20_mcart_1 @ A )
= ( k2_mcart_1 @ ( k2_mcart_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_mcart_1) ).
thf(6013,plain,
! [A: $i] :
( ( k20_mcart_1 @ A )
= ( k2_mcart_1 @ ( k2_mcart_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(147,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/sandbox2/benchmark/theBenchmark.p',t1_waybel10) ).
thf(2960,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)],[147]) ).
thf(601,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/sandbox2/benchmark/theBenchmark.p',t12_functor0) ).
thf(4944,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)],[601]) ).
thf(538,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/sandbox2/benchmark/theBenchmark.p',t30_borsuk_1) ).
thf(4656,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)],[538]) ).
thf(285,axiom,
! [A: $i] :
( ( ~ ( v1_xboole_0 @ A )
& ( v1_classes2 @ A ) )
=> ? [B: $i] :
( ( m1_subset_1 @ B @ A )
& ~ ( v1_xboole_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_classes2) ).
thf(3533,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)],[285]) ).
thf(817,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_funct_1 @ ( k2_cat_2 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k2_cat_2 @ A @ B @ C @ D ) @ A @ ( k1_fraenkel @ B @ C ) )
& ( m2_relset_1 @ ( k2_cat_2 @ A @ B @ C @ D ) @ A @ ( k1_fraenkel @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_cat_2) ).
thf(5966,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_funct_1 @ ( k2_cat_2 @ A @ B @ C @ D ) )
& ( v1_funct_2 @ ( k2_cat_2 @ A @ B @ C @ D ) @ A @ ( k1_fraenkel @ B @ C ) )
& ( m2_relset_1 @ ( k2_cat_2 @ A @ B @ C @ D ) @ A @ ( k1_fraenkel @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(909,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/sandbox2/benchmark/theBenchmark.p',t46_funct_4) ).
thf(6390,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)],[909]) ).
thf(2140,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/sandbox2/benchmark/theBenchmark.p',dt_k2_borsuk_1) ).
thf(12633,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)],[2140]) ).
thf(1692,axiom,
! [A: $i,B: $i,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 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ E ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 )
=> ( ( k8_relset_2 @ A @ B @ ( k4_subset_1 @ A @ C @ D ) @ E )
= ( k8_relset_2 @ A @ B @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_relset_2) ).
thf(10199,plain,
! [A: $i,B: $i,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 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ E ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 )
=> ( ( k8_relset_2 @ A @ B @ ( k4_subset_1 @ A @ C @ D ) @ E )
= ( k8_relset_2 @ A @ B @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1692]) ).
thf(291,axiom,
! [A: $i] :
( ( r2_wellord2 @ A @ k1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_card_1) ).
thf(3548,plain,
! [A: $i] :
( ( ( r2_wellord2 @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( r2_wellord2 @ A @ k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1183,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/sandbox2/benchmark/theBenchmark.p',t3_pboole) ).
thf(7765,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)],[1183]) ).
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 @ ( 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/sandbox2/benchmark/theBenchmark.p',t52_funcop_1) ).
thf(4780,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)],[561]) ).
thf(385,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/sandbox2/benchmark/theBenchmark.p',t145_funct_2) ).
thf(3928,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)],[385]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i] :
( ( r1_tarski @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ C ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_zfmisc_1) ).
thf(4185,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)],[441]) ).
thf(1013,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/sandbox2/benchmark/theBenchmark.p',t15_funct_1) ).
thf(6980,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)],[1013]) ).
thf(2117,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(12495,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2117]) ).
thf(308,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( k4_xboole_0 @ ( k2_tarski @ A @ B ) @ ( k1_tarski @ B ) )
= ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_zfmisc_1) ).
thf(3625,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)],[308]) ).
thf(335,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/sandbox2/benchmark/theBenchmark.p',t65_classes2) ).
thf(3725,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)],[335]) ).
thf(805,axiom,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_zfmisc_1) ).
thf(5907,plain,
! [A: $i,B: $i] : ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(970,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/sandbox2/benchmark/theBenchmark.p',t16_funcop_1) ).
thf(6674,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)],[970]) ).
thf(1778,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/sandbox2/benchmark/theBenchmark.p',dt_k7_funcop_1) ).
thf(10637,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)],[1778]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funcop_1) ).
thf(4102,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( r2_hidden @ B @ C )
=> ( ( k10_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(1722,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/sandbox2/benchmark/theBenchmark.p',dt_k2_multop_1) ).
thf(10376,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)],[1722]) ).
thf(1852,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/sandbox2/benchmark/theBenchmark.p',t26_filter_1) ).
thf(11044,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)],[1852]) ).
thf(2379,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/sandbox2/benchmark/theBenchmark.p',dt_k2_cantor_1) ).
thf(13615,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)],[2379]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= k1_xboole_0 ) )
=> ( ( k7_relat_1 @ B @ A )
= ( k6_relat_1 @ A ) ) )
& ( ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ) )
=> ( ( k8_relat_1 @ A @ B )
= ( k6_relat_1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_sysrel) ).
thf(2919,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( ( ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( ( k5_relat_1 @ ( k6_relat_1 @ A ) @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) )
= k1_xboole_0 ) )
=> ( ( k7_relat_1 @ B @ A )
= ( k6_relat_1 @ A ) ) )
& ( ( ( r1_tarski @ ( k6_relat_1 @ A ) @ B )
& ( ( k5_relat_1 @ ( k4_xboole_0 @ B @ ( k6_relat_1 @ A ) ) @ ( k6_relat_1 @ A ) )
= k1_xboole_0 ) )
=> ( ( k8_relat_1 @ A @ B )
= ( k6_relat_1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(437,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/sandbox2/benchmark/theBenchmark.p',t34_partfun1) ).
thf(4170,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)],[437]) ).
thf(1451,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_partfun1) ).
thf(9078,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ k1_xboole_0 ) )
=> ( ( k10_relat_1 @ C @ B )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(725,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/sandbox2/benchmark/theBenchmark.p',d14_binop_1) ).
thf(5485,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)],[725]) ).
thf(550,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/sandbox2/benchmark/theBenchmark.p',t32_mcart_1) ).
thf(4730,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)],[550]) ).
thf(160,axiom,
! [A: $i] :
( ( m1_subset_1 @ A @ k5_numbers )
=> ( m1_subset_1 @ ( k3_urysohn1 @ A ) @ ( k1_zfmisc_1 @ k1_numbers ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_urysohn1) ).
thf(3039,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)],[160]) ).
thf(1237,axiom,
k5_numbers != k1_numbers,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_numbers) ).
thf(8075,plain,
k5_numbers != k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(299,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/sandbox2/benchmark/theBenchmark.p',d3_funct_2) ).
thf(3593,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)],[299]) ).
thf(2070,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/sandbox2/benchmark/theBenchmark.p',t76_relat_1) ).
thf(12302,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)],[2070]) ).
thf(594,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/sandbox2/benchmark/theBenchmark.p',t5_relat_1) ).
thf(4913,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)],[594]) ).
thf(896,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/sandbox2/benchmark/theBenchmark.p',t152_funct_2) ).
thf(6322,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)],[896]) ).
thf(2147,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/sandbox2/benchmark/theBenchmark.p',t76_funct_3) ).
thf(12662,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)],[2147]) ).
thf(1280,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/sandbox2/benchmark/theBenchmark.p',d4_funcop_1) ).
thf(8292,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)],[1280]) ).
thf(830,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/sandbox2/benchmark/theBenchmark.p',t28_mcart_1) ).
thf(6023,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)],[830]) ).
thf(1535,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/sandbox2/benchmark/theBenchmark.p',rc5_tex_2) ).
thf(9459,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)],[1535]) ).
thf(1889,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/sandbox2/benchmark/theBenchmark.p',fc1_waybel_2) ).
thf(11259,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)],[1889]) ).
thf(2169,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/sandbox2/benchmark/theBenchmark.p',t3_funct_7) ).
thf(12758,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)],[2169]) ).
thf(40,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/sandbox2/benchmark/theBenchmark.p',t91_finseq_2) ).
thf(2591,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)],[40]) ).
thf(272,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/sandbox2/benchmark/theBenchmark.p',t75_zfmisc_1) ).
thf(3465,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)],[272]) ).
thf(1602,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/sandbox2/benchmark/theBenchmark.p',redefinition_k5_funcsdom) ).
thf(9755,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)],[1602]) ).
thf(1859,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/sandbox2/benchmark/theBenchmark.p',t34_finsub_1) ).
thf(11076,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)],[1859]) ).
thf(1022,axiom,
! [A: $i,B: $i,C: $i] : ( r1_tarski @ ( k9_relat_1 @ ( k2_funcop_1 @ A @ B ) @ C ) @ ( k1_tarski @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_borsuk_1) ).
thf(7034,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)],[1022]) ).
thf(336,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/sandbox2/benchmark/theBenchmark.p',t30_finseq_2) ).
thf(3729,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)],[336]) ).
thf(427,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/sandbox2/benchmark/theBenchmark.p',t68_funct_3) ).
thf(4121,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)],[427]) ).
thf(2128,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/sandbox2/benchmark/theBenchmark.p',t1_group_6) ).
thf(12544,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)],[2128]) ).
thf(381,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k6_partfun1 @ A ) @ ( k6_partfun1 @ B ) )
<=> ( r1_tarski @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_funct_4) ).
thf(3911,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)],[381]) ).
thf(1969,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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(11732,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)],[1969]) ).
thf(2048,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 )
<=> ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relset_2) ).
thf(12157,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2048]) ).
thf(2202,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/sandbox2/benchmark/theBenchmark.p',cc5_tex_2) ).
thf(12915,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)],[2202]) ).
thf(1463,axiom,
! [A: $i] :
( ! [B: $i] :
( ( r2_hidden @ B @ A )
=> ( v2_membered @ B ) )
=> ( v2_membered @ ( k3_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_membered) ).
thf(9147,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)],[1463]) ).
thf(2319,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/sandbox2/benchmark/theBenchmark.p',dt_k12_domain_1) ).
thf(13364,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)],[2319]) ).
thf(121,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( k1_relat_1 @ A ) )
=> ( ( ( k3_funct_5 @ A )
= k1_xboole_0 )
& ( ( k5_funct_5 @ A )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_5) ).
thf(2853,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i,C: $i] :
~ ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( k1_relat_1 @ A ) )
=> ( ( ( k3_funct_5 @ A )
= k1_xboole_0 )
& ( ( k5_funct_5 @ A )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(529,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t176_relat_1) ).
thf(4615,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) ) @ ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(357,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/sandbox2/benchmark/theBenchmark.p',t26_finseq_1) ).
thf(3825,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)],[357]) ).
thf(1901,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/sandbox2/benchmark/theBenchmark.p',t30_partfun1) ).
thf(11319,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)],[1901]) ).
thf(933,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/sandbox2/benchmark/theBenchmark.p',t1_funcop_1) ).
thf(6489,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)],[933]) ).
thf(974,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/sandbox2/benchmark/theBenchmark.p',d8_monoid_0) ).
thf(6689,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)],[974]) ).
thf(1104,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/sandbox2/benchmark/theBenchmark.p',d8_funct_3) ).
thf(7344,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)],[1104]) ).
thf(419,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/sandbox2/benchmark/theBenchmark.p',t15_binop_1) ).
thf(4089,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)],[419]) ).
thf(1226,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/sandbox2/benchmark/theBenchmark.p',t8_lattice2) ).
thf(8011,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)],[1226]) ).
thf(491,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/sandbox2/benchmark/theBenchmark.p',t121_funct_1) ).
thf(4468,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)],[491]) ).
thf(2309,axiom,
m1_subset_1 @ k5_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_urysohn1) ).
thf(13333,plain,
m1_subset_1 @ k5_urysohn1 @ ( k1_zfmisc_1 @ k1_numbers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2309]) ).
thf(1335,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/sandbox2/benchmark/theBenchmark.p',t38_partfun1) ).
thf(8584,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)],[1335]) ).
thf(1261,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/sandbox2/benchmark/theBenchmark.p',d12_binop_1) ).
thf(8197,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)],[1261]) ).
thf(1439,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/sandbox2/benchmark/theBenchmark.p',t84_funcop_1) ).
thf(9029,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)],[1439]) ).
thf(1839,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/sandbox2/benchmark/theBenchmark.p',d1_cantor_1) ).
thf(10969,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)],[1839]) ).
thf(1746,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( m1_relset_1 @ C @ A @ B )
& ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(10468,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)],[1746]) ).
thf(1195,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( B
= ( k3_funct_5 @ A ) )
<=> ( ( ( k1_relat_1 @ B )
= ( k1_funct_5 @ ( k1_relat_1 @ A ) ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ ( k1_funct_5 @ ( k1_relat_1 @ A ) ) )
& ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( ( k1_funct_1 @ B @ C )
= D )
& ( ( k1_relat_1 @ D )
= ( k2_funct_5 @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k2_funct_5 @ ( k1_relat_1 @ A ) ) ) ) ) )
& ! [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ D ) )
=> ( ( k1_funct_1 @ D @ E )
= ( k1_funct_1 @ A @ ( k4_tarski @ C @ E ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_funct_5) ).
thf(7840,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( ( B
= ( k3_funct_5 @ A ) )
=> ( ( ( k1_relat_1 @ B )
= ( k1_funct_5 @ ( k1_relat_1 @ A ) ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ ( k1_funct_5 @ ( k1_relat_1 @ A ) ) )
& ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( ( k1_funct_1 @ B @ C )
= D )
& ( ( k1_relat_1 @ D )
= ( k2_funct_5 @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k2_funct_5 @ ( k1_relat_1 @ A ) ) ) ) ) )
& ! [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ D ) )
=> ( ( k1_funct_1 @ D @ E )
= ( k1_funct_1 @ A @ ( k4_tarski @ C @ E ) ) ) ) ) ) ) ) )
& ( ( ( ( k1_relat_1 @ B )
= ( k1_funct_5 @ ( k1_relat_1 @ A ) ) )
& ! [C: $i] :
~ ( ( r2_hidden @ C @ ( k1_funct_5 @ ( k1_relat_1 @ A ) ) )
& ! [D: $i] :
( ( ( v1_relat_1 @ D )
& ( v1_funct_1 @ D ) )
=> ~ ( ( ( k1_funct_1 @ B @ C )
= D )
& ( ( k1_relat_1 @ D )
= ( k2_funct_5 @ ( k3_xboole_0 @ ( k1_relat_1 @ A ) @ ( k2_zfmisc_1 @ ( k1_tarski @ C ) @ ( k2_funct_5 @ ( k1_relat_1 @ A ) ) ) ) ) )
& ! [E: $i] :
( ( r2_hidden @ E @ ( k1_relat_1 @ D ) )
=> ( ( k1_funct_1 @ D @ E )
= ( k1_funct_1 @ A @ ( k4_tarski @ C @ E ) ) ) ) ) ) ) )
=> ( B
= ( k3_funct_5 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(2154,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/sandbox2/benchmark/theBenchmark.p',dt_m1_functor0) ).
thf(12685,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)],[2154]) ).
thf(984,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/sandbox2/benchmark/theBenchmark.p',t41_funcop_1) ).
thf(6790,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)],[984]) ).
thf(212,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/sandbox2/benchmark/theBenchmark.p',t4_realset1) ).
thf(3220,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)],[212]) ).
thf(409,axiom,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(4042,plain,
( ( k1_zfmisc_1 @ k1_xboole_0 )
= ( k1_tarski @ k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(110,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/sandbox2/benchmark/theBenchmark.p',t44_finseq_2) ).
thf(2811,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)],[110]) ).
thf(565,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/sandbox2/benchmark/theBenchmark.p',t59_setwiseo) ).
thf(4791,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)],[565]) ).
thf(2269,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) )
& ~ ( v1_tex_2 @ B @ ( k1_zfmisc_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tex_2) ).
thf(13188,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)],[2269]) ).
thf(1290,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/sandbox2/benchmark/theBenchmark.p',t18_card_3) ).
thf(8336,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)],[1290]) ).
thf(1737,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/sandbox2/benchmark/theBenchmark.p',t82_funcop_1) ).
thf(10428,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)],[1737]) ).
thf(1743,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/sandbox2/benchmark/theBenchmark.p',t56_mcart_1) ).
thf(10447,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)],[1743]) ).
thf(1030,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/sandbox2/benchmark/theBenchmark.p',t13_sysrel) ).
thf(7082,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)],[1030]) ).
thf(773,axiom,
! [A: $i] :
( ( k3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k9_setwiseo @ A ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_setwiseo) ).
thf(5756,plain,
! [A: $i] :
( ( k3_binop_1 @ ( k5_finsub_1 @ A ) @ ( k9_setwiseo @ A ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(1156,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_2_domain_1) ).
thf(7638,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)],[1156]) ).
thf(365,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/sandbox2/benchmark/theBenchmark.p',t49_xboole_1) ).
thf(3859,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)],[365]) ).
thf(2255,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/sandbox2/benchmark/theBenchmark.p',t18_yellow_9) ).
thf(13128,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)],[2255]) ).
thf(2183,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/sandbox2/benchmark/theBenchmark.p',t15_cantor_1) ).
thf(12836,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)],[2183]) ).
thf(1041,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 )
<=> ( r5_binop_1 @ A @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_binop_1) ).
thf(7114,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 )
=> ( r5_binop_1 @ A @ C @ B ) )
& ( ( r5_binop_1 @ A @ C @ B )
=> ( r6_binop_1 @ A @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1045,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ( ( k3_pua2mss1 @ A )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_relset_2) ).
thf(7125,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( ( k3_pua2mss1 @ A )
= k1_xboole_0 ) )
& ( ( ( k3_pua2mss1 @ A )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(2092,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/sandbox2/benchmark/theBenchmark.p',t64_domain_1) ).
thf(12387,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)],[2092]) ).
thf(2026,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/sandbox2/benchmark/theBenchmark.p',t48_subset_1) ).
thf(12050,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)],[2026]) ).
thf(1342,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/sandbox2/benchmark/theBenchmark.p',t73_mcart_1) ).
thf(8617,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)],[1342]) ).
thf(2065,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/sandbox2/benchmark/theBenchmark.p',redefinition_k10_domain_1) ).
thf(12268,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)],[2065]) ).
thf(507,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/sandbox2/benchmark/theBenchmark.p',t39_mcart_1) ).
thf(4527,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)],[507]) ).
thf(1878,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( v1_funct_1 @ ( k5_relset_2 @ A @ C ) )
& ( v1_funct_2 @ ( k5_relset_2 @ A @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) )
& ( m2_relset_1 @ ( k5_relset_2 @ A @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relset_2) ).
thf(11187,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( v1_funct_1 @ ( k5_relset_2 @ A @ C ) )
& ( v1_funct_2 @ ( k5_relset_2 @ A @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) )
& ( m2_relset_1 @ ( k5_relset_2 @ A @ C ) @ ( k1_zfmisc_1 @ A ) @ ( k1_zfmisc_1 @ ( k2_relat_1 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1878]) ).
thf(744,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_tarski @ ( k1_tarski @ A ) @ ( k2_tarski @ B @ C ) )
& ( A != B )
& ( A != C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_zfmisc_1) ).
thf(5600,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)],[744]) ).
thf(2216,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/sandbox2/benchmark/theBenchmark.p',t4_waybel20) ).
thf(12976,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)],[2216]) ).
thf(2002,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_xboole_0 @ ( k2_funct_5 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_yellow_3) ).
thf(11918,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_xboole_0 @ ( k2_funct_5 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2002]) ).
thf(1728,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
& ( v1_xboole_0 @ B )
& ( v1_finset_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_setwiseo) ).
thf(10400,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)],[1728]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ D ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_relset_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ D ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ E ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(2394,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( m1_subset_1 @ F @ ( k1_zfmisc_1 @ D ) )
=> ( m1_subset_1 @ ( a_6_0_relset_2 @ A @ B @ C @ D @ E @ F ) @ ( k1_zfmisc_1 @ ( k1_zfmisc_1 @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(788,axiom,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(5828,plain,
! [A: $i] :
( ( k3_xboole_0 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(894,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/sandbox2/benchmark/theBenchmark.p',t2_pre_circ) ).
thf(6305,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)],[894]) ).
thf(648,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/sandbox2/benchmark/theBenchmark.p',t35_funct_4) ).
thf(5162,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)],[648]) ).
thf(860,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/sandbox2/benchmark/theBenchmark.p',t80_funct_4) ).
thf(6181,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)],[860]) ).
thf(1975,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/sandbox2/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(11755,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)],[1975]) ).
thf(1922,axiom,
! [A: $i,B: $i] :
( ( ( v1_finset_1 @ A )
& ( v1_finset_1 @ B ) )
=> ( v1_finset_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(11405,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)],[1922]) ).
thf(749,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/sandbox2/benchmark/theBenchmark.p',t157_funct_1) ).
thf(5672,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)],[749]) ).
thf(1902,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ A @ k1_xboole_0 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_partfun1) ).
thf(11322,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)],[1902]) ).
thf(1468,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/sandbox2/benchmark/theBenchmark.p',t74_funct_3) ).
thf(9162,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)],[1468]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ ( k1_setfam_1 @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_setfam_1) ).
thf(2447,plain,
! [A: $i,B: $i] :
( ( r2_hidden @ A @ B )
=> ( r1_tarski @ ( k1_setfam_1 @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1375,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ ( k2_zfmisc_1 @ A @ A ) )
& ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ A ) ) )
=> ( m1_pboole @ ( k3_altcat_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ A @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_altcat_1) ).
thf(8749,plain,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ ( k2_zfmisc_1 @ A @ A ) )
& ( m1_pboole @ C @ ( k2_zfmisc_1 @ A @ A ) ) )
=> ( m1_pboole @ ( k3_altcat_1 @ A @ B @ C ) @ ( k3_zfmisc_1 @ A @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(939,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k8_relat_1 @ B @ ( k8_relat_1 @ A @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_relat_1) ).
thf(6516,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k8_relat_1 @ B @ ( k8_relat_1 @ A @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(816,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/sandbox2/benchmark/theBenchmark.p',t148_partfun1) ).
thf(5963,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)],[816]) ).
thf(1324,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_ens_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ens_1) ).
thf(8506,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k2_ens_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(1933,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/sandbox2/benchmark/theBenchmark.p',reflexivity_r4_nattra_1) ).
thf(11497,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)],[1933]) ).
thf(1592,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/sandbox2/benchmark/theBenchmark.p',t158_relat_1) ).
thf(9718,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)],[1592]) ).
thf(2197,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/sandbox2/benchmark/theBenchmark.p',t1_qc_lang1) ).
thf(12900,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)],[2197]) ).
thf(2163,axiom,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(12730,plain,
? [A: $i] :
~ ( v1_xboole_0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2163]) ).
thf(102,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( k10_relat_1 @ ( k3_pralg_3 @ A @ B ) @ ( k1_funct_1 @ A @ B ) )
= ( k4_card_3 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_yellow17) ).
thf(2786,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( k10_relat_1 @ ( k3_pralg_3 @ A @ B ) @ ( k1_funct_1 @ A @ B ) )
= ( k4_card_3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1648,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( r1_tarski @ A @ B )
& ( r1_tarski @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(9972,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)],[1648]) ).
thf(1085,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/sandbox2/benchmark/theBenchmark.p',d6_partfun1) ).
thf(7256,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)],[1085]) ).
thf(1318,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/sandbox2/benchmark/theBenchmark.p',t12_setwiseo) ).
thf(8488,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)],[1318]) ).
thf(993,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/sandbox2/benchmark/theBenchmark.p',t69_funcop_1) ).
thf(6854,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)],[993]) ).
thf(2079,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k7_relset_2 @ A @ B @ C @ D )
= ( k8_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relset_2) ).
thf(12338,plain,
! [A: $i,B: $i,C: $i] :
( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ A ) )
=> ! [D: $i] :
( ( m1_subset_1 @ D @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k7_relset_2 @ A @ B @ C @ D )
= ( k8_setfam_1 @ B @ ( k4_relset_2 @ ( k1_zfmisc_1 @ A ) @ B @ ( k6_relset_2 @ B @ A @ D ) @ ( k3_pua2mss1 @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2079]) ).
thf(704,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/sandbox2/benchmark/theBenchmark.p',t51_funcop_1) ).
thf(5408,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)],[704]) ).
thf(1126,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/sandbox2/benchmark/theBenchmark.p',t15_funct_3) ).
thf(7451,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)],[1126]) ).
thf(371,axiom,
! [A: $i,B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( k9_funct_7 @ ( k6_partfun1 @ A ) @ B )
= ( k6_partfun1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_funct_7) ).
thf(3879,plain,
! [A: $i,B: $i] :
( ( m2_subset_1 @ B @ k1_numbers @ k5_numbers )
=> ( ( k9_funct_7 @ ( k6_partfun1 @ A ) @ B )
= ( k6_partfun1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(1644,axiom,
! [A: $i] :
( ( m1_pboole @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_pboole) ).
thf(9962,plain,
! [A: $i] :
( ( m1_pboole @ A @ k1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644]) ).
thf(362,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/sandbox2/benchmark/theBenchmark.p',t5_functor0) ).
thf(3844,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)],[362]) ).
thf(58,axiom,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_funct_1) ).
thf(2648,plain,
? [A: $i] :
( ( v1_relat_1 @ A )
& ( v2_relat_1 @ A )
& ( v1_funct_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1521,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k8_relat_1 @ A @ C ) ) )
<=> ( ( r2_hidden @ B @ ( k1_relat_1 @ C ) )
& ( r2_hidden @ ( k1_funct_1 @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_funct_1) ).
thf(9393,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r2_hidden @ B @ ( k1_relat_1 @ ( k8_relat_1 @ A @ C ) ) )
=> ( ( 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 @ ( k8_relat_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521]) ).
thf(779,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/sandbox2/benchmark/theBenchmark.p',t131_zfmisc_1) ).
thf(5781,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)],[779]) ).
thf(559,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/sandbox2/benchmark/theBenchmark.p',t15_borsuk_1) ).
thf(4774,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)],[559]) ).
thf(627,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).
thf(5040,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(1791,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/sandbox2/benchmark/theBenchmark.p',t9_domain_1) ).
thf(10695,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)],[1791]) ).
thf(1116,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/sandbox2/benchmark/theBenchmark.p',t112_partfun1) ).
thf(7399,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)],[1116]) ).
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] :
( ( k5_relat_1 @ ( k4_funcop_1 @ C @ B @ D ) @ A )
= ( k4_funcop_1 @ ( k5_relat_1 @ C @ A ) @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_funcop_1) ).
thf(3896,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)],[376]) ).
thf(916,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/sandbox2/benchmark/theBenchmark.p',t49_partfun1) ).
thf(6412,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)],[916]) ).
thf(758,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ ( k3_xboole_0 @ B @ C ) @ ( k3_pua2mss1 @ A ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ B @ ( k3_pua2mss1 @ A ) ) @ ( k9_relat_1 @ C @ ( k3_pua2mss1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_relset_2) ).
thf(5699,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k9_relat_1 @ ( k3_xboole_0 @ B @ C ) @ ( k3_pua2mss1 @ A ) ) @ ( k3_xboole_0 @ ( k9_relat_1 @ B @ ( k3_pua2mss1 @ A ) ) @ ( k9_relat_1 @ C @ ( k3_pua2mss1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(2386,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/sandbox2/benchmark/theBenchmark.p',fc4_yellow_3) ).
thf(13642,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)],[2386]) ).
thf(941,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( v1_fraenkel @ ( k1_tarski @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_fraenkel) ).
thf(6521,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( v1_fraenkel @ ( k1_tarski @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(1054,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/sandbox2/benchmark/theBenchmark.p',t16_binop_1) ).
thf(7157,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)],[1054]) ).
thf(885,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_relat_1) ).
thf(6277,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ( r1_tarski @ ( k2_relat_1 @ ( k8_relat_1 @ A @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(734,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/sandbox2/benchmark/theBenchmark.p',t139_partfun1) ).
thf(5549,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)],[734]) ).
thf(1876,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/sandbox2/benchmark/theBenchmark.p',t19_funct_2) ).
thf(11172,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)],[1876]) ).
thf(70,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/sandbox2/benchmark/theBenchmark.p',t3_grcat_1) ).
thf(2680,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)],[70]) ).
thf(1526,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/sandbox2/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
thf(9421,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)],[1526]) ).
thf(1244,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/sandbox2/benchmark/theBenchmark.p',t30_setwiseo) ).
thf(8102,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)],[1244]) ).
thf(1471,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/sandbox2/benchmark/theBenchmark.p',t81_funct_4) ).
thf(9173,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)],[1471]) ).
thf(957,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/sandbox2/benchmark/theBenchmark.p',t164_funct_2) ).
thf(6586,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)],[957]) ).
thf(485,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 ) )
=> ( ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ D ) @ ( k1_relat_1 @ E ) ) @ A )
=> ( ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) )
= ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t93_partfun1) ).
thf(4404,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 ) )
=> ( ( r1_tarski @ ( k3_xboole_0 @ ( k2_relat_1 @ D ) @ ( k1_relat_1 @ E ) ) @ A )
=> ( ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) )
= ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(1018,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(7017,plain,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ B )
= ( k3_xboole_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(1666,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/sandbox2/benchmark/theBenchmark.p',t10_altcat_1) ).
thf(10087,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)],[1666]) ).
thf(1750,axiom,
! [A: $i,B: $i] :
( ( ( v1_funct_1 @ B )
& ( m2_relset_1 @ B @ k1_xboole_0 @ A ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_partfun1) ).
thf(10483,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)],[1750]) ).
thf(795,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_funct_3) ).
thf(5869,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( r1_tarski @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(769,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/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(5739,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)],[769]) ).
thf(644,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/sandbox2/benchmark/theBenchmark.p',dt_k13_funct_3) ).
thf(5144,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)],[644]) ).
thf(2015,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k6_relat_1 @ A )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relset_1) ).
thf(11982,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( ( k6_relat_1 @ A )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2015]) ).
thf(2258,axiom,
! [A: $i,B: $i] :
( ( m1_subset_1 @ B @ ( k5_finsub_1 @ A ) )
=> ( v1_finset_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_finsub_1) ).
thf(13143,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)],[2258]) ).
thf(31,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/sandbox2/benchmark/theBenchmark.p',fc38_membered) ).
thf(2494,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)],[31]) ).
thf(997,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/sandbox2/benchmark/theBenchmark.p',d11_binop_2) ).
thf(6871,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)],[997]) ).
thf(1937,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( r3_relat_2 @ A @ B )
<=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_2) ).
thf(11537,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ! [B: $i] :
( ( ( r3_relat_2 @ A @ B )
=> ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) ) )
& ( ! [C: $i,D: $i] :
( ( ( r2_hidden @ C @ B )
& ( r2_hidden @ D @ B )
& ( r2_hidden @ ( k4_tarski @ C @ D ) @ A ) )
=> ( r2_hidden @ ( k4_tarski @ D @ C ) @ A ) )
=> ( r3_relat_2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1937]) ).
thf(2326,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/sandbox2/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(13389,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)],[2326]) ).
thf(935,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/sandbox2/benchmark/theBenchmark.p',t14_borsuk_1) ).
thf(6499,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)],[935]) ).
thf(404,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/sandbox2/benchmark/theBenchmark.p',t16_funct_2) ).
thf(4025,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)],[404]) ).
thf(691,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/sandbox2/benchmark/theBenchmark.p',t10_metric_1) ).
thf(5336,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)],[691]) ).
thf(1052,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/sandbox2/benchmark/theBenchmark.p',t85_funct_2) ).
thf(7152,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)],[1052]) ).
thf(531,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/sandbox2/benchmark/theBenchmark.p',d2_mcart_1) ).
thf(4619,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)],[531]) ).
thf(1364,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t137_funct_1) ).
thf(8710,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k10_relat_1 @ C @ ( k3_xboole_0 @ A @ B ) )
= ( k3_xboole_0 @ ( k10_relat_1 @ C @ A ) @ ( k10_relat_1 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(1883,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/sandbox2/benchmark/theBenchmark.p',t154_funct_2) ).
thf(11208,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)],[1883]) ).
thf(1527,axiom,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(9427,plain,
! [A: $i,B: $i] :
( ( r1_tarski @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527]) ).
thf(259,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/sandbox2/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(3420,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)],[259]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',t27_finseq_2) ).
thf(2421,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)],[8]) ).
thf(584,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/sandbox2/benchmark/theBenchmark.p',t17_funct_1) ).
thf(4880,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)],[584]) ).
thf(573,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/sandbox2/benchmark/theBenchmark.p',t36_funcop_1) ).
thf(4816,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)],[573]) ).
thf(1199,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( m1_eqrel_1 @ C @ ( k1_relat_1 @ B ) ) )
=> ( ( r2_hidden @ A @ ( a_2_1_pua2mss1 @ B @ C ) )
<=> ? [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) @ C )
& ( A
= ( k7_relat_1 @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_1_pua2mss1) ).
thf(7883,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( v1_xboole_0 @ B )
& ( v1_relat_1 @ B )
& ( v1_funct_1 @ B )
& ( m1_eqrel_1 @ C @ ( k1_relat_1 @ B ) ) )
=> ( ( ( r2_hidden @ A @ ( a_2_1_pua2mss1 @ B @ C ) )
=> ? [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) @ C )
& ( A
= ( k7_relat_1 @ B @ D ) ) ) )
& ( ? [D: $i] :
( ( m2_subset_1 @ D @ ( k1_zfmisc_1 @ ( k1_relat_1 @ B ) ) @ C )
& ( A
= ( k7_relat_1 @ B @ D ) ) )
=> ( r2_hidden @ A @ ( a_2_1_pua2mss1 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(1380,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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_realset1) ).
thf(8769,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)],[1380]) ).
thf(1188,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/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
thf(7787,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)],[1188]) ).
thf(1908,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).
thf(11341,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)],[1908]) ).
thf(905,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/sandbox2/benchmark/theBenchmark.p',t81_funct_3) ).
thf(6366,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)],[905]) ).
thf(1973,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/sandbox2/benchmark/theBenchmark.p',t11_binop_1) ).
thf(11744,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)],[1973]) ).
thf(976,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/sandbox2/benchmark/theBenchmark.p',t25_setwiseo) ).
thf(6703,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)],[976]) ).
thf(1511,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/sandbox2/benchmark/theBenchmark.p',t35_partfun1) ).
thf(9361,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)],[1511]) ).
thf(629,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k10_relat_1 @ C @ A )
= ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) )
& ( r1_tarski @ B @ ( k2_relat_1 @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t161_funct_1) ).
thf(5051,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( ( k10_relat_1 @ C @ A )
= ( k10_relat_1 @ C @ B ) )
& ( r1_tarski @ A @ ( k2_relat_1 @ C ) )
& ( r1_tarski @ B @ ( k2_relat_1 @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(1483,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) )
=> ( ( k10_relat_1 @ B @ ( k3_tarski @ A ) )
= ( k3_tarski @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_3) ).
thf(9239,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r1_tarski @ A @ ( k1_zfmisc_1 @ ( k2_relat_1 @ B ) ) )
=> ( ( k10_relat_1 @ B @ ( k3_tarski @ A ) )
= ( k3_tarski @ ( k10_relat_1 @ ( k1_funct_3 @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483]) ).
thf(2118,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/sandbox2/benchmark/theBenchmark.p',d6_realset1) ).
thf(12498,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)],[2118]) ).
thf(1960,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/sandbox2/benchmark/theBenchmark.p',t7_ens_1) ).
thf(11690,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)],[1960]) ).
thf(2333,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/sandbox2/benchmark/theBenchmark.p',dt_k1_cantor_1) ).
thf(13413,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)],[2333]) ).
thf(71,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/sandbox2/benchmark/theBenchmark.p',t60_funct_1) ).
thf(2683,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)],[71]) ).
thf(566,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/sandbox2/benchmark/theBenchmark.p',t195_orders_1) ).
thf(4794,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)],[566]) ).
thf(898,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/sandbox2/benchmark/theBenchmark.p',t1_closure3) ).
thf(6326,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)],[898]) ).
thf(1220,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(7991,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_funct_2 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(329,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 @ ( k1_fraenkel @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k1_fraenkel @ B @ C ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k1_funct_1 @ ( k1_isocat_2 @ A @ B @ C @ D ) @ ( k4_tarski @ E @ F ) )
= ( k8_funct_2 @ B @ C @ ( k1_cat_2 @ A @ B @ C @ ( k1_fraenkel @ B @ C ) @ D @ E ) @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_isocat_2) ).
thf(3705,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 @ ( k1_fraenkel @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k1_fraenkel @ B @ C ) ) )
=> ! [E: $i] :
( ( m1_subset_1 @ E @ A )
=> ! [F: $i] :
( ( m1_subset_1 @ F @ B )
=> ( ( k1_funct_1 @ ( k1_isocat_2 @ A @ B @ C @ D ) @ ( k4_tarski @ E @ F ) )
= ( k8_funct_2 @ B @ C @ ( k1_cat_2 @ A @ B @ C @ ( k1_fraenkel @ B @ C ) @ D @ E ) @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(483,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/sandbox2/benchmark/theBenchmark.p',t31_mcart_1) ).
thf(4399,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)],[483]) ).
thf(547,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/sandbox2/benchmark/theBenchmark.p',t105_relat_1) ).
thf(4687,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)],[547]) ).
thf(1105,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/sandbox2/benchmark/theBenchmark.p',t90_funct_3) ).
thf(7355,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)],[1105]) ).
thf(1408,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/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(8886,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)],[1408]) ).
thf(542,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/sandbox2/benchmark/theBenchmark.p',t67_funct_2) ).
thf(4670,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)],[542]) ).
thf(2137,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/sandbox2/benchmark/theBenchmark.p',t53_subset_1) ).
thf(12615,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)],[2137]) ).
thf(746,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/sandbox2/benchmark/theBenchmark.p',t64_setwiseo) ).
thf(5606,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)],[746]) ).
thf(1182,axiom,
! [A: $i] :
~ ( ( A != k1_xboole_0 )
& ! [B: $i] :
~ ( ( r2_hidden @ B @ A )
& ( r1_xboole_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_mcart_1) ).
thf(7759,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)],[1182]) ).
thf(1707,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/sandbox2/benchmark/theBenchmark.p',t17_relset_1) ).
thf(10291,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)],[1707]) ).
thf(215,axiom,
! [A: $i] : ( v2_funct_2 @ ( k6_partfun1 @ A ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_functor1) ).
thf(3232,plain,
! [A: $i] : ( v2_funct_2 @ ( k6_partfun1 @ A ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(1788,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/sandbox2/benchmark/theBenchmark.p',rc2_waybel_7) ).
thf(10681,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)],[1788]) ).
thf(825,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/sandbox2/benchmark/theBenchmark.p',t73_funct_4) ).
thf(6007,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)],[825]) ).
thf(1196,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_relat_1) ).
thf(7868,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r1_tarski @ A @ B )
=> ( ( k8_relat_1 @ A @ ( k8_relat_1 @ B @ C ) )
= ( k8_relat_1 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(989,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/sandbox2/benchmark/theBenchmark.p',t4_cat_1) ).
thf(6822,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)],[989]) ).
thf(379,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/sandbox2/benchmark/theBenchmark.p',fc17_finseq_1) ).
thf(3907,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)],[379]) ).
thf(783,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/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
thf(5796,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)],[783]) ).
thf(982,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ B @ ( k8_relat_1 @ A @ C ) ) @ ( k5_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_relat_1) ).
thf(6786,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ B @ ( k8_relat_1 @ A @ C ) ) @ ( k5_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(367,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/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
thf(3865,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)],[367]) ).
thf(79,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/sandbox2/benchmark/theBenchmark.p',t57_classes2) ).
thf(2719,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)],[79]) ).
thf(1799,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/sandbox2/benchmark/theBenchmark.p',t15_subset_1) ).
thf(10733,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)],[1799]) ).
thf(2007,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/sandbox2/benchmark/theBenchmark.p',t47_funcop_1) ).
thf(11928,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)],[2007]) ).
thf(452,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/sandbox2/benchmark/theBenchmark.p',redefinition_k1_relset_2) ).
thf(4254,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)],[452]) ).
thf(1609,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(9823,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1609]) ).
thf(619,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/sandbox2/benchmark/theBenchmark.p',symmetry_r1_filter_2) ).
thf(5004,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)],[619]) ).
thf(2089,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/sandbox2/benchmark/theBenchmark.p',dt_k10_cat_2) ).
thf(12380,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)],[2089]) ).
thf(337,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/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(3733,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)],[337]) ).
thf(301,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/sandbox2/benchmark/theBenchmark.p',dt_m2_finseq_1) ).
thf(3601,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)],[301]) ).
thf(2192,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/sandbox2/benchmark/theBenchmark.p',t53_mcart_1) ).
thf(12876,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)],[2192]) ).
thf(2308,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/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_2) ).
thf(13329,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)],[2308]) ).
thf(372,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 @ ( k1_fraenkel @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k1_fraenkel @ B @ C ) ) )
=> ( r4_nattra_1 @ A @ ( k1_fraenkel @ B @ C ) @ A @ ( k1_fraenkel @ B @ C ) @ ( k2_cat_2 @ A @ B @ C @ ( k1_isocat_2 @ A @ B @ C @ D ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_isocat_2) ).
thf(3882,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 @ ( k1_fraenkel @ B @ C ) )
& ( m2_relset_1 @ D @ A @ ( k1_fraenkel @ B @ C ) ) )
=> ( r4_nattra_1 @ A @ ( k1_fraenkel @ B @ C ) @ A @ ( k1_fraenkel @ B @ C ) @ ( k2_cat_2 @ A @ B @ C @ ( k1_isocat_2 @ A @ B @ C @ D ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(666,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/sandbox2/benchmark/theBenchmark.p',t108_relat_1) ).
thf(5232,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)],[666]) ).
thf(2271,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/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(13192,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)],[2271]) ).
thf(836,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/sandbox2/benchmark/theBenchmark.p',t49_domain_1) ).
thf(6050,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)],[836]) ).
thf(2041,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/sandbox2/benchmark/theBenchmark.p',dt_k7_metric_1) ).
thf(12117,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)],[2041]) ).
thf(1741,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_membered @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_membered) ).
thf(10443,plain,
! [A: $i,B: $i] :
( ( v1_membered @ B )
=> ( ( r1_tarski @ A @ B )
=> ( v1_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1741]) ).
thf(1474,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/sandbox2/benchmark/theBenchmark.p',t162_partfun1) ).
thf(9183,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)],[1474]) ).
thf(698,axiom,
! [A: $i] :
( ( k10_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t172_relat_1) ).
thf(5356,plain,
! [A: $i] :
( ( k10_relat_1 @ k1_xboole_0 @ A )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ ( k1_tarski @ A ) @ ( k1_tarski @ B ) )
= k1_xboole_0 )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(2604,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)],[46]) ).
thf(1734,axiom,
! [A: $i,B: $i,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 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k8_relset_2 @ A @ B @ ( k4_subset_1 @ A @ C @ D ) @ E )
= ( k5_subset_1 @ B @ ( k8_relset_2 @ A @ B @ C @ E ) @ ( k8_relset_2 @ A @ B @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_relset_2) ).
thf(10418,plain,
! [A: $i,B: $i,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 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
=> ( ( k8_relset_2 @ A @ B @ ( k4_subset_1 @ A @ C @ D ) @ E )
= ( k5_subset_1 @ B @ ( k8_relset_2 @ A @ B @ C @ E ) @ ( k8_relset_2 @ A @ B @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( C
= ( k3_partfun1 @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_partfun1) ).
thf(2815,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ ( k1_relat_1 @ C ) @ A )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( C
= ( k3_partfun1 @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(86,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/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(2736,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)],[86]) ).
thf(2383,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/sandbox2/benchmark/theBenchmark.p',s5_filter_1) ).
thf(13624,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)],[2383]) ).
thf(245,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_relat_1 @ A ) @ ( k1_relat_1 @ C ) )
& ( B
= ( k5_relat_1 @ A @ C ) ) )
=> ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_finseq_2) ).
thf(3337,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_relat_1 @ A ) @ ( k1_relat_1 @ C ) )
& ( B
= ( k5_relat_1 @ A @ C ) ) )
=> ( ( k3_finseq_1 @ B )
= ( k3_finseq_1 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(499,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/sandbox2/benchmark/theBenchmark.p',d3_monoid_0) ).
thf(4491,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)],[499]) ).
thf(1504,axiom,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
& ( r2_hidden @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_zfmisc_1) ).
thf(9329,plain,
! [A: $i,B: $i] :
~ ( ( r1_xboole_0 @ ( k1_tarski @ A ) @ B )
& ( r2_hidden @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504]) ).
thf(519,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/sandbox2/benchmark/theBenchmark.p',t27_zfmisc_1) ).
thf(4579,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)],[519]) ).
thf(1072,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/sandbox2/benchmark/theBenchmark.p',d3_funcop_1) ).
thf(7210,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)],[1072]) ).
thf(1638,axiom,
( ( v1_relat_1 @ a_0_0_altcat_2 )
& ( v1_funct_1 @ a_0_0_altcat_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_altcat_2) ).
thf(9944,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)],[1638]) ).
thf(96,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/sandbox2/benchmark/theBenchmark.p',t84_finseq_2) ).
thf(2768,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)],[96]) ).
thf(955,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/sandbox2/benchmark/theBenchmark.p',t151_pboole) ).
thf(6580,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)],[955]) ).
thf(1536,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/sandbox2/benchmark/theBenchmark.p',t23_setwiseo) ).
thf(9463,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)],[1536]) ).
thf(525,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/sandbox2/benchmark/theBenchmark.p',t25_binop_1) ).
thf(4597,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)],[525]) ).
thf(671,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/sandbox2/benchmark/theBenchmark.p',t154_relat_1) ).
thf(5247,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)],[671]) ).
thf(1962,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/sandbox2/benchmark/theBenchmark.p',redefinition_k17_domain_1) ).
thf(11695,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)],[1962]) ).
thf(474,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/sandbox2/benchmark/theBenchmark.p',t53_funct_1) ).
thf(4367,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)],[474]) ).
thf(1941,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/sandbox2/benchmark/theBenchmark.p',s4_funct_2) ).
thf(11563,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)],[1941]) ).
thf(2199,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/sandbox2/benchmark/theBenchmark.p',t56_funct_3) ).
thf(12904,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)],[2199]) ).
thf(944,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k10_relat_1 @ C @ B )
= ( k4_relset_1 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_partfun1) ).
thf(6535,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_funct_1 @ C )
& ( m2_relset_1 @ C @ A @ B ) )
=> ( ( k10_relat_1 @ C @ B )
= ( k4_relset_1 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(1686,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/sandbox2/benchmark/theBenchmark.p',t37_mcart_1) ).
thf(10168,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)],[1686]) ).
thf(1815,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/sandbox2/benchmark/theBenchmark.p',t83_funct_3) ).
thf(10804,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)],[1815]) ).
thf(692,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i] : ( m1_fraenkel @ ( k1_funct_2 @ B @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_fraenkel) ).
thf(5339,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)],[692]) ).
thf(2390,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/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_2) ).
thf(13663,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)],[2390]) ).
thf(738,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/sandbox2/benchmark/theBenchmark.p',t3_pralg_1) ).
thf(5559,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)],[738]) ).
thf(55,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/sandbox2/benchmark/theBenchmark.p',t16_sysrel) ).
thf(2636,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)],[55]) ).
thf(2172,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/sandbox2/benchmark/theBenchmark.p',t66_funcop_1) ).
thf(12766,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)],[2172]) ).
thf(1387,axiom,
! [A: $i] : ( v2_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_setwiseo) ).
thf(8790,plain,
! [A: $i] : ( v2_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k8_relat_1 @ B @ C ) ) )
<=> ( ( r2_hidden @ A @ B )
& ( r2_hidden @ A @ ( k2_relat_1 @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_relat_1) ).
thf(3956,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r2_hidden @ A @ ( k2_relat_1 @ ( k8_relat_1 @ B @ C ) ) )
=> ( ( r2_hidden @ A @ B )
& ( r2_hidden @ A @ ( k2_relat_1 @ C ) ) ) )
& ( ( ( r2_hidden @ A @ B )
& ( r2_hidden @ A @ ( k2_relat_1 @ C ) ) )
=> ( r2_hidden @ A @ ( k2_relat_1 @ ( k8_relat_1 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(1659,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/sandbox2/benchmark/theBenchmark.p',dt_k1_nattra_1) ).
thf(10064,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)],[1659]) ).
thf(242,axiom,
! [A: $i] : ( v1_setwiseo @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_setwiseo) ).
thf(3328,plain,
! [A: $i] : ( v1_setwiseo @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(2251,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/sandbox2/benchmark/theBenchmark.p',s1_funct_7) ).
thf(13101,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)],[2251]) ).
thf(2338,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/sandbox2/benchmark/theBenchmark.p',dt_k2_cat_5) ).
thf(13432,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)],[2338]) ).
thf(553,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/sandbox2/benchmark/theBenchmark.p',t81_funcop_1) ).
thf(4755,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)],[553]) ).
thf(1263,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/sandbox2/benchmark/theBenchmark.p',t55_subset_1) ).
thf(8207,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)],[1263]) ).
thf(891,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/sandbox2/benchmark/theBenchmark.p',t12_lattice2) ).
thf(6294,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)],[891]) ).
thf(1459,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/sandbox2/benchmark/theBenchmark.p',t11_relset_2) ).
thf(9134,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)],[1459]) ).
thf(493,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/sandbox2/benchmark/theBenchmark.p',t90_relat_1) ).
thf(4474,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)],[493]) ).
thf(398,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) )
=> ( r1_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ A ) @ B ) @ ( k9_relat_1 @ ( k1_funct_3 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_3) ).
thf(4007,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) )
=> ( r1_tarski @ ( k10_relat_1 @ ( k3_funct_3 @ A ) @ B ) @ ( k9_relat_1 @ ( k1_funct_3 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(1267,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/sandbox2/benchmark/theBenchmark.p',t24_funcop_1) ).
thf(8241,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)],[1267]) ).
thf(1419,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/sandbox2/benchmark/theBenchmark.p',t3_mcart_1) ).
thf(8921,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)],[1419]) ).
thf(1932,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/sandbox2/benchmark/theBenchmark.p',redefinition_k1_cat_5) ).
thf(11494,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)],[1932]) ).
thf(952,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k9_relat_1 @ A @ B ) ) @ B )
=> ( v2_funct_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_funct_1) ).
thf(6558,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ! [B: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k9_relat_1 @ A @ B ) ) @ B )
=> ( v2_funct_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(1434,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/sandbox2/benchmark/theBenchmark.p',d4_mcart_1) ).
thf(9002,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)],[1434]) ).
thf(1938,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( k4_tarski @ A @ B )
= ( k4_tarski @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(11548,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)],[1938]) ).
thf(2063,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/sandbox2/benchmark/theBenchmark.p',free_g2_quantal1) ).
thf(12252,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)],[2063]) ).
thf(740,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/sandbox2/benchmark/theBenchmark.p',t22_funct_2) ).
thf(5564,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)],[740]) ).
thf(2257,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/sandbox2/benchmark/theBenchmark.p',rc2_triang_1) ).
thf(13139,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)],[2257]) ).
thf(1874,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/sandbox2/benchmark/theBenchmark.p',t4_altcat_1) ).
thf(11162,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)],[1874]) ).
thf(1954,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/sandbox2/benchmark/theBenchmark.p',dt_k36_binop_2) ).
thf(11644,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)],[1954]) ).
thf(1747,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/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(10472,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)],[1747]) ).
thf(741,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/sandbox2/benchmark/theBenchmark.p',dt_k2_setwiseo) ).
thf(5586,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)],[741]) ).
thf(1477,axiom,
! [A: $i] : ( v4_finsub_1 @ ( k5_finsub_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
thf(9215,plain,
! [A: $i] : ( v4_finsub_1 @ ( k5_finsub_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477]) ).
thf(241,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/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
thf(3323,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)],[241]) ).
thf(1090,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( ( r1_tarski @ D @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ C @ A ) )
=> ( ( k7_relat_1 @ D @ C )
= ( k3_xboole_0 @ D @ ( k2_zfmisc_1 @ C @ B ) ) ) )
& ( ( ( r1_tarski @ D @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ C @ B ) )
=> ( ( k8_relat_1 @ C @ D )
= ( k3_xboole_0 @ D @ ( k2_zfmisc_1 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_sysrel) ).
thf(7280,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( v1_relat_1 @ D )
=> ( ( ( ( r1_tarski @ D @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ C @ A ) )
=> ( ( k7_relat_1 @ D @ C )
= ( k3_xboole_0 @ D @ ( k2_zfmisc_1 @ C @ B ) ) ) )
& ( ( ( r1_tarski @ D @ ( k2_zfmisc_1 @ A @ B ) )
& ( r1_tarski @ C @ B ) )
=> ( ( k8_relat_1 @ C @ D )
= ( k3_xboole_0 @ D @ ( k2_zfmisc_1 @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_partfun1) ).
thf(3426,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( ( r1_tarski @ A @ ( k1_relat_1 @ C ) )
& ( r1_tarski @ ( k2_relat_1 @ C ) @ B ) )
=> ( v1_partfun1 @ ( k3_partfun1 @ C @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(626,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( k2_tarski @ A @ B )
= ( k2_tarski @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(5036,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)],[626]) ).
thf(2203,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/sandbox2/benchmark/theBenchmark.p',t67_funcop_1) ).
thf(12919,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)],[2203]) ).
thf(701,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/sandbox2/benchmark/theBenchmark.p',t27_funct_2) ).
thf(5378,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)],[701]) ).
thf(2078,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/sandbox2/benchmark/theBenchmark.p',t2_realset1) ).
thf(12335,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)],[2078]) ).
thf(406,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( m1_fraenkel @ ( k1_fraenkel @ A @ B ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_fraenkel) ).
thf(4034,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ( m1_fraenkel @ ( k1_fraenkel @ A @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(1604,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/sandbox2/benchmark/theBenchmark.p',t23_binop_1) ).
thf(9795,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)],[1604]) ).
thf(340,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/sandbox2/benchmark/theBenchmark.p',d2_setwiseo) ).
thf(3765,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)],[340]) ).
thf(2159,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/sandbox2/benchmark/theBenchmark.p',rc3_tex_2) ).
thf(12707,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)],[2159]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k3_funct_3 @ B ) ) )
=> ( ( k1_funct_1 @ ( k3_funct_3 @ B ) @ A )
= ( k10_relat_1 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_funct_3) ).
thf(2795,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ A @ ( k1_relat_1 @ ( k3_funct_3 @ B ) ) )
=> ( ( k1_funct_1 @ ( k3_funct_3 @ B ) @ A )
= ( k10_relat_1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(311,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( m2_fraenkel @ D @ B @ A @ ( k1_fraenkel @ B @ A ) )
=> ( ( k7_relat_1 @ D @ C )
= ( k7_relat_1 @ D @ ( k3_xboole_0 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_fraenkel) ).
thf(3633,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( m2_fraenkel @ D @ B @ A @ ( k1_fraenkel @ B @ A ) )
=> ( ( k7_relat_1 @ D @ C )
= ( k7_relat_1 @ D @ ( k3_xboole_0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(2042,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/sandbox2/benchmark/theBenchmark.p',t31_finset_1) ).
thf(12121,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)],[2042]) ).
thf(963,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_funct_2 @ A @ k1_xboole_0 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_funct_2) ).
thf(6612,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)],[963]) ).
thf(1611,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/sandbox2/benchmark/theBenchmark.p',d3_zfmisc_1) ).
thf(9827,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)],[1611]) ).
thf(834,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/sandbox2/benchmark/theBenchmark.p',t14_card_fil) ).
thf(6040,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)],[834]) ).
thf(1497,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/sandbox2/benchmark/theBenchmark.p',t161_relat_1) ).
thf(9293,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)],[1497]) ).
thf(1092,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/sandbox2/benchmark/theBenchmark.p',t59_zfmisc_1) ).
thf(7291,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)],[1092]) ).
thf(1599,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/sandbox2/benchmark/theBenchmark.p',t55_relat_1) ).
thf(9742,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)],[1599]) ).
thf(652,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/sandbox2/benchmark/theBenchmark.p',t20_functor0) ).
thf(5176,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)],[652]) ).
thf(1718,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/sandbox2/benchmark/theBenchmark.p',t110_zfmisc_1) ).
thf(10355,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)],[1718]) ).
thf(1651,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/sandbox2/benchmark/theBenchmark.p',t1_closure2) ).
thf(9987,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)],[1651]) ).
thf(2324,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/sandbox2/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(13377,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)],[2324]) ).
thf(1517,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/sandbox2/benchmark/theBenchmark.p',fc6_finset_1) ).
thf(9382,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)],[1517]) ).
thf(101,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/sandbox2/benchmark/theBenchmark.p',t6_realset1) ).
thf(2783,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)],[101]) ).
thf(1864,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/sandbox2/benchmark/theBenchmark.p',t162_funct_1) ).
thf(11114,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)],[1864]) ).
thf(464,axiom,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ ( k8_relat_1 @ A @ B ) @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_relat_1) ).
thf(4318,plain,
! [A: $i,B: $i] :
( ( v1_relat_1 @ B )
=> ! [C: $i] :
( ( v1_relat_1 @ C )
=> ( r1_tarski @ ( k5_relat_1 @ ( k8_relat_1 @ A @ B ) @ C ) @ ( k5_relat_1 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(1897,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/sandbox2/benchmark/theBenchmark.p',dt_k2_yellow_3) ).
thf(11290,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)],[1897]) ).
thf(1189,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/sandbox2/benchmark/theBenchmark.p',t37_card_3) ).
thf(7819,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)],[1189]) ).
thf(882,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_orders_1) ).
thf(6269,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ~ ( v1_xboole_0 @ ( k1_orders_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(936,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/sandbox2/benchmark/theBenchmark.p',t7_lattice2) ).
thf(6503,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)],[936]) ).
thf(1409,axiom,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(8889,plain,
! [A: $i] :
~ ( v1_xboole_0 @ ( k1_tarski @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409]) ).
thf(426,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/sandbox2/benchmark/theBenchmark.p',t44_funct_1) ).
thf(4118,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)],[426]) ).
thf(632,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/sandbox2/benchmark/theBenchmark.p',t20_funct_5) ).
thf(5061,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)],[632]) ).
thf(1712,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_1_yellow_9) ).
thf(10308,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)],[1712]) ).
thf(948,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/sandbox2/benchmark/theBenchmark.p',t3_isocat_2) ).
thf(6548,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)],[948]) ).
thf(1283,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/sandbox2/benchmark/theBenchmark.p',t33_borsuk_1) ).
thf(8305,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)],[1283]) ).
thf(1931,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/sandbox2/benchmark/theBenchmark.p',t8_realset1) ).
thf(11489,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)],[1931]) ).
thf(1532,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/sandbox2/benchmark/theBenchmark.p',t15_finseq_1) ).
thf(9441,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)],[1532]) ).
thf(2290,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/sandbox2/benchmark/theBenchmark.p',dt_k3_relset_2) ).
thf(13262,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)],[2290]) ).
thf(677,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/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
thf(5275,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)],[677]) ).
thf(1996,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/sandbox2/benchmark/theBenchmark.p',t6_mssubfam) ).
thf(11886,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)],[1996]) ).
thf(2095,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/sandbox2/benchmark/theBenchmark.p',t60_partfun1) ).
thf(12395,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)],[2095]) ).
thf(1357,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/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_3) ).
thf(8692,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)],[1357]) ).
thf(1838,axiom,
! [A: $i] :
? [B: $i] :
( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k5_finsub_1 @ A ) ) )
& ~ ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_triang_1) ).
thf(10966,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)],[1838]) ).
thf(812,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/sandbox2/benchmark/theBenchmark.p',t14_binop_1) ).
thf(5945,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)],[812]) ).
thf(863,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/sandbox2/benchmark/theBenchmark.p',t22_relat_1) ).
thf(6190,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)],[863]) ).
thf(729,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/sandbox2/benchmark/theBenchmark.p',t12_sysrel) ).
thf(5500,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)],[729]) ).
thf(2101,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/sandbox2/benchmark/theBenchmark.p',t8_mssubfam) ).
thf(12420,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)],[2101]) ).
thf(2372,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/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(13599,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)],[2372]) ).
thf(852,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/sandbox2/benchmark/theBenchmark.p',t9_functor0) ).
thf(6136,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)],[852]) ).
thf(1265,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/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(8213,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)],[1265]) ).
thf(158,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/sandbox2/benchmark/theBenchmark.p',dt_k2_card_fil) ).
thf(3025,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)],[158]) ).
thf(1735,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/sandbox2/benchmark/theBenchmark.p',dt_k35_binop_2) ).
thf(10421,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)],[1735]) ).
thf(2106,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/sandbox2/benchmark/theBenchmark.p',t18_cantor_1) ).
thf(12435,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)],[2106]) ).
thf(289,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/sandbox2/benchmark/theBenchmark.p',t27_sysrel) ).
thf(3543,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)],[289]) ).
thf(1818,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/sandbox2/benchmark/theBenchmark.p',redefinition_r4_nattra_1) ).
thf(10836,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)],[1818]) ).
thf(1442,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/sandbox2/benchmark/theBenchmark.p',t18_funcop_1) ).
thf(9038,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)],[1442]) ).
thf(165,axiom,
! [A: $i] :
( ( k1_setfam_1 @ ( k1_tarski @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_setfam_1) ).
thf(3057,plain,
! [A: $i] :
( ( k1_setfam_1 @ ( k1_tarski @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(859,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/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
thf(6155,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)],[859]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( m2_finseq_1 @ D @ A )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( C
= ( k1_partfun1 @ k5_numbers @ A @ A @ B @ D @ E ) )
=> ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_finseq_2) ).
thf(2803,plain,
! [A: $i,B: $i] :
( ~ ( v1_xboole_0 @ B )
=> ! [C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C )
& ( v1_finseq_1 @ C ) )
=> ! [D: $i] :
( ( m2_finseq_1 @ D @ A )
=> ! [E: $i] :
( ( ( v1_funct_1 @ E )
& ( v1_funct_2 @ E @ A @ B )
& ( m2_relset_1 @ E @ A @ B ) )
=> ( ( C
= ( k1_partfun1 @ k5_numbers @ A @ A @ B @ D @ E ) )
=> ( ( k3_finseq_1 @ C )
= ( k3_finseq_1 @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(1584,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/sandbox2/benchmark/theBenchmark.p',t6_relset_1) ).
thf(9679,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)],[1584]) ).
thf(899,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/sandbox2/benchmark/theBenchmark.p',t1_pralg_3) ).
thf(6329,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)],[899]) ).
thf(1075,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( r1_xboole_0 @ ( k2_tarski @ A @ B ) @ C )
& ( r2_hidden @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_zfmisc_1) ).
thf(7227,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)],[1075]) ).
thf(1947,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/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).
thf(11621,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)],[1947]) ).
thf(119,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/sandbox2/benchmark/theBenchmark.p',commutativity_k5_setwiseo) ).
thf(2847,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)],[119]) ).
thf(2126,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/sandbox2/benchmark/theBenchmark.p',t7_multop_1) ).
thf(12530,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)],[2126]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( k3_partfun1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_partfun1) ).
thf(3605,plain,
! [A: $i,B: $i] :
( ( k3_partfun1 @ k1_xboole_0 @ A @ B )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(609,axiom,
! [A: $i] :
( ( k8_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_relat_1) ).
thf(4972,plain,
! [A: $i] :
( ( k8_relat_1 @ A @ k1_xboole_0 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(1437,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( m1_pboole @ B @ A )
& ( m1_pboole @ C @ A ) )
=> ( r6_pboole @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r6_pboole) ).
thf(9023,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)],[1437]) ).
thf(2373,axiom,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(13601,plain,
! [A: $i] : ( m1_subset_1 @ ( k2_subset_1 @ A ) @ ( k1_zfmisc_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2373]) ).
thf(1967,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/sandbox2/benchmark/theBenchmark.p',t120_funct_2) ).
thf(11707,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)],[1967]) ).
thf(2010,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(11958,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)],[2010]) ).
thf(928,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/sandbox2/benchmark/theBenchmark.p',t19_closure2) ).
thf(6473,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)],[928]) ).
thf(1626,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/sandbox2/benchmark/theBenchmark.p',t5_closure2) ).
thf(9895,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)],[1626]) ).
thf(38,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/sandbox2/benchmark/theBenchmark.p',dt_k11_binop_2) ).
thf(2583,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)],[38]) ).
thf(1192,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/sandbox2/benchmark/theBenchmark.p',t19_funcop_1) ).
thf(7829,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)],[1192]) ).
thf(1533,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/sandbox2/benchmark/theBenchmark.p',t1_filter_2) ).
thf(9446,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)],[1533]) ).
thf(1151,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/sandbox2/benchmark/theBenchmark.p',t21_funct_3) ).
thf(7616,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)],[1151]) ).
thf(393,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/sandbox2/benchmark/theBenchmark.p',t79_funct_4) ).
thf(3965,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)],[393]) ).
thf(1369,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/sandbox2/benchmark/theBenchmark.p',fc29_membered) ).
thf(8730,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)],[1369]) ).
thf(2223,axiom,
! [A: $i,B: $i] :
( ( v1_finset_1 @ ( k2_zfmisc_1 @ B @ A ) )
=> ( ( A = k1_xboole_0 )
| ( v1_finset_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_finset_1) ).
thf(12997,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)],[2223]) ).
thf(1108,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/sandbox2/benchmark/theBenchmark.p',t42_mcart_1) ).
thf(7370,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)],[1108]) ).
thf(844,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/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).
thf(6082,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)],[844]) ).
thf(539,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/sandbox2/benchmark/theBenchmark.p',t72_partfun1) ).
thf(4659,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)],[539]) ).
thf(287,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/sandbox2/benchmark/theBenchmark.p',t50_xboole_1) ).
thf(3538,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)],[287]) ).
thf(1825,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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(10877,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)],[1825]) ).
thf(1740,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/sandbox2/benchmark/theBenchmark.p',t16_borsuk_1) ).
thf(10440,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)],[1740]) ).
thf(1032,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/sandbox2/benchmark/theBenchmark.p',t86_funct_3) ).
thf(7088,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)],[1032]) ).
thf(2295,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/sandbox2/benchmark/theBenchmark.p',s3_subset_1) ).
thf(13279,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)],[2295]) ).
thf(664,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r1_tarski @ A @ B )
& ( r1_xboole_0 @ B @ C ) )
=> ( r1_xboole_0 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(5219,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)],[664]) ).
thf(1258,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/sandbox2/benchmark/theBenchmark.p',t98_zfmisc_1) ).
thf(8189,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)],[1258]) ).
thf(386,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/sandbox2/benchmark/theBenchmark.p',t29_funct_4) ).
thf(3939,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)],[386]) ).
thf(1250,axiom,
! [A: $i,B: $i,C: $i] :
( ( k4_enumset1 @ A @ A @ A @ A @ B @ C )
= ( k1_enumset1 @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t84_enumset1) ).
thf(8147,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)],[1250]) ).
thf(2261,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/sandbox2/benchmark/theBenchmark.p',dt_k12_mcart_1) ).
thf(13161,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)],[2261]) ).
thf(170,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/sandbox2/benchmark/theBenchmark.p',t58_funct_1) ).
thf(3076,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)],[170]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i] :
( ( m1_fraenkel @ C @ A @ B )
=> ( ~ ( v1_xboole_0 @ C )
& ( v1_fraenkel @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
thf(6778,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(1917,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/sandbox2/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(11373,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)],[1917]) ).
thf(1399,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/sandbox2/benchmark/theBenchmark.p',t67_xboole_1) ).
thf(8857,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)],[1399]) ).
thf(1845,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/sandbox2/benchmark/theBenchmark.p',t4_waybel18) ).
thf(11021,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)],[1845]) ).
thf(246,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/sandbox2/benchmark/theBenchmark.p',t25_finseq_3) ).
thf(3341,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)],[246]) ).
thf(543,axiom,
! [A: $i,B: $i,C: $i] :
( ( k1_enumset1 @ A @ B @ C )
= ( k1_enumset1 @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_enumset1) ).
thf(4674,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)],[543]) ).
thf(1900,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/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
thf(11298,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)],[1900]) ).
thf(624,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( r1_tarski @ ( k2_funct_4 @ ( k2_funct_4 @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_4) ).
thf(5029,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)],[624]) ).
thf(1361,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/sandbox2/benchmark/theBenchmark.p',redefinition_k6_funcop_1) ).
thf(8702,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)],[1361]) ).
thf(2141,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/sandbox2/benchmark/theBenchmark.p',t4_filter_2) ).
thf(12637,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)],[2141]) ).
thf(240,axiom,
! [A: $i,B: $i] :
( ( ( k4_xboole_0 @ A @ ( k1_tarski @ B ) )
= A )
<=> ~ ( r2_hidden @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(3316,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)],[240]) ).
thf(1093,axiom,
! [A: $i,B: $i] :
( ( k3_xboole_0 @ A @ ( k3_tarski @ B ) )
= ( k3_tarski @ ( k3_setfam_1 @ ( k1_tarski @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_setfam_1) ).
thf(7295,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)],[1093]) ).
thf(509,axiom,
! [A: $i] :
( ~ ( ~ ( r1_xboole_0 @ A @ A )
& ( A = k1_xboole_0 ) )
& ~ ( ( A != k1_xboole_0 )
& ( r1_xboole_0 @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_xboole_1) ).
thf(4533,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)],[509]) ).
thf(2166,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/sandbox2/benchmark/theBenchmark.p',redefinition_k1_metric_1) ).
thf(12749,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)],[2166]) ).
thf(390,axiom,
r1_tarski @ k5_numbers @ k1_numbers,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_numbers) ).
thf(3960,plain,
r1_tarski @ k5_numbers @ k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(2359,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/sandbox2/benchmark/theBenchmark.p',s2_subset_1) ).
thf(13524,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)],[2359]) ).
thf(1066,axiom,
! [A: $i,B: $i] :
( ( k3_setfam_1 @ A @ B )
= ( k3_setfam_1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_setfam_1) ).
thf(7195,plain,
! [A: $i,B: $i] :
( ( k3_setfam_1 @ A @ B )
= ( k3_setfam_1 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(1202,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/sandbox2/benchmark/theBenchmark.p',d7_binop_1) ).
thf(7900,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)],[1202]) ).
thf(1725,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/sandbox2/benchmark/theBenchmark.p',dt_k4_card_fil) ).
thf(10389,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)],[1725]) ).
thf(651,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( v2_funct_1 @ A )
<=> ! [B: $i] :
? [C: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_1) ).
thf(5172,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ( ( v2_funct_1 @ A )
=> ! [B: $i] :
? [C: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) ) )
& ( ! [B: $i] :
? [C: $i] : ( r1_tarski @ ( k10_relat_1 @ A @ ( k1_tarski @ B ) ) @ ( k1_tarski @ C ) )
=> ( v2_funct_1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(1256,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/sandbox2/benchmark/theBenchmark.p',t59_funct_4) ).
thf(8184,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)],[1256]) ).
thf(283,axiom,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( r2_wellord2 @ ( k2_finseq_1 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_finseq_1) ).
thf(3528,plain,
! [A: $i] :
( ( m2_subset_1 @ A @ k1_numbers @ k5_numbers )
=> ( r2_wellord2 @ ( k2_finseq_1 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(91,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 ) )
=> ( m2_fraenkel @ ( k1_cat_2 @ A @ B @ C @ D @ E @ F ) @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_cat_2) ).
thf(2754,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 ) )
=> ( m2_fraenkel @ ( k1_cat_2 @ A @ B @ C @ D @ E @ F ) @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(892,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( v2_funct_1 @ A )
=> ( r1_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ A ) @ B ) @ ( k10_relat_1 @ ( k3_funct_3 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_funct_3) ).
thf(6297,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( v2_funct_1 @ A )
=> ( r1_tarski @ ( k9_relat_1 @ ( k1_funct_3 @ A ) @ B ) @ ( k10_relat_1 @ ( k3_funct_3 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',dt_k4_closure2) ).
thf(2672,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)],[66]) ).
thf(534,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v2_funct_1 @ A )
& ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( ( k10_relat_1 @ ( k3_funct_3 @ A ) @ B )
= ( k9_relat_1 @ ( k1_funct_3 @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_funct_3) ).
thf(4642,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( ( v2_funct_1 @ A )
& ( r1_tarski @ B @ ( k1_zfmisc_1 @ ( k1_relat_1 @ A ) ) ) )
=> ( ( k10_relat_1 @ ( k3_funct_3 @ A ) @ B )
= ( k9_relat_1 @ ( k1_funct_3 @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(214,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/sandbox2/benchmark/theBenchmark.p',t42_sysrel) ).
thf(3227,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)],[214]) ).
thf(1423,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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_3) ).
thf(8940,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)],[1423]) ).
thf(1745,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_card_fil) ).
thf(10460,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)],[1745]) ).
thf(1689,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/sandbox2/benchmark/theBenchmark.p',t10_ens_1) ).
thf(10187,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)],[1689]) ).
thf(384,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/sandbox2/benchmark/theBenchmark.p',t156_funct_1) ).
thf(3924,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)],[384]) ).
thf(2020,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/sandbox2/benchmark/theBenchmark.p',fraenkel_a_3_2_domain_1) ).
thf(12017,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)],[2020]) ).
thf(1760,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/sandbox2/benchmark/theBenchmark.p',t10_mssubfam) ).
thf(10522,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)],[1760]) ).
thf(1268,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/sandbox2/benchmark/theBenchmark.p',t32_funcop_1) ).
thf(8245,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)],[1268]) ).
thf(1887,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/sandbox2/benchmark/theBenchmark.p',t38_funct_4) ).
thf(11251,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)],[1887]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ C @ ( k4_xboole_0 @ B @ ( k10_relat_1 @ C @ A ) ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_setwiseo) ).
thf(3299,plain,
! [A: $i,B: $i,C: $i] :
( ( ( v1_relat_1 @ C )
& ( v1_funct_1 @ C ) )
=> ( ( k9_relat_1 @ C @ ( k4_xboole_0 @ B @ ( k10_relat_1 @ C @ A ) ) )
= ( k4_xboole_0 @ ( k9_relat_1 @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1553,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/sandbox2/benchmark/theBenchmark.p',redefinition_k3_cat_5) ).
thf(9536,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)],[1553]) ).
thf(1176,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/sandbox2/benchmark/theBenchmark.p',t60_funct_4) ).
thf(7723,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)],[1176]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( k1_card_fil @ A @ B )
= ( k4_xboole_0 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_card_fil) ).
thf(3096,plain,
! [A: $i,B: $i] :
( ( k1_card_fil @ A @ B )
= ( k4_xboole_0 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(364,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/sandbox2/benchmark/theBenchmark.p',t8_funct_5) ).
thf(3854,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)],[364]) ).
thf(130,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ~ ( r2_hidden @ k1_xboole_0 @ ( k2_relat_1 @ A ) )
=> ( ( v2_funct_1 @ ( k7_funct_6 @ A ) )
<=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
=> ( v2_funct_1 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_6) ).
thf(2887,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ( ~ ( r2_hidden @ k1_xboole_0 @ ( k2_relat_1 @ A ) )
=> ( ( ( v2_funct_1 @ ( k7_funct_6 @ A ) )
=> ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
=> ( v2_funct_1 @ B ) ) ) )
& ( ! [B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( r2_hidden @ B @ ( k2_relat_1 @ A ) )
=> ( v2_funct_1 @ B ) ) )
=> ( v2_funct_1 @ ( k7_funct_6 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(603,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/sandbox2/benchmark/theBenchmark.p',fc1_functor0) ).
thf(4949,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)],[603]) ).
thf(557,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/sandbox2/benchmark/theBenchmark.p',t28_setwiseo) ).
thf(4767,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)],[557]) ).
thf(1025,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/sandbox2/benchmark/theBenchmark.p',t46_funcop_1) ).
thf(7056,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)],[1025]) ).
thf(1491,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/sandbox2/benchmark/theBenchmark.p',t62_funct_4) ).
thf(9267,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)],[1491]) ).
thf(855,axiom,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r7_relat_2 @ C @ A )
& ( r1_tarski @ B @ A ) )
=> ( r7_relat_2 @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t96_orders_1) ).
thf(6145,plain,
! [A: $i,B: $i,C: $i] :
( ( v1_relat_1 @ C )
=> ( ( ( r7_relat_2 @ C @ A )
& ( r1_tarski @ B @ A ) )
=> ( r7_relat_2 @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(2115,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/sandbox2/benchmark/theBenchmark.p',d1_card_fil) ).
thf(12471,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)],[2115]) ).
thf(1372,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/sandbox2/benchmark/theBenchmark.p',fc4_card_3) ).
thf(8741,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)],[1372]) ).
thf(2016,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/sandbox2/benchmark/theBenchmark.p',t11_tops_2) ).
thf(11985,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)],[2016]) ).
thf(2351,axiom,
m1_subset_1 @ k3_qc_lang1 @ ( k1_zfmisc_1 @ k1_qc_lang1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_qc_lang1) ).
thf(13493,plain,
m1_subset_1 @ k3_qc_lang1 @ ( k1_zfmisc_1 @ k1_qc_lang1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2351]) ).
thf(436,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/sandbox2/benchmark/theBenchmark.p',t14_realset1) ).
thf(4161,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)],[436]) ).
thf(780,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/sandbox2/benchmark/theBenchmark.p',t58_funct_4) ).
thf(5788,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)],[780]) ).
thf(713,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/sandbox2/benchmark/theBenchmark.p',redefinition_k4_setwiseo) ).
thf(5436,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)],[713]) ).
thf(512,axiom,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( ( k4_card_3 @ A )
= k1_xboole_0 )
| ( ( k2_relat_1 @ ( k3_pralg_3 @ A @ B ) )
= ( k1_funct_1 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_yellow17) ).
thf(4547,plain,
! [A: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A ) )
=> ! [B: $i] :
( ( r2_hidden @ B @ ( k1_relat_1 @ A ) )
=> ( ( ( k4_card_3 @ A )
= k1_xboole_0 )
| ( ( k2_relat_1 @ ( k3_pralg_3 @ A @ B ) )
= ( k1_funct_1 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(1782,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/sandbox2/benchmark/theBenchmark.p',free_g3_quantal1) ).
thf(10654,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)],[1782]) ).
thf(1341,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/sandbox2/benchmark/theBenchmark.p',t4_mcart_1) ).
thf(8611,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)],[1341]) ).
thf(2076,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/sandbox2/benchmark/theBenchmark.p',t4_closure2) ).
thf(12331,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)],[2076]) ).
thf(1224,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( v2_funct_1 @ ( k8_relat_1 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_funct_1) ).
thf(8006,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ B )
& ( v1_funct_1 @ B ) )
=> ( ( v2_funct_1 @ B )
=> ( v2_funct_1 @ ( k8_relat_1 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(994,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( ( v1_xboole_0 @ ( k2_relat_1 @ A ) )
& ( v1_relat_1 @ ( k2_relat_1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(6857,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)],[994]) ).
thf(1275,axiom,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k10_relat_1 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc18_finseq_1) ).
thf(8273,plain,
! [A: $i,B: $i] :
( ( ( v1_relat_1 @ A )
& ( v1_funct_1 @ A )
& ( v1_finset_1 @ A ) )
=> ( v1_finset_1 @ ( k10_relat_1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(716,axiom,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( m1_card_fil @ ( k1_tarski @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_card_fil) ).
thf(5445,plain,
! [A: $i] :
( ~ ( v1_xboole_0 @ A )
=> ( m1_card_fil @ ( k1_tarski @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(1541,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/sandbox2/benchmark/theBenchmark.p',t3_waybel20) ).
thf(9479,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)],[1541]) ).
thf(263,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 ) )
=> ( r1_tarski @ ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) ) @ ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_partfun1) ).
thf(3432,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 ) )
=> ( r1_tarski @ ( k1_partfun1 @ C @ A @ A @ B @ ( k3_partfun1 @ D @ C @ A ) @ ( k3_partfun1 @ E @ A @ B ) ) @ ( k3_partfun1 @ ( k5_relat_1 @ D @ E ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(1853,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/sandbox2/benchmark/theBenchmark.p',t50_funct_4) ).
thf(11048,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)],[1853]) ).
thf(49,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/sandbox2/benchmark/theBenchmark.p',t106_xboole_1) ).
thf(2615,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)],[49]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( v1_finset_1 @ ( k3_enumset1 @ A @ B @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_finset_1) ).
thf(4908,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)],[592]) ).
thf(2300,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/sandbox2/benchmark/theBenchmark.p',t49_subset_1) ).
thf(13306,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)],[2300]) ).
thf(414,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/sandbox2/benchmark/theBenchmark.p',t34_funcop_1) ).
thf(4056,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)],[414]) ).
thf(832,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/sandbox2/benchmark/theBenchmark.p',t2_tex_2) ).
thf(6035,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)],[832]) ).
thf(206,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/sandbox2/benchmark/theBenchmark.p',t31_finseq_2) ).
thf(3200,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)],[206]) ).
thf(881,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/sandbox2/benchmark/theBenchmark.p',t69_funct_3) ).
thf(6265,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)],[881]) ).
thf(1685,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/sandbox2/benchmark/theBenchmark.p',t63_funct_4) ).
thf(10161,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)],[1685]) ).
thf(2301,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/sandbox2/benchmark/theBenchmark.p',dt_k16_domain_1) ).
thf(13311,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)],[2301]) ).
thf(2111,axiom,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_xboole_0 @ ( k1_funct_5 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_yellow_3) ).
thf(12456,plain,
! [A: $i] :
( ( v1_xboole_0 @ A )
=> ( v1_xboole_0 @ ( k1_funct_5 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2111]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(2470,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)],[25]) ).
thf(1428,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/sandbox2/benchmark/theBenchmark.p',t20_funct_4) ).
thf(8961,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)],[1428]) ).
thf(1955,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/sandbox2/benchmark/theBenchmark.p',t50_relat_1) ).
thf(11648,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)],[1955]) ).
thf(1935,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/sandbox2/benchmark/theBenchmark.p',rc8_finseq_1) ).
thf(11529,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)],[1935]) ).
thf(807,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/sandbox2/benchmark/theBenchmark.p',t11_yellow_9) ).
thf(5911,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)],[807]) ).
thf(1000,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/sandbox2/benchmark/theBenchmark.p',t38_relset_1) ).
thf(6886,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)],[1000]) ).
thf(1311,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/sandbox2/benchmark/theBenchmark.p',t41_setwiseo) ).
thf(8465,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)],[1311]) ).
thf(1668,axiom,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(10096,plain,
! [A: $i,B: $i] :
~ ( ( v1_xboole_0 @ A )
& ( A != B )
& ( v1_xboole_0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1668]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( r2_wellord2 @ A @ B )
& ( r2_wellord2 @ B @ C ) )
=> ( r2_wellord2 @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_wellord2) ).
thf(2655,plain,
! [A: $i,B: $i,C: $i] :
( ( ( r2_wellord2 @ A @ B )
& ( r2_wellord2 @ B @ C ) )
=> ( r2_wellord2 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(396,axiom,
! [A: $i] : ( v1_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_setwiseo) ).
thf(4002,plain,
! [A: $i] : ( v1_binop_1 @ ( k9_setwiseo @ A ) @ ( k5_finsub_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(1549,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/sandbox2/benchmark/theBenchmark.p',free_g2_vectsp_1) ).
thf(9519,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)],[1549]) ).
thf(321,axiom,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k4_relat_1 @ ( k4_relat_1 @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(3669,plain,
! [A: $i] :
( ( v1_relat_1 @ A )
=> ( ( k4_relat_1 @ ( k4_relat_1 @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(13745,plain,
$false,
inference(cvc4,[status(thm)],[5469,5918,10577,11922,5320,10134,9864,9032,9929,8062,7304,13052,13266,4188,7373,4201,2452,10609,13321,6387,8186,5116,10410,6405,2744,12710,12607,10259,10373,7890,9653,9886,4571,3053,12721,10177,5896,2778,13402,11895,7445,3434,7922,8514,4183,10730,3698,11164,9731,4852,8784,9685,11752,5676,2595,2499,12148,9076,8266,5205,10081,6819,6121,3449,12383,6555,10319,5733,9965,7285,7396,10901,4376,2622,7958,9704,5669,10039,8366,6214,11008,10844,6142,9342,12458,3185,12575,11352,12674,10299,9573,13244,7358,4500,13520,10431,4339,13110,6868,5696,8797,3762,12666,6883,13341,5292,10542,12376,12299,3417,9456,10277,11409,6199,9324,4391,3460,4807,6798,8695,2676,10562,13283,12774,7253,13424,3108,7198,3012,12221,5405,11266,4326,12789,3498,7182,8943,8563,7341,5348,9152,13212,6480,4592,9950,4105,5425,3530,9212,8298,8204,3794,4633,3120,11112,11848,13219,9127,2607,9233,8150,7405,10772,3135,3942,10093,7556,9052,2740,10881,6359,3044,5288,8913,11058,7824,8915,6127,8057,7096,8353,3446,12097,8667,8490,8519,9565,2933,9813,10138,5701,10511,6851,7467,10209,8370,5713,2476,12398,5674,2459,8210,13113,3414,6551,3481,10726,2901,7871,3313,12165,8650,8881,11055,9433,13145,9246,4980,13056,5192,9672,2575,6236,3236,4266,13251,3777,13287,8699,12062,5024,10351,11684,6138,4047,12447,3103,3545,2723,11335,12929,5977,2432,2491,8086,8898,12833,11834,8325,3502,13516,10908,12763,9735,5195,7136,13392,9159,8239,3308,4124,7240,6904,5825,8866,12960,11024,9708,5301,4198,8705,2400,10530,6483,13223,12785,5269,12324,6291,4610,13346,10153,3688,7311,10633,2869,12879,2957,12718,6208,5836,7386,9960,12351,3248,5953,13191,5765,3263,13313,10955,10286,7620,10121,9989,4524,9287,7914,11976,5306,4896,6242,11844,7262,12943,8967,7696,9410,3275,8494,2698,8996,6538,3131,8875,3116,2667,7401,10997,13429,4151,10751,10486,3046,11913,5759,9084,6095,10053,9332,3495,9693,12046,4761,5188,2708,2501,11966,4654,2444,4334,8951,3148,6506,8787,4778,9552,6968,3125,12993,12065,11200,4130,8654,4275,3410,3280,9909,10010,13170,10337,4023,2488,2897,9668,6332,6662,9805,6519,9230,13067,11628,6130,2703,12693,2713,6781,11741,9475,8257,8907,7835,7997,6010,3099,8054,3374,7711,6681,6470,9612,4788,8389,6455,2403,4617,11264,6396,4194,10516,13226,10110,6149,9155,10891,8571,4664,8717,5604,9843,9941,8468,11247,5397,3919,7436,3657,12864,11991,2730,5746,13489,3835,3708,5727,8632,13044,4471,5493,8738,6382,3268,12517,12782,10764,8870,7733,7236,6364,3788,4595,2456,9636,12347,3887,4733,3973,5311,6259,9854,4988,6002,9298,4396,13195,7268,8284,10641,5892,12924,10746,13166,4903,12069,7564,7423,4018,4857,7300,7245,7969,3295,11500,11926,9071,13647,2893,5333,4820,6523,7104,11154,7775,8929,7376,4847,5680,6187,6300,4050,12296,10757,10085,8065,11398,6841,12703,12276,3093,4115,10378,8759,7139,12582,8479,4783,3771,4810,12888,11036,12981,11632,11325,8575,2483,4825,2750,3389,8050,6591,12504,5929,10404,12678,2437,7036,10670,9897,5353,10145,8727,2618,2833,3189,10303,4842,8774,5210,9970,9255,6110,9167,3505,13479,7336,13668,5772,3808,11806,9140,11413,12315,7909,4307,8347,7954,10784,13072,5343,12249,5169,9035,13397,10895,8459,3243,2809,7213,4038,9368,9236,11270,10574,11954,8892,2965,11596,4519,11143,11367,4379,9007,5819,9923,7688,9272,7460,11357,5970,6860,2884,13248,4483,9584,7230,3510,4065,9738,13494,13231,8508,9720,5157,8927,10506,6684,12333,12927,6250,9209,5562,11456,4576,10216,5298,9026,6282,8751,9997,7657,11159,9472,9917,3899,8999,11555,13337,11897,6560,4893,4323,7782,7179,13228,4962,8640,6020,4407,2473,9308,13017,13019,8375,5411,7725,8078,4480,6047,13038,6064,5167,11820,13426,4370,4910,12565,12985,5540,4031,9688,12127,2660,4059,10477,9041,2905,12169,6442,4999,11202,9384,13644,9881,11698,11292,12110,6124,12970,8608,10612,12687,8081,6496,6509,13547,7730,6652,13260,4915,12437,9722,12385,6343,6079,2601,3711,2733,13002,6247,5002,8476,5794,12664,8756,12700,6773,6528,13186,13572,7994,5266,8582,12190,3022,5455,11865,8724,5366,8910,9849,13443,4204,3884,7984,13078,9745,3664,8878,11191,13094,11371,13583,12037,4021,13622,12058,5843,6582,12525,8746,4044,5924,9217,4192,10490,11152,5690,9539,9626,11284,6090,3282,9264,5769,10721,3271,8810,2464,2758,8255,13034,3618,4585,8270,7185,4725,8145,8386,2663,2826,6445,13568,10116,5021,5460,9758,4553,13070,3718,13359,5341,9301,5551,10794,3144,4402,6392,8964,5201,6402,12095,6666,11624,8287,13411,9868,3647,12991,4080,4680,13269,13063,3799,5066,8155,5221,2946,10791,12506,7481,12372,11234,5313,12760,6795,8895,12645,8462,13463,3784,3782,3909,9493,8446,12987,12769,6324,4957,8068,8314,7142,3831,13587,13222,13297,5006,7205,5238,5423,3862,6477,4486,4544,8319,7838,4845,5428,8014,10335,3963,8884,2726,11435,2631,13163,7593,10445,10434,5889,9063,10398,4883,11089,5081,8800,13074,4012,3916,13344,8662,2638,7222,4109,13084,8815,3205,5497,5951,12974,3060,3176,4263,13434,8105,12906,8687,7604,3194,11097,4180,9530,8792,7101,4320,2798,7091,3311,10107,8835,7189,5031,10946,4582,8864,12449,3179,7631,12967,4983,9397,7054,11364,7453,9662,3407,7717,8251,7629,7111,9387,5992,5791,3714,9714,8008,12746,12885,4750,9609,10798,11642,9878,9477,4513,5588,5213,8499,6256,7930,4648,3428,10539,7059,13184,7577,3723,3643,5905,6541,3555,7313,6275,6271,12622,7448,3573,2781,4530,11432,12859,5481,7966,9893,2505,6239,12641,4804,13081,11023,3611,7609,3654,13415,7927,13597,12393,3541,13366,6033,7463,2836,12218,7014,12429,13607,9498,6788,7169,10904,13483,12004,2581,10158,11888,6211,10518,5058,11184,5776,7385,7027,5683,12838,13277,13451,13316,9144,3628,7614,6450,6005,12946,6908,6465,2862,2766,9846,8090,11261,10550,11610,6784,13591,10513,9900,7826,6152,4689,5026,7333,2756,11000,3162,7174,10252,3215,9068,12138,10651,5711,13404,11407,5833,8279,12553,4004,4995,4550,10143,3454,12902,9534,4148,6409,7020,10802,13507,3802,9081,13436,2926,7770,9468,12305,7407,10614,3587,3183,6486,12889,9436,3173,10689,12442,6279,6647,5447,9104,2440,6891,2793,11065,8378,5417,4036,2645,12823,5909,3841,5295,9137,5249,5840,7106,2423,13326,11414,9985,7133,8708,6922,12238,11705,8195,11148,5715,7160,12628,4921,6901,9107,9484,12106,8164,6053,11692,12857,13264,9352,11033,13603,10175,6615,4613,3871,5359,2585,12233,10202,3890,9939,8713,7010,3491,13135,7155,4412,13466,11332,2941,10079,6578,7753,9181,10289,7031,13372,7491,3289,4503,10274,11063,7920,6546,6228,3111,11561,4365,11011,13031,3396,11920,5241,8807,3343,3158,2970,11836,2789,13060,10480,12541,6606,3213,3536,4786,7611,12028,7709,3372,10068,10425,3187,11682,10155,7714,4268,3070,10194,3636,3234,2859,2938,8762,13368,6881,3240,9602,2657,7233,9733,8470,11703,3081,3945,4926,4677,3266,2674,8684,5831,9295,10700,10100,12862,8697,4465,12840,4605,5099,8777,12909,7704,13363,8332,5097,8167,2398,4328,7963,2716,4381,5271,5350,4590,4975,9339,3404,3868,4758,5799,9820,4946,9952,13685,11714,12964,3599,13319,8656,11237,10596,3091,9967,9390,8381,4251,13197,3796,5185,13633,4127,7191,6385,11846,13217,7270,4645,8152,12067,10083,12053,11060,8841,13497,8629,3695,8566,3330,3208,5331,9178,2935,3002,13380,4822,10348,8359,8624,7109,13621,4573,5086,11924,11968,4764,7094,7924,5190,5207,8344,9555,9496,7465,7455,3579,4854,8497,3641,9354,11765,3302,4887,7394,12509,11038,7746,6016,12867,9439,6061,10565,6340,6604,4388,8042,12032,9560,10842,2721,13609,10370,8276,6059,11686,4929,10532,8088,7933,3631,11002,6308,3251,9349,11127,11117,3815,9592,5506,6920,3238,5244,7077,2415,11932,10204,9377,9903,4305,7907,8970,10677,6147,2774,6217,12034,3683,4828,3779,7607,5303,7438,10898,11735,12413,5901,12354,3106,5880,11355,9920,5054,11268,2669,8047,12263,4139,12656,9570,2943,13005,11338,7265,13334,4073,12791,13221,3197,8485,10296,4667,10766,8937,8502,6184,13348,5972,8794,9491,11438,11979,2871,4509,6460,7307,4477,12369,7238,12246,8958,4009,5439,4985,12755,13518,2461,11078,5552,2824,10645,5511,8735,8605,9857,8192,4541,10957,2610,3027,7119,12114,5730,5894,12433,4462,13323,3073,11893,9830,6989,9642,9691,3165,10778,9487,13653,11569,9280,2593,3451,7778,7654,5318,8372,12562,11640,8782,10412,9905,8473,11814,12587,9528,11767,7250,9074,10380,6553,9101,11761,4684,13486,5838,9327,2578,12680,8084,12556,5042,11607,10707,9150,2770,12092,10147,2418,4933,12460,6589,13593,5742,9751,11348,9619,13630,13000,5442,12432,8456,6687,5216,6609,3759,3838,7479,8573,11041,5094,3423,11262,10852,12135,11701,12672,10782,10076,13339,13666,9841,9249,6288,12358,11380,9371,7960,3674,3016,10407,4918,9366,11605,9871,11130,12409,2633,7200,3142,4954,2967,7366,12178,4196,7339,3512,12341,5693,13613,13214,5495,4890,13208,3876,4965,7458,11535,10499,11361,4158,9582,2867,10226,12192,8689,7172,9958,8954,6977,7117,3576,10920,4052,8637,13117,7070,5463,10456,4331,3009,9097,4207,3444,12207,2952,13371,4394,9170,12941,6417,9227,4260,6225,7650,10269,7681,9563,9259,2652,9430,7298,8804,3672,9826,9646,3146,7897,2449,9408,6056,10132,4177,2629,9639,4566,7679,6076,10829,7420,7122,2597,10788,11391,3292,11795,11758,13027,4812,6973,4336,11626,5414,10672,5822,8143,13477,5871,4272,12271,8598,3659,3129,3786,9631,11738,7600,5452,8593,8003,7085,12487,10196,7166,8772,12502,7635,11327,10685,6453,5927,5514,3507,9253,6399,13047,12313,11808,10856,12390,12056,12648,3904,6826,13285,5074,10553,10667,2678,10704,12772,5721,8904,12873,4287,2821,9005,8350,4630,8364,8295,3608,8813,13496,2850,9270,10392,11988,13229,8744,12659,11650,12514,12752,11257,3769,13172,7672,3019,2747,4409,10820,10915,4522,5262,8060,5235,8396,11823,12937,5431,10504,9991,8111,12071,4092,4905,5420,11842,7494,2454,3305,4190,3691,3114,3273,3334,3791,7693,9065,6037,9599,9649,7243,13617,5753,11295,5555,3202,9518,10861,10211,9550,2429,12733,7662,5948,7149,13149,8917,9815,12202,6966,12405,3774,10365,5152,8391,8327,7583,8248,2903,11198,2599,9413,3847,4800,3623,3412,6994,12163,10846,12983,3041,5106,4802,3652,7207,11830,4488,9983,5685,8108,5717,5596,6793,12424,13545,5147,6457,10129,6650,6701,3488,12328,7876,13461,13570,10536,4959,2838,3970,5736,6899,10023,2426,4133,13585,7580,10293,6775,5998,5613,13605,10415,7067,7391,13175,2711,9947,4991,6193,8317,8602,7163,9242,3224,2728,7202,3961,5472,9274,5083,6245,12402,3156,2807,9374,13076,8861,7720,3007,10769,7690,7488,4257,13595,10674,4111,6975,12829,6220,6420,7676,3401,10526,8579,5068,2865,8681,2875,3168,12145,2435,10712,2760,10261,6286,13036,2924,13012,7659,4278,3584,3139,11862,3620,5873,7146,3457,11123,3589,13406,12360,2818,3067,11393,4770,12467,9665,10114,13087,2696,9628,7904,11789,6013,2960,4944,4656,3533,5966,6390,12633,10199,3548,7765,4780,3928,4185,6980,12495,3625,3725,5907,6674,10637,4102,10376,11044,13615,2919,4170,9078,5485,4730,3039,8075,3593,12302,4913,6322,12662,8292,6023,9459,11259,12758,2591,3465,9755,11076,7034,3729,4121,12544,3911,11732,12157,12915,9147,13364,2853,4615,3825,11319,6489,6689,7344,4089,8011,4468,13333,8584,8197,9029,10969,10468,7840,12685,6790,3220,4042,2811,4791,13188,8336,10428,10447,7082,5756,7638,3859,13128,12836,7114,7125,12387,12050,8617,12268,4527,11187,5600,12976,11918,10400,2394,5828,6305,5162,6181,11755,11405,5672,11322,9162,2447,8749,6516,5963,8506,11497,9718,12900,12730,2786,9972,7256,8488,6854,12338,5408,7451,3879,9962,3844,2648,9393,5781,4774,5040,10695,7399,3896,6412,5699,13642,6521,7157,6277,5549,11172,2680,9421,8102,9173,6586,4404,7017,10087,10483,5869,5739,5144,11982,13143,2494,6871,11537,13389,6499,4025,5336,7152,4619,8710,11208,9427,3420,2421,4880,4816,7883,8769,7787,11341,6366,11744,6703,9361,5051,9239,12498,11690,13413,2683,4794,6326,7991,3705,4399,4687,7355,8886,4670,12615,5606,7759,10291,3232,10681,6007,7868,6822,3907,5796,6786,3865,2719,10733,11928,4254,9823,5004,12380,3733,3601,12876,13329,3882,5232,13192,6050,12117,10443,9183,5356,2604,10418,2815,2736,13624,3337,4491,9329,4579,7210,9944,2768,6580,9463,4597,5247,11695,4367,11563,12904,6535,10168,10804,5339,13663,5559,2636,12766,8790,3956,10064,3328,13101,13432,4755,8207,6294,9134,4474,4007,8241,8921,11494,6558,9002,11548,12252,5564,13139,11162,11644,10472,5586,9215,3323,7280,3426,5036,12919,5378,12335,4034,9795,3765,12707,2795,3633,12121,6612,9827,6040,9293,7291,9742,5176,10355,9987,13377,9382,2783,11114,4318,11290,7819,6269,6503,8889,4118,5061,10308,6548,8305,11489,9441,13262,5275,11886,12395,8692,10966,5945,6190,5500,12420,13599,6136,8213,3025,10421,12435,3543,10836,9038,3057,6155,2803,9679,6329,7227,11621,2847,12530,3605,4972,9023,13601,11707,11958,6473,9895,2583,7829,9446,7616,3965,8730,12997,7370,6082,4659,3538,10877,10440,7088,13279,5219,8189,3939,8147,13161,3076,6778,11373,8857,11021,3341,4674,11298,5029,8702,12637,3316,7295,4533,12749,3960,13524,7195,7900,10389,5172,8184,3528,2754,6297,2672,4642,3227,8940,10460,10187,3924,12017,10522,8245,11251,3299,9536,7723,3096,3854,2887,4949,4767,7056,9267,6145,12471,8741,11985,13493,4161,5788,5436,4547,10654,8611,12331,8006,6857,8273,5445,9479,3432,11048,2615,4908,13306,4056,6035,3200,6265,10161,13311,12456,2470,8961,11648,11529,5911,6886,8465,10096,2655,4002,9519,3669]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU435+3 : TPTP v8.1.2. Released v3.4.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 13:25:08 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 4.16/1.92 % [INFO] Parsing done (1067ms).
% 4.29/1.93 % [INFO] Running in sequential loop mode.
% 4.70/2.12 % [INFO] eprover registered as external prover.
% 4.70/2.12 % [INFO] cvc4 registered as external prover.
% 4.70/2.13 % [INFO] Scanning for conjecture ...
% 7.10/2.94 % [INFO] Found a conjecture and 19108 axioms. Running axiom selection ...
% 12.03/5.37 % [INFO] Axiom selection finished. Selected 2391 axioms (removed 16717 axioms).
% 14.78/6.36 % [INFO] Problem is first-order (TPTP FOF).
% 15.00/6.42 % [INFO] Type checking passed.
% 15.00/6.42 % [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 ...
% 59.08/20.22 % External prover 'cvc4' found a proof!
% 59.08/20.22 % [INFO] Killing All external provers ...
% 59.08/20.22 % Time passed: 19706ms (effective reasoning time: 18290ms)
% 59.08/20.22 % 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)>
% 59.08/20.23 % Axioms used in derivation (2391): rc2_setfam_1, t119_funct_2, t106_xboole_1, t15_finset_1, t158_relat_1, t1_filter_2, t34_funct_3, s1_altcat_2, t63_mcart_1, fraenkel_a_4_2_domain_1, t189_relat_1, t86_partfun1, t60_funct_4, d5_monoid_0, t62_partfun1, redefinition_k2_card_fil, t23_funct_2, t75_finseq_1, rc2_lopclset, t38_funct_4, t28_funct_3, t75_funct_3, fraenkel_a_0_0_altcat_2, dt_m2_pua2mss1, dt_k1_funct_3, dt_k15_domain_1, t34_subset_1, t39_funct_5, t39_relset_1, t75_enumset1, t34_sysrel, t14_realset1, d1_enumset1, t1_yellow17, t76_funct_3, t10_funct_7, free_g2_quantal1, redefinition_m2_relset_1, t56_funct_3, fraenkel_a_1_0_domain_1, t51_partfun1, t87_funct_1, cc1_pre_circ, t5_fraenkel, t32_funcop_1, t92_enumset1, t21_zfmisc_1, t84_finseq_2, fc2_altcat_1, t30_funct_2, existence_m1_triang_1, t55_funcop_1, t10_lattice2, t13_relset_1, t70_setwiseo, t181_relat_1, t38_funcop_1, t4_functor0, t19_yellow_9, t131_partfun1, redefinition_k1_functor0, redefinition_k1_oppcat_1, dt_k2_borsuk_1, t4_grcat_1, t48_funcop_1, fraenkel_a_4_0_pua2mss1, t36_funcop_1, t177_relat_1, fraenkel_a_3_2_domain_1, redefinition_k1_metric_1, t177_orders_1, t4_cantor_1, dt_k11_binop_2, fc1_zfmisc_1, d4_funct_1, t45_setwiseo, t53_subset_1, t14_finseq_2, free_g1_group_1, t1_altcat_2, t19_xboole_1, t99_relat_1, t12_borsuk_1, s2_filter_1, t17_xboole_1, t90_relat_1, t4_funct_4, t42_subset_1, t55_mcart_1, t30_setwiseo, t43_subset_1, t86_funct_1, commutativity_k3_setwiseo, t15_setwiseo, d1_funcsdom, t14_cantor_1, cc2_finset_1, t7_multop_1, t20_zfmisc_1, t36_funct_3, 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, dt_k3_cantor_1, s1_setwiseo, t8_altcat_1, t14_fraenkel, t25_relset_1, d3_mcart_1, t148_funct_1, d20_binop_1, t66_funct_2, t143_funct_1, t57_classes2, t11_yellow_9, t67_relat_1, t18_finsub_1, t66_partfun1, t147_funct_1, t15_card_4, t4_closure2, dt_k9_funct_3, t5_relset_2, t154_relat_1, t53_setwiseo, t60_funcop_1, t64_card_1, t49_setfam_1, t13_funct_3, t70_funct_2, t6_setfam_1, t35_funct_2, cc2_tex_2, t15_finseq_1, t1_funct_4, t63_funcop_1, t38_mcart_1, dt_k8_funcop_1, redefinition_k8_relset_2, s1_yellow_3, dt_k4_relset_1, dt_k9_domain_1, dt_k1_cat_2, d14_binop_1, dt_k5_relset_1, d5_relat_1, t9_wellord1, redefinition_k6_funct_3, t49_setwiseo, redefinition_k12_mcart_1, d9_setfam_1, t1_closure3, t109_xboole_1, idempotence_k3_xboole_0, t5_ens_1, t77_partfun1, t67_funcop_1, d1_funct_5, rc4_finset_1, d10_binop_1, t57_funcop_1, t47_relset_1, t13_sysrel, t161_funct_2, t62_relat_1, t7_subset_1, t84_mcart_1, t32_funct_2, d11_binop_1, t2_realset1, t3_lattice5, rc3_triang_1, t66_xboole_1, t95_partfun1, t27_relset_2, 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, redefinition_k19_pralg_1, t85_mcart_1, t195_orders_1, t29_mcart_1, redefinition_k5_subset_1, t16_yellow_9, t20_funct_2, fraenkel_a_1_1_ens_1, t9_setfam_1, dt_k7_setwiseo, t3_xboole_1, t3_realset1, t137_funct_1, d3_subset_1, t40_funct_5, t12_pua2mss1, dt_m1_functor0, t183_relat_1, t98_relat_1, t18_funcop_1, t42_sysrel, t8_subset_1, t156_funct_1, t4_ordinal1, t45_funcop_1, fc1_functor0, cc1_setfam_1, fc1_xboole_0, t6_ens_1, t97_funct_3, t10_tops_2, t1_pboole, t5_borsuk_1, t25_funct_1, t16_funct_2, t73_funct_4, t113_zfmisc_1, t140_partfun1, t187_orders_1, idempotence_k5_setwiseo, t32_relset_2, t7_lattice2, t27_setwiseo, t116_partfun1, t48_domain_1, t92_funct_3, t4_altcat_1, t34_xboole_1, 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, d1_lattice2, dt_m1_triang_1, t68_card_1, t81_partfun1, t56_partfun1, d4_urysohn1, involutiveness_k8_binop_2, t38_funct_1, t62_classes2, t53_funct_2, t29_borsuk_1, d5_tarski, t13_funct_7, t29_funct_3, rc1_borsuk_1, t6_funct_4, t83_mcart_1, t15_funct_1, dt_k11_domain_1, fc4_relat_1, d12_relat_1, t37_funct_4, t139_funct_1, t1_group_6, t39_funct_3, t59_partfun1, s12_funct_2, t53_funcop_1, t158_funct_1, t44_relat_1, fc4_funct_1, t1_subset, s3_filter_1, t66_funct_6, s3_funct_2, t74_finseq_1, fraenkel_a_1_0_lattice5, redefinition_k7_funct_2, t70_funct_6, t147_relat_1, t10_partfun1, t158_partfun1, t10_mssubfam, t54_partfun1, t10_relset_1, t30_filter_1, d5_xboole_0, dt_k7_relset_1, t32_mcart_1, t29_subset_1, dt_k2_card_fil, t151_funct_1, t52_zfmisc_1, t144_relat_1, t57_domain_1, t33_setwiseo, t9_lattice2, fc4_subset_1, t71_funct_1, t22_funct_1, fc3_realset1, free_g3_vectsp_1, t9_borsuk_1, t79_funcop_1, fc1_numbers, dt_k3_funct_2, t74_funct_2, t168_funct_2, fraenkel_a_8_0_domain_1, dt_k2_funcsdom, t16_fraenkel, d6_altcat_1, t52_funct_4, fraenkel_a_0_0_pre_circ, t25_filter_1, fc3_functor0, t7_funct_2, t135_partfun1, t55_domain_1, t146_funct_2, fc3_setfam_1, t10_funcop_1, t18_xboole_1, t17_yellow_9, t42_setwiseo, t4_funcop_1, d17_mcart_1, dt_k35_binop_2, d5_relat_2, redefinition_k1_funcsdom, cc4_yellow21, t3_mcart_1, t155_funct_1, t78_funct_3, s23_fraenkel, t16_setwiseo, fc3_relat_1, redefinition_k2_multop_1, t42_zfmisc_1, t18_cantor_1, t85_funct_1, t14_binop_1, dt_k1_subset_1, t69_funct_3, t117_partfun1, t13_funcop_1, t19_zfmisc_1, d8_funct_1, idempotence_k1_relset_2, dt_k5_urysohn1, t19_relat_1, t28_binop_1, d4_zfmisc_1, dt_k13_domain_1, t33_mcart_1, dt_k2_urysohn1, t31_setwiseo, t166_funct_2, t117_relat_1, dt_k2_funct_4, t2_card_fil, dt_m1_nat_lat, d9_monoid_0, t11_realset1, t73_funcop_1, t64_domain_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, t61_card_1, t35_relset_2, t2_boole, dt_m1_filter_1, t35_zfmisc_1, t93_enumset1, t27_wellord2, t12_relset_2, d5_setfam_1, t28_funcop_1, t5_funct_3, t1_funcop_1, t11_pua2mss1, t82_relat_1, 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, d2_funct_3, involutiveness_k2_card_fil, t117_funct_1, t26_funct_5, t1_qc_lang1, dt_k4_subset_1, t6_altcat_2, 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, t139_relat_1, t98_funct_3, fc6_funcop_1, dt_m1_realset1, t110_zfmisc_1, t65_classes2, fc3_card_3, t3_pralg_1, t24_relset_2, dt_k19_pralg_1, t34_relset_2, t9_pre_circ, t55_funct_4, redefinition_k3_pre_circ, fraenkel_a_1_2_domain_1, dt_k1_funct_7, rc2_partfun1, t18_relat_1, cc1_fraenkel, t5_card_fil, t27_finseq_2, t162_partfun1, dt_m3_pboole, t95_enumset1, t103_zfmisc_1, t1_pua2mss1, fraenkel_a_0_0_yellow_3, fc1_urysohn1, t63_partfun1, t153_funct_1, t95_zfmisc_1, t96_partfun1, t63_setwiseo, t91_finseq_2, t78_funcop_1, t15_relset_1, redefinition_k3_setwiseo, t20_funct_3, t19_funct_3, t18_funct_3, t29_numbers, t99_zfmisc_1, t15_fraenkel, 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, rc3_finseq_1, t7_orders_1, t171_relat_1, 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, rc1_finseq_1, dt_k6_partfun1, t86_funct_6, t57_funct_4, t123_relat_1, t50_funct_2, t63_domain_1, t75_funct_4, dt_m2_filter_1, rc4_triang_1, t70_zfmisc_1, t39_relat_1, dt_k3_metric_1, t69_zfmisc_1, t25_setwiseo, t84_funct_1, t39_setwiseo, t10_metric_1, d7_partfun1, t4_multop_1, dt_k14_domain_1, t29_relset_2, t56_relat_1, rc2_classes2, t93_funct_3, t41_relat_1, t27_zfmisc_1, t37_xboole_1, t26_funct_2, t17_funct_1, d1_card_fil, t82_funct_1, t59_subset_1, t41_zfmisc_1, fc2_functor0, dt_m2_relset_1, t10_borsuk_1, t9_mssubfam, t18_finset_1, t37_card_3, cc1_relat_1, fc9_funcop_1, t7_yellow17, dt_k5_funct_5, t6_card_fil, t26_wellord2, t1_funct_3, dt_k7_funct_2, t131_zfmisc_1, d4_monoid_0, redefinition_k2_funct_2, t11_funct_6, fc3_ens_1, t12_funct_5, idempotence_k5_subset_1, t2_funct_1, t36_subset_1, fc8_finset_1, t16_funct_5, redefinition_k6_setfam_1, t45_yellow20, t102_relat_1, t1_waybel10, t42_yellow_9, commutativity_k3_xboole_0, t154_funct_1, t29_partfun1, t31_relset_1, t176_partfun1, t12_binop_1, fc2_pboole, t62_funct_2, t55_funct_1, dt_k2_realset1, t6_relset_2, t70_partfun1, t3_funcop_1, fc28_membered, t138_funct_1, t3_setfam_1, t130_funct_2, t152_funct_2, t80_funcop_1, t25_relset_2, rc1_funct_1, d1_relset_2, t150_pboole, redefinition_m1_triang_1, t64_funct_2, t4_setwiseo, t80_funct_3, 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, t65_funct_2, fc30_membered, t19_funct_1, t56_setwiseo, free_g2_lattices, fc11_finset_1, dt_k14_mcart_1, t5_tex_2, s13_funct_2, t30_funct_5, dt_k8_relset_2, fraenkel_a_2_0_domain_1, t23_funct_7, t13_funct_4, d2_tarski, t24_funct_2, t29_finset_1, t42_funct_5, existence_m2_fraenkel, dt_k2_binop_1, t127_relat_1, t137_zfmisc_1, fraenkel_a_2_2_domain_1, t129_zfmisc_1, d4_subset_1, t2_binop_1, t30_funcop_1, fc6_funct_1, t30_relset_2, t86_xboole_1, involutiveness_k3_subset_1, t99_funct_1, t89_xboole_1, redefinition_k14_domain_1, t83_funcop_1, t17_binop_1, d1_fraenkel, t25_funct_2, t87_partfun1, t11_finseq_2, dt_k3_pralg_3, t97_finseq_2, t15_binop_1, t26_finseq_1, dt_m2_realset1, t9_funct_3, t32_subset_1, t168_relat_1, d6_binop_1, t85_funct_6, t22_funcop_1, t29_funct_5, t76_partfun1, dt_k32_binop_2, dt_k3_setwiseo, t44_card_1, d2_funcop_1, t112_relat_1, dt_k10_funcop_1, t31_finset_1, t175_partfun1, t21_funct_4, t15_relat_1, t41_setwiseo, t19_relset_2, t154_funct_2, t48_funct_2, t173_relat_1, fraenkel_a_3_7_domain_1, t12_funct_4, t49_mcart_1, t172_relat_1, t27_relat_1, t58_mcart_1, t156_funct_2, t18_funct_5, t78_funct_4, d1_yellow_3, 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, d4_cantor_1, t34_partfun1, s4_filter_1, redefinition_k1_nattra_1, t14_card_fil, t40_funct_1, redefinition_k8_funcop_1, t2_mssubfam, d2_tex_2, t29_setwiseo, t80_enumset1, t3_mssubfam, t2_zfrefle1, t15_toler_1, dt_k5_funcsdom, t3_waybel20, t64_relat_1, t138_zfmisc_1, t59_funct_5, rc6_finseq_1, t25_subset_1, t74_enumset1, t133_relat_1, d5_urysohn1, t96_funct_3, t16_pua2mss1, t12_functor0, t30_finset_1, d5_funcop_1, redefinition_k2_cat_2, fraenkel_a_2_0_card_fil, t23_funct_1, t130_zfmisc_1, t3_filter_2, t20_functor0, t46_funct_2, t36_mcart_1, cc1_tex_2, t108_zfmisc_1, t96_relat_1, t2_pua2mss1, t28_funct_4, t165_funct_2, t32_funct_3, t75_funct_2, t60_partfun1, t6_closure2, d13_relat_1, t56_zfmisc_1, t47_funct_2, t27_relset_1, t52_domain_1, t40_setwiseo, t15_funcop_1, t79_funct_3, t11_pre_circ, t52_relset_1, 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, t1_cat_2, fc10_finset_1, t37_funct_3, t56_funct_4, fraenkel_a_2_0_cantor_1, t118_funct_2, fc2_setfam_1, 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, t92_finseq_2, t53_relset_1, d6_enumset1, t30_sysrel, t6_mcart_1, s1_funct_7, d3_enumset1, t31_partfun1, t37_partfun1, dt_k2_relset_2, t171_partfun1, t164_funct_2, fc2_funct_2, t6_boole, t12_funct_1, t10_funct_3, t4_orders_1, t67_setwiseo, t3_funct_2, t18_subset_1, dt_k1_functor0, rc2_subset_1, t1_closure2, fc1_cantor_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, t59_setfam_1, d1_relat_1, t24_finsub_1, existence_m2_pua2mss1, dt_k3_relset_2, t37_setwiseo, t185_partfun1, t9_cantor_1, d3_funct_5, t20_funct_1, t5_functor0, fc1_fraenkel, t116_relat_1, t75_xboole_1, dt_k6_pralg_1, s17_fraenkel, redefinition_k13_mcart_1, t131_relat_1, t57_mcart_1, t1_xboole_1, redefinition_k4_relset_2, redefinition_m1_nat_lat, t15_yellow_9, t37_finseq_2, t26_relset_1, t72_relat_1, t66_funct_5, dt_k1_funct_4, t27_funct_3, t122_relat_1, d3_realset1, t64_partfun1, fc3_cantor_1, t52_relat_1, t35_funcop_1, t136_relat_1, t77_funct_2, t59_domain_1, free_g1_pre_topc, t82_finseq_2, t12_sysrel, rc2_waybel_7, dt_k4_card_fil, t104_relat_1, t28_wellord2, t39_funcop_1, t60_card_1, t55_relat_1, t32_relset_1, t68_partfun1, t17_domain_1, t7_setfam_1, dt_k10_binop_2, t59_setwiseo, t4_setfam_1, t32_partfun1, t73_relat_1, redefinition_k4_funct_2, t83_partfun1, t4_relat_1, t46_card_1, t28_subset_1, t26_binop_1, fc5_funcop_1, t21_finset_1, t160_funct_1, t44_finseq_2, t28_relset_2, dt_k10_setwiseo, t34_funct_4, dt_k3_urysohn1, t15_domain_1, t79_partfun1, fc3_subset_1, t128_zfmisc_1, t39_partfun1, t149_funct_1, t5_altcat_1, t5_subset, symmetry_r4_nattra_1, t94_zfmisc_1, t7_mssubfam, fraenkel_a_0_32_fraenkel, t20_finseq_1, t45_funct_2, t100_enumset1, t25_zfmisc_1, d4_relat_1, t50_frechet2, t75_zfmisc_1, t24_borsuk_1, t4_xboole_0, t41_funcop_1, t65_finseq_1, d2_realset1, t81_enumset1, t3_functor0, t6_lattice2, d17_nattra_1, d4_wellord2, fc6_finset_1, free_g1_cat_1, t63_funct_5, t65_xboole_1, t43_funct_4, t38_card_3, t22_filter_1, fc17_finseq_1, t23_binop_1, d6_partfun1, t61_setwiseo, t150_relat_1, existence_m1_relset_1, commutativity_k5_subset_1, t55_setfam_1, t36_finseq_2, t1_zfmisc_1, t77_mcart_1, t68_funct_3, s8_domain_1, t19_funct_6, t12_setfam_1, 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, t84_enumset1, t77_funct_3, t5_funct_2, cc1_yellow13, t176_relat_1, dt_k8_funct_2, fraenkel_a_2_0_lattice5, t7_closure2, t128_relat_1, t50_setwiseo, d2_finseq_1, d4_relset_2, t9_altcat_1, t97_zfmisc_1, fraenkel_a_0_0_domain_1, t24_binop_1, s9_domain_1, t10_funct_4, t18_setwiseo, t167_funct_2, t53_partfun1, rc6_tex_2, t72_funct_3, t60_zfmisc_1, t24_filter_1, cc1_finseq_1, t24_finset_1, t1_pralg_3, fc2_pre_circ, fc1_orders_1, t11_funct_2, t21_funct_5, d3_zfmisc_1, dt_k3_funcsdom, t28_partfun1, fc2_funct_1, t73_funct_1, dt_k3_realset1, t40_funct_2, t4_waybel20, cc1_altcat_1, redefinition_k1_card_fil, t102_zfmisc_1, d2_ens_1, t27_funcop_1, t28_relset_1, t72_partfun1, t8_funct_1, t51_funcop_1, t121_funct_1, rc3_pboole, t72_mcart_1, t1_funct_7, t9_relat_1, t2_tarski, t56_mcart_1, t23_setwiseo, t18_relset_2, 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, t19_card_3, t122_funct_1, t13_setwiseo, t52_setfam_1, t25_borsuk_1, d1_filter_1, t166_relat_1, t2_zfmisc_1, t31_funct_3, dt_k1_borsuk_1, t74_funct_3, t16_funct_4, t61_funcop_1, t8_zfmisc_1, d6_realset1, t67_zfmisc_1, t74_funcop_1, dt_k1_partfun1, t11_tops_2, t61_funct_4, d2_fraenkel, t25_funcop_1, t29_funcop_1, t71_setwiseo, t99_enumset1, t74_zfmisc_1, cc1_funct_2, t14_funct_1, d4_tarski, t3_yellow17, t52_subset_1, t5_ordinal1, t4_boole, t36_funct_2, t146_funct_1, d2_funct_2, cc2_eqrel_1, t84_xboole_1, t77_finseq_1, t23_zfmisc_1, d13_funct_1, t109_relat_1, t133_funct_2, t4_cat_1, t57_zfmisc_1, t125_funct_1, t46_funcop_1, t120_relat_1, t98_zfmisc_1, t114_partfun1, dt_k11_relset_1, dt_k16_funct_3, dt_k5_metric_1, dt_k4_relat_1, t162_funct_1, t32_domain_1, dt_k9_relset_2, rc5_tex_2, t4_subset, dt_k10_cat_2, t28_funct_5, t76_xboole_1, t38_subset_1, t178_relat_1, t29_sysrel, t176_orders_1, t16_funcop_1, t169_funct_2, t33_sysrel, cc1_closure2, dt_k2_funct_1, t81_funct_4, dt_k8_domain_1, t15_realset1, t3_altcat_2, t39_subset_1, t1_waybel20, s2_altcat_1, t89_funct_3, cc3_pua2mss1, t8_functor0, t76_relat_1, dt_k1_cat_5, t20_ens_1, t32_xboole_1, t52_funct_5, t43_funct_1, redefinition_k7_filter_1, t174_relat_1, redefinition_k10_relset_1, t93_partfun1, t129_relat_1, fc1_qc_lang1, t179_relat_1, s3_domain_1, t65_funcop_1, t61_partfun1, t5_filter_2, dt_k1_yellow_3, dt_k14_funct_3, rc2_realset1, t2_relset_2, t80_xboole_1, d11_altcat_1, t20_finsub_1, t147_partfun1, t58_funct_1, t25_finset_1, t88_enumset1, t9_zfmisc_1, t148_funct_2, t79_xboole_1, t106_relat_1, t51_funct_2, reflexivity_r2_wellord2, t67_xboole_1, d12_binop_1, t12_zfmisc_1, d2_pua2mss1, t35_setwiseo, fc1_rfinseq, t39_setfam_1, existence_m2_realset1, dt_m2_fraenkel, existence_m3_realset1, t12_tops_2, t56_subset_1, redefinition_k6_setwiseo, redefinition_k14_mcart_1, t8_funct_5, redefinition_k5_setfam_1, s6_filter_1, t47_funcop_1, t1_isocat_2, dt_k1_domain_1, t58_zfmisc_1, t20_borsuk_1, t21_funct_3, t17_funct_2, t3_grcat_1, t74_card_1, t21_finsub_1, involutiveness_k4_relat_1, t35_sysrel, d4_partfun1, t50_funct_4, t5_orders_1, t13_lattice2, rc5_triang_1, t89_funct_1, fc1_realset1, dt_k1_urysohn1, t63_classes2, t11_funct_5, t74_mcart_1, t7_realset1, dt_k6_relset_2, t22_relset_2, t59_funct_1, t132_funct_2, dt_k3_altcat_1, t139_zfmisc_1, dt_k4_closure2, t143_relat_1, t77_relat_1, t13_finset_1, t32_lopclset, rc5_funct_1, t6_realset1, t16_lattice2, t64_classes2, t7_boole, t7_altcat_1, t37_sysrel, t11_card_fil, t160_funct_2, cc1_funct_1, t51_finseq_2, t31_relset_2, t4_funct_2, t2_altcat_1, d2_filter_1, t24_funcop_1, t17_funct_5, t27_membered, d3_relset_2, d3_funcop_1, t95_funct_3, t136_partfun1, t14_funct_6, t36_setfam_1, s11_funct_2, t86_funct_3, t138_relat_1, d3_partfun1, fc4_qc_lang1, t104_zfmisc_1, t11_binop_1, t118_relat_1, t42_mcart_1, t86_enumset1, t12_funct_7, d3_relat_2, t138_partfun1, s2_domain_1, fc3_pre_circ, d10_relat_1, t55_zfmisc_1, 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, fc5_funct_1, t29_finseq_1, t33_funct_4, fc29_membered, t22_relat_1, redefinition_k6_partfun1, t105_relat_1, d1_setwiseo, rc3_tex_2, dt_k3_finseq_1, t82_funct_7, t120_funct_1, t91_funct_3, t48_xboole_1, dt_k3_pua2mss1, dt_k6_domain_1, t157_funct_1, t85_partfun1, t3_ordinal1, t9_domain_1, fc38_membered, t45_relset_1, dt_k16_domain_1, t8_pua2mss1, dt_k4_urysohn1, fc2_membered, t23_borsuk_1, t152_funct_1, t85_xboole_1, t21_funct_2, t20_cantor_1, t3_altcat_1, t14_functor0, dt_k12_binop_2, t66_funcop_1, t16_subset_1, dt_k2_partfun1, dt_m1_card_fil, t26_zfmisc_1, t13_altcat_1, t70_enumset1, t69_partfun1, dt_k9_binop_2, t7_ordinal1, t38_relset_1, rc2_funct_1, t49_partfun1, redefinition_m2_fraenkel, t85_funct_7, dt_k31_binop_2, t34_funct_5, 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, s8_domain_1__e1_46__relset_2, t158_funct_2, d16_pboole, 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, t1_functor1, t63_zfmisc_1, dt_k6_funcop_1, t4_subset_1, t19_funct_2, fc4_card_3, t51_funct_1, t13_borsuk_1, t8_fraenkel, t26_filter_1, t130_relat_1, t7_funct_5, t22_finset_1, t67_funct_1, t8_lattice2, t74_relat_1, t162_funct_2, redefinition_k1_domain_1, d2_pralg_3, t90_funct_3, t42_funct_4, t30_relset_1, redefinition_k3_cat_5, rc1_funct_2, t91_orders_1, d7_realset1, t88_funct_7, dt_k10_funct_3, t76_funcop_1, d14_relat_1, t70_funct_4, t56_funct_1, existence_m1_pboole, t110_relat_1, t113_funct_2, t71_partfun1, dt_m1_pboole, t69_xboole_1, t17_fraenkel, t27_sysrel, t12_setwiseo, cc1_triang_1, d4_realset1, redefinition_k2_yellow_3, existence_m3_pboole, t59_funct_4, t4_realset1, t11_fraenkel, t159_funct_2, t116_zfmisc_1, redefinition_k13_domain_1, t64_zfmisc_1, dt_k2_cat_2, d7_xboole_0, redefinition_k6_relset_2, fc5_relat_1, t125_relat_1, t83_xboole_1, d6_setwiseo, t151_relat_1, t1_zfrefle1, t51_setfam_1, t4_borsuk_1, dt_m1_fraenkel, t45_relat_1, dt_m2_finseq_1, t2_lattice2, redefinition_k23_qc_lang1, t17_relset_2, t7_card_fil, t5_altcat_2, d1_tex_2, t4_ens_1, t14_funct_2, t155_funct_2, t27_binop_1, t137_relat_1, t77_funct_4, t20_xboole_1, redefinition_k1_fraenkel, t178_orders_1, s2_subset_1, t6_tex_2, t12_funct_3, commutativity_k3_setfam_1, t97_relat_1, t31_funct_5, d3_funct_4, t16_zfmisc_1, t17_cantor_1, t4_isocat_2, d3_funct_2, d1_eqrel_1, t38_funct_3, t2_t_0topsp, redefinition_k8_domain_1, t65_funct_1, d2_funct_5, t140_relat_1, t3_cat_2, t134_pboole, t124_zfmisc_1, t188_relat_1, d9_binop_2, fraenkel_a_3_1_domain_1, t35_funct_4, t60_funct_2, t82_xboole_1, t78_finseq_2, t4_filter_2, dt_k1_eqrel_1, dt_k2_monoid_0, t32_zfmisc_1, dt_k1_isocat_2, t186_relat_1, d26_waybel_4, t3_multop_1, d7_relat_1, t89_relat_1, t10_ens_1, cc2_funct_1, t21_funcop_1, t46_setfam_1, t9_relset_2, t169_partfun1, t3_funct_3, t49_funct_5, 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, dt_k6_funct_3, t46_funct_1, t51_setwiseo, idempotence_k1_funct_4, dt_k6_setfam_1, t94_funct_3, free_g3_quantal1, t44_setwiseo, t115_relat_1, t56_funcop_1, 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, t51_funct_5, t10_altcat_1, existence_m1_subset_1, fc5_subset_1, t1_waybel18, d2_mcart_1, d8_binop_2, t41_funct_4, t3_relat_1, t13_finseq_2, t31_finseq_3, commutativity_k2_tarski, t26_funct_7, t24_relat_1, t8_relset_1, fraenkel_a_6_0_relset_2, t124_relat_1, redefinition_r6_pboole, redefinition_k5_domain_1, t17_relset_1, dt_k9_setwiseo, t118_funct_1, t35_xboole_1, t49_domain_1, fc3_yellow_3, t7_functor0, t106_zfmisc_1, dt_k11_setwiseo, t12_cantor_1, fraenkel_a_6_0_domain_1, fc2_qc_lang1, t16_relset_2, d5_card_3, t125_zfmisc_1, t73_funct_2, t30_subset_1, d17_binop_1, t54_mcart_1, dt_k2_funct_2, fc3_qc_lang1, t84_funcop_1, dt_k7_relat_1, t1_monoid_0, rc4_tex_2, t44_setfam_1, t11_relset_1, t35_funct_3, t4_yellow17, t5_funct_5, t11_funct_4, fraenkel_a_2_1_pua2mss1, t83_finseq_2, t155_relat_1, d8_relat_1, t2_pre_circ, t47_xboole_1, t134_funct_2, t19_numbers, t145_funct_1, t61_funct_1, d2_card_fil, fc1_finset_1, t36_funct_5, t15_subset_1, t99_funct_3, t5_lattice2, free_g2_struct_0, t37_funct_2, t94_relat_1, t48_setfam_1, t86_finseq_2, t5_isocat_2, t39_sysrel, t31_funcop_1, t91_enumset1, d9_binop_1, dt_k3_funct_5, t18_borsuk_1, d5_subset_1, t2_altcat_2, redefinition_k16_funct_3, t146_relat_1, t92_zfmisc_1, redefinition_k4_setwiseo, fc5_card_3, t99_partfun1, t54_setwiseo, t107_zfmisc_1, t9_realset1, existence_m2_subset_1, t95_relat_1, t98_finseq_2, t100_zfmisc_1, t22_zfmisc_1, t7_tex_2, t27_funct_4, redefinition_k1_relset_2, dt_k1_nattra_1, dt_k5_subset_1, dt_k9_funcop_1, rc1_pua2mss1, t7_ens_1, t3_funct_7, t64_funct_4, t19_funct_5, t94_enumset1, t8_cantor_1, t142_partfun1, 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, dt_k2_altcat_1, t58_partfun1, t60_setwiseo, redefinition_k7_pboole, d24_waybel_4, t81_funct_3, t19_funcop_1, t2_multop_1, d1_zfmisc_1, t16_xboole_1, free_g2_vectsp_1, dt_k8_relat_1, d8_setfam_1, t3_zfrefle1, t1_ens_1, t69_enumset1, t26_xboole_1, s24_fraenkel, t63_xboole_1, redefinition_k7_funcop_1, t8_funct_4, t43_funct_2, commutativity_k4_subset_1, t91_partfun1, rc2_relat_1, t2_isocat_2, t60_funct_5, existence_m2_relset_1, t16_membered, t2_tex_2, d4_binop_1, t21_funct_6, t49_funcop_1, t54_domain_1, t38_zfmisc_1, t63_funct_4, t145_partfun1, t15_cantor_1, t65_mcart_1, t16_ens_1, t4_funct_7, t34_funcop_1, t55_setwiseo, dt_k3_cat_2, t31_yellow18, d8_ens_1, dt_k3_pre_circ, t37_mcart_1, t73_enumset1, d5_enumset1, t116_funct_2, fraenkel_a_3_6_domain_1, t23_relset_2, t17_finseq_1, t73_partfun1, redefinition_k3_cantor_1, dt_k7_funcop_1, fc4_funcop_1, t6_funct_2, t40_sysrel, t69_funcop_1, t76_funct_7, t28_finseq_2, t61_card_3, t72_funct_1, d2_relat_2, fc5_closure2, s4_domain_1, t25_funct_3, t168_partfun1, t1_isocat_1, t157_relat_1, cc3_finsub_1, t82_funct_3, s14_funct_2, redefinition_k4_domain_1, t62_setwiseo, t9_functor0, t142_funct_1, t92_partfun1, t26_subset_1, redefinition_k2_binop_1, t82_partfun1, existence_m2_filter_1, t51_subset_1, t97_funct_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, t2_funct_3, involutiveness_k10_funcop_1, t5_pua2mss1, t13_funct_5, t76_enumset1, t67_classes2, t29_card_1, t4_cat_2, t27_borsuk_1, t62_funct_4, reflexivity_r1_filter_2, t3_pua2mss1, t8_setfam_1, t36_zfmisc_1, d8_monoid_0, d7_monoid_0, t41_subset_1, t26_membered, redefinition_k6_funcop_1, t94_partfun1, dt_k12_mcart_1, redefinition_k17_domain_1, t84_funct_3, t37_relat_1, d3_tarski, t43_funcop_1, dt_k8_binop_2, d8_realset1, fraenkel_a_0_0_card_fil, t73_finseq_1, redefinition_k18_pralg_1, t20_card_3, t14_setwiseo, dt_k3_partfun1, t8_realset1, t58_funcop_1, t6_relset_1, t28_xboole_1, t16_borsuk_1, d1_relset_1, t74_partfun1, t31_filter_1, t53_domain_1, d1_funct_3, d1_multop_1, t46_subset_1, d7_relat_2, t151_pboole, t18_binop_1, redefinition_k16_domain_1, cc6_funct_2, t76_funct_4, t33_domain_1, t60_subset_1, t39_zfmisc_1, d1_realset1, d3_finseq_1, dt_k7_pboole, t58_funct_4, t72_setwiseo, t131_funct_2, t119_zfmisc_1, t121_relat_1, redefinition_k1_cat_5, rc1_relat_1, t34_mcart_1, t60_relat_1, t54_funct_1, t13_cantor_1, t42_funcop_1, t19_setwiseo, redefinition_k2_funcsdom, t83_zfmisc_1, t170_relat_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, dt_k6_relat_1, t20_finset_1, t32_setwiseo, cc17_membered, t11_funcop_1, t6_zfmisc_1, dt_k14_borsuk_1, t1_mssubfam, t48_relat_1, dt_k10_relset_1, symmetry_r1_filter_2, d2_orders_1, redefinition_k3_cat_2, t27_finsub_1, d15_funct_1, s3_subset_1, t143_funct_2, t32_finseq_2, t5_mcart_1, t93_relat_1, t33_borsuk_1, t18_funct_2, t144_funct_1, dt_k4_relset_2, t10_subset_1, t161_relat_1, dt_k7_filter_1, d9_relat_1, t51_funct_4, t56_setfam_1, t27_finset_1, t96_orders_1, t70_funct_3, dt_k7_funct_6, fc2_urysohn1, redefinition_k1_partfun1, t69_funct_6, rc2_setwiseo, t1_realset1, t7_cqc_lang, t36_setwiseo, reflexivity_r4_nattra_1, t2_xboole_1, t87_funct_6, t4_relset_2, t57_partfun1, t141_partfun1, d12_funct_1, t9_relset_1, redefinition_k2_realset1, t17_funct_4, fc2_yellow_3, t9_mcart_1, t7_msualg_1, 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, t32_funct_5, s1_card_fil, t150_funct_1, t34_funct_2, t11_funct_7, t83_enumset1, t57_subset_1, d15_binop_1, d1_funct_2, t12_funct_6, t3_lattice4, dt_k6_setwiseo, t84_partfun1, t6_pua2mss1, t25_funct_4, t20_relat_1, t90_xboole_1, t8_relset_2, t2_ens_1, t31_domain_1, free_g3_lattices, t113_partfun1, redefinition_k11_domain_1, t2_setfam_1, t11_setwiseo, t46_relat_1, fc1_setfam_1, t30_funct_3, t39_mcart_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, t14_pua2mss1, t12_zfrefle1, t35_funct_1, s1_funct_1, t18_zfmisc_1, t29_relset_1, rc1_realset1, redefinition_k7_relset_1, t3_monoid_0, t3_isocat_2, t17_funcop_1, dt_k5_setfam_1, rc3_finset_1, t68_funct_1, d6_eqrel_1, dt_k2_nattra_1, dt_k5_setwiseo, t30_finseq_2, redefinition_k11_relset_1, commutativity_k5_setwiseo, dt_k1_metric_1, existence_m1_eqrel_1, fc18_finseq_1, t36_xboole_1, t51_zfmisc_1, redefinition_k14_funct_3, dt_k8_subset_1, rc8_finseq_1, t3_ens_1, t38_funct_5, t144_partfun1, t20_funct_5, fc12_binop_2, t83_funct_7, existence_m1_nat_lat, t4_card_fil, t73_zfmisc_1, t47_subset_1, redefinition_k4_multop_1, t151_funct_2, dt_k12_domain_1, t46_relset_1, t47_funct_4, d5_binop_1, t64_xboole_1, t49_xboole_1, t64_mcart_1, t16_sysrel, t102_enumset1, dt_m2_subset_1, dt_k5_numbers, t51_relset_1, dt_k8_setwiseo, 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, 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, t35_partfun1, d1_yellow18, d8_binop_1, t21_funct_1, t50_funct_1, fc12_finset_1, t87_enumset1, t41_funct_5, t42_funct_1, t126_relat_1, t26_finsub_1, t8_card_fil, t73_mcart_1, t2_nattra_1, fc1_relat_1, d3_setwiseo, d10_binop_2, t4_mssubfam, t47_partfun1, t1_relset_2, cc6_membered, t46_finseq_2, t77_xboole_1, t8_boole, t169_relat_1, rc1_xboole_0, existence_m1_fraenkel, fc1_waybel_2, t21_borsuk_1, t18_sysrel, t16_funct_3, t1_funct_5, t1_mcart_1, t23_finset_1, t81_finseq_2, t24_partfun1, redefinition_k8_funct_2, t35_mcart_1, d1_orders_1, t80_zfmisc_1, t18_card_3, t34_zfmisc_1, t18_functor0, fc3_funct_1, t6_multop_1, t26_setwiseo, t5_relat_1, t24_zfmisc_1, t68_zfmisc_1, rc2_tex_2, t22_membered, dt_k36_binop_2, dt_k3_cat_5, t28_filter_1, d12_binop_2, t24_sysrel, rc7_tex_2, t1_functor0, t23_relat_1, dt_k7_metric_1, dt_m1_orders_1, dt_k12_funct_3, t182_relat_1, t54_funcop_1, t120_funct_2, d1_borsuk_1, redefinition_k3_funct_2, t31_mcart_1, t46_funct_4, involutiveness_k7_binop_2, redefinition_k9_relset_2, t59_funct_2, dt_k33_binop_2, t22_funct_3, t10_zfmisc_1, t56_classes2, t2_subset, s1_binop_2, t100_funct_3, reflexivity_r1_partfun1, t38_funct_2, t33_partfun1, rc1_closure2, t34_finsub_1, d3_relat_1, t85_funct_2, fc1_tex_2, dt_k1_funcsdom, t46_yellow20, t16_finset_1, d2_multop_1, dt_k2_multop_1, t75_funcop_1, fc7_relat_1, t14_funcop_1, t4_qc_lang1, s1_pre_circ, t111_relat_1, t180_relat_1, t60_funct_1, t21_yellow_9, t149_finseq_2, t24_funct_4, t11_functor0, t14_finseq_1, t37_zfmisc_1, t52_setwiseo, t65_relat_1, t21_relat_1, t3_pboole, t156_relat_1, t23_finsub_1, t54_sysrel, t53_zfmisc_1, t30_finsub_1, d5_funct_5, t149_pboole, t135_relat_1, t20_funcop_1, dt_k23_qc_lang1, d5_altcat_1, t14_borsuk_1, d4_setwiseo, d4_mcart_1, t109_zfmisc_1, fraenkel_a_2_3_domain_1, t60_domain_1, dt_k9_funct_7, d1_setfam_1, t152_relat_1, symmetry_r1_xboole_0, t20_relset_2, t10_finseq_2, t49_funct_4, t134_zfmisc_1, t86_relat_1, free_g1_rlvect_1, t48_card_1, t100_relat_1, t25_partfun1, t49_relat_1, rc3_closure2, dt_k2_cantor_1, t13_finsub_1, fc8_relat_1, t161_funct_1, t27_funct_1, t10_realset1, t92_relat_1, d11_binop_2, t82_funcop_1, redefinition_k2_cat_5, t175_orders_1, s10_fraenkel, dt_k3_binop_1, t15_functor0, t27_funct_5, fraenkel_a_0_18_fraenkel, t48_funct_4, t33_relset_2, t59_funct_6, fc2_funcop_1, fraenkel_a_2_1_card_fil, t11_relset_2, d18_binop_1, t22_wellord2, t58_domain_1, t115_funct_2, free_g1_quantal1, t4_waybel18, t32_finsub_1, t48_subset_1, fc3_pralg_1, rc1_setwiseo, d18_pboole, dt_k1_pcomps_1, t28_relat_1, d1_funct_1, d1_filter_2, t32_borsuk_1, t31_finseq_2, t115_partfun1, t33_funct_3, 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, d10_xboole_0, t1_tex_2, symmetry_r2_wellord2, 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_0_33_fraenkel, redefinition_k18_group_2, redefinition_k10_domain_1, t2_grcat_1, fc3_funcop_1, t37_funct_1, t59_classes2, t3_xboole_0, cc1_realset1, t58_setfam_1, t12_relset_1, t77_funcop_1, d2_funct_4, dt_k18_group_2, 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, t3_setwiseo, rc1_partfun1, redefinition_r1_filter_2, t28_setwiseo, t159_funct_1, dt_k3_funct_4, redefinition_k5_relset_1, redefinition_k2_nattra_1, t57_funct_1, t88_funct_6, fraenkel_a_3_0_ens_1, t27_partfun1, symmetry_r1_partfun1, t9_funct_4, dt_k2_setwiseo, t33_finseq_2, t23_filter_1, t2_funct_7, t126_funct_1, t67_partfun1, t132_relat_1, t3_boole, redefinition_k2_setwiseo, d8_funct_3, t26_relset_2, d9_funct_3, d5_funct_1, t6_ordinal1, t24_funct_3, fc2_fraenkel, t146_partfun1, t53_mcart_1, fc1_ens_1, redefinition_k6_subset_1, dt_k2_funct_3, t21_relset_2, t59_card_1, redefinition_k4_relset_1, t44_funct_1, cc5_funct_2, t48_relset_1, redefinition_m2_subset_1, dt_k3_funct_3, t57_sysrel, dt_k1_fraenkel, t69_setwiseo, d4_enumset1, redefinition_k1_borsuk_1, t87_funct_3, t59_funcop_1, t25_relat_1, t22_funct_2, t14_funct_3, t4_pralg_1, t62_finseq_3, t16_domain_1, fc1_sysrel, t5_funct_4, fc16_finset_1, t13_binop_1, dt_k34_binop_2, t83_funct_3, d5_setwiseo, t143_partfun1, dt_k13_funct_3, t67_funct_2, dt_k18_pralg_1, t26_partfun1, t112_zfmisc_1, t8_funct_3, redefinition_k2_partfun1, fc14_finset_1, dt_k15_funct_3, t8_multop_1, t17_funct_3, t78_enumset1, t26_funct_4, t103_relat_1, t40_mcart_1, rc1_tex_2, cc4_pua2mss1, dt_k5_finsub_1, t30_zfmisc_1, dt_k10_domain_1, t80_relat_1, cc16_membered, t15_sysrel, fraenkel_a_0_1_domain_1, t16_binop_1, fc13_finset_1, rc1_setfam_1, t15_funct_4, t139_partfun1, dt_k2_zfrefle1, dt_k1_oppcat_1, t84_funct_6, d13_binop_1, t9_card_fil, fc7_finset_1, idempotence_k4_subset_1, symmetry_r6_pboole, t21_closure2, t34_setwiseo, d5_finsub_1, d2_setwiseo, fraenkel_a_0_39_fraenkel, t81_relat_1, d1_binop_1, t40_zfmisc_1, t72_funcop_1, t22_funct_4, rc2_xboole_0, dt_k3_card_fil, t174_partfun1, t80_partfun1, t55_funct_2, fraenkel_a_3_5_domain_1, t82_funct_4, redefinition_r4_nattra_1, t66_relat_1, t38_partfun1, fc27_membered, existence_m1_card_fil, s7_domain_1, d3_monoid_0, existence_m1_orders_1, dt_m3_realset1, t5_closure2, t78_partfun1, s18_fraenkel, redefinition_k4_finseq_1, d3_xboole_0, d2_relat_1, redefinition_k9_cat_2, d4_funcop_1, t71_relat_1, t53_relat_1, t167_relat_1, t61_funct_2, t52_mcart_1, t36_funct_4, t62_domain_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, t6_pre_circ, existence_m2_finseq_1, t2_funct_4, t4_funct_3, t37_funct_5, t38_setwiseo, t96_enumset1, cc1_binop_1, t6_relat_1, t172_partfun1, t33_subset_1, t13_toler_1, t14_lattice2, t31_borsuk_1, t15_ens_1, t159_relat_1, t13_relset_2, t29_filter_1, dt_k3_qc_lang1, t10_card_fil, fraenkel_a_3_8_domain_1, t6_yellow21, t65_zfmisc_1, t30_partfun1, t80_funct_4, cc6_tex_2, redefinition_k9_funcop_1, t63_subset_1, t112_partfun1, t2_cat_2, fraenkel_a_4_1_domain_1, t38_xboole_1, t19_funct_4, redefinition_k8_setwiseo, t23_funcop_1, d7_binop_2, t119_relat_1, t20_funct_4, antisymmetry_r2_hidden, t23_relset_1, t15_relset_2, t88_funct_3, t53_setfam_1, fc15_finset_1, dt_k1_setwiseo, d19_binop_1, t45_funct_4, t88_relat_1, redefinition_k15_domain_1, fc3_binop_2, t22_subset_1, redefinition_k6_domain_1
% 59.08/20.23 % No. of inferences in proof: 4786
% 59.08/20.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19706 ms resp. 18290 ms w/o parsing
% 61.81/21.22 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 61.95/21.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------