%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU435+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:38:55 AM UTC 2026
% Result : Theorem 115.87s 39.87s
% Output : Refutation 120.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2392
% Syntax : Number of formulae : 4786 ( 437 unt; 0 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 : 0 ( 0 >; 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_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(a_6_0_relset_2_decl,type,
a_6_0_relset_2: $i > $i > $i > $i > $i > $i > $i ).
thf(k5_finsub_1_decl,type,
k5_finsub_1: $i > $i ).
thf(k6_setwiseo_decl,type,
k6_setwiseo: $i > $i > $i > $i ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(v9_monoid_0_decl,type,
v9_monoid_0: $i > $i > $o ).
thf(v1_setwiseo_decl,type,
v1_setwiseo: $i > $i > $o ).
thf(k2_binop_1_decl,type,
k2_binop_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k3_binop_1_decl,type,
k3_binop_1: $i > $i > $i ).
thf(k1_numbers_decl,type,
k1_numbers: $i ).
thf(k9_binop_2_decl,type,
k9_binop_2: $i > $i > $i ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(m2_finseq_1_decl,type,
m2_finseq_1: $i > $i > $o ).
thf(m2_subset_1_decl,type,
m2_subset_1: $i > $i > $i > $o ).
thf(k5_numbers_decl,type,
k5_numbers: $i ).
thf(k9_funct_7_decl,type,
k9_funct_7: $i > $i > $i ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(k7_relat_1_decl,type,
k7_relat_1: $i > $i > $i ).
thf(m2_pua2mss1_decl,type,
m2_pua2mss1: $i > $i > $o ).
thf(k3_funct_5_decl,type,
k3_funct_5: $i > $i ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k3_partfun1_decl,type,
k3_partfun1: $i > $i > $i > $i ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k1_relat_1_decl,type,
k1_relat_1: $i > $i ).
thf(r2_wellord2_decl,type,
r2_wellord2: $i > $i > $o ).
thf(v2_relat_1_decl,type,
v2_relat_1: $i > $o ).
thf(m1_pboole_decl,type,
m1_pboole: $i > $i > $o ).
thf(k4_card_3_decl,type,
k4_card_3: $i > $i ).
thf(v1_fraenkel_decl,type,
v1_fraenkel: $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k1_setfam_1_decl,type,
k1_setfam_1: $i > $i ).
thf(k4_relset_1_decl,type,
k4_relset_1: $i > $i > $i > $i ).
thf(k2_relat_1_decl,type,
k2_relat_1: $i > $i ).
thf(k3_xboole_0_decl,type,
k3_xboole_0: $i > $i > $i ).
thf(k9_relat_1_decl,type,
k9_relat_1: $i > $i > $i ).
thf(k4_relat_1_decl,type,
k4_relat_1: $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k6_relat_1_decl,type,
k6_relat_1: $i > $i ).
thf(k5_funct_5_decl,type,
k5_funct_5: $i > $i ).
thf(m3_pboole_decl,type,
m3_pboole: $i > $i > $i > $i > $o ).
thf(k1_funct_1_decl,type,
k1_funct_1: $i > $i > $i ).
thf(m1_card_fil_decl,type,
m1_card_fil: $i > $i > $o ).
thf(k2_card_fil_decl,type,
k2_card_fil: $i > $i > $i ).
thf(k7_setfam_1_decl,type,
k7_setfam_1: $i > $i > $i ).
thf(r1_xboole_0_decl,type,
r1_xboole_0: $i > $i > $o ).
thf(k1_setwiseo_decl,type,
k1_setwiseo: $i > $i ).
thf(v2_membered_decl,type,
v2_membered: $i > $o ).
thf(v1_membered_decl,type,
v1_membered: $i > $o ).
thf(v5_monoid_0_decl,type,
v5_monoid_0: $i > $i > $o ).
thf(v3_monoid_0_decl,type,
v3_monoid_0: $i > $i > $o ).
thf(v4_monoid_0_decl,type,
v4_monoid_0: $i > $i > $o ).
thf(v1_binop_1_decl,type,
v1_binop_1: $i > $i > $o ).
thf(v2_binop_1_decl,type,
v2_binop_1: $i > $i > $o ).
thf(k7_setwiseo_decl,type,
k7_setwiseo: $i > $i > $i > $i > $i > $i ).
thf(k8_funct_2_decl,type,
k8_funct_2: $i > $i > $i > $i > $i ).
thf(r3_binop_1_decl,type,
r3_binop_1: $i > $i > $i > $o ).
thf(k2_setwiseo_decl,type,
k2_setwiseo: $i > $i > $i ).
thf(k5_setwiseo_decl,type,
k5_setwiseo: $i > $i > $i > $i ).
thf(k2_tarski_decl,type,
k2_tarski: $i > $i > $i ).
thf(k11_binop_2_decl,type,
k11_binop_2: $i > $i > $i ).
thf(k5_funcop_1_decl,type,
k5_funcop_1: $i > $i > $i > $i ).
thf(k7_pboole_decl,type,
k7_pboole: $i > $i > $i > $i > $i ).
thf(v1_finseq_1_decl,type,
v1_finseq_1: $i > $o ).
thf(k3_finseq_1_decl,type,
k3_finseq_1: $i > $i ).
thf(k10_binop_2_decl,type,
k10_binop_2: $i > $i > $i ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(k1_funct_2_decl,type,
k1_funct_2: $i > $i > $i ).
thf(m2_fraenkel_decl,type,
m2_fraenkel: $i > $i > $i > $i > $o ).
thf(k1_fraenkel_decl,type,
k1_fraenkel: $i > $i > $i ).
thf(m1_fraenkel_decl,type,
m1_fraenkel: $i > $i > $i > $o ).
thf(k3_funcop_1_decl,type,
k3_funcop_1: $i > $i > $i > $i ).
thf(k2_finseq_1_decl,type,
k2_finseq_1: $i > $i ).
thf(k6_subset_1_decl,type,
k6_subset_1: $i > $i > $i > $i ).
thf(k10_setwiseo_decl,type,
k10_setwiseo: $i > $i > $i > $i > $i ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(k3_funct_3_decl,type,
k3_funct_3: $i > $i ).
thf(k5_relat_1_decl,type,
k5_relat_1: $i > $i > $i ).
thf(k10_relat_1_decl,type,
k10_relat_1: $i > $i > $i ).
thf(k2_funct_1_decl,type,
k2_funct_1: $i > $i ).
thf(k1_closure2_decl,type,
k1_closure2: $i > $i > $i ).
thf(k4_closure2_decl,type,
k4_closure2: $i > $i > $i > $i ).
thf(v2_funct_2_decl,type,
v2_funct_2: $i > $i > $i > $o ).
thf(k1_functor0_decl,type,
k1_functor0: $i > $i > $i > $i > $i ).
thf(v1_classes2_decl,type,
v1_classes2: $i > $o ).
thf(k3_mcart_1_decl,type,
k3_mcart_1: $i > $i > $i > $i ).
thf(k4_mcart_1_decl,type,
k4_mcart_1: $i > $i > $i > $i > $i ).
thf(k3_pua2mss1_decl,type,
k3_pua2mss1: $i > $i ).
thf(k4_finseq_1_decl,type,
k4_finseq_1: $i > $i ).
thf(k10_funct_6_decl,type,
k10_funct_6: $i > $i ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(k1_cat_2_decl,type,
k1_cat_2: $i > $i > $i > $i > $i > $i > $i ).
thf(r1_partfun1_decl,type,
r1_partfun1: $i > $i > $o ).
thf(k1_funct_4_decl,type,
k1_funct_4: $i > $i > $i ).
thf(m1_orders_1_decl,type,
m1_orders_1: $i > $i > $o ).
thf(k3_tarski_decl,type,
k3_tarski: $i > $i ).
thf(v1_realset1_decl,type,
v1_realset1: $i > $o ).
thf(k3_pralg_3_decl,type,
k3_pralg_3: $i > $i > $i ).
thf(m1_eqrel_1_decl,type,
m1_eqrel_1: $i > $i > $o ).
thf(k1_partfun1_decl,type,
k1_partfun1: $i > $i > $i > $i > $i > $i > $i ).
thf(k8_relat_1_decl,type,
k8_relat_1: $i > $i > $i ).
thf(k7_funct_2_decl,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(k4_tarski_decl,type,
k4_tarski: $i > $i > $i ).
thf(k2_funct_4_decl,type,
k2_funct_4: $i > $i ).
thf(k7_funct_6_decl,type,
k7_funct_6: $i > $i ).
thf(k3_urysohn1_decl,type,
k3_urysohn1: $i > $i ).
thf(k2_funcop_1_decl,type,
k2_funcop_1: $i > $i > $i ).
thf(k2_funct_5_decl,type,
k2_funct_5: $i > $i ).
thf(v3_binop_1_decl,type,
v3_binop_1: $i > $i > $o ).
thf(m2_card_fil_decl,type,
m2_card_fil: $i > $i > $o ).
thf(k15_funct_3_decl,type,
k15_funct_3: $i > $i > $i ).
thf(k6_setfam_1_decl,type,
k6_setfam_1: $i > $i > $i ).
thf(k2_cat_2_decl,type,
k2_cat_2: $i > $i > $i > $i > $i ).
thf(k1_card_fil_decl,type,
k1_card_fil: $i > $i > $i ).
thf(k5_partfun1_decl,type,
k5_partfun1: $i > $i > $i > $i ).
thf(k3_setfam_1_decl,type,
k3_setfam_1: $i > $i > $i ).
thf(k4_funcop_1_decl,type,
k4_funcop_1: $i > $i > $i > $i ).
thf(k1_funct_3_decl,type,
k1_funct_3: $i > $i ).
thf(k2_funcsdom_decl,type,
k2_funcsdom: $i > $i > $i > $i > $i > $i > $i ).
thf(v1_setfam_1_decl,type,
v1_setfam_1: $i > $o ).
thf(k1_domain_1_decl,type,
k1_domain_1: $i > $i > $i > $i > $i ).
thf(k2_partfun1_decl,type,
k2_partfun1: $i > $i > $i > $i > $i ).
thf(a_2_1_pua2mss1_decl,type,
a_2_1_pua2mss1: $i > $i > $i ).
thf(k6_partfun1_decl,type,
k6_partfun1: $i > $i ).
thf(k7_ens_1_decl,type,
k7_ens_1: $i > $i > $i > $i ).
thf(a_3_0_ens_1_decl,type,
a_3_0_ens_1: $i > $i > $i > $i ).
thf(k3_cat_2_decl,type,
k3_cat_2: $i > $i > $i > $i > $i ).
thf(v8_monoid_0_decl,type,
v8_monoid_0: $i > $i > $o ).
thf(v6_monoid_0_decl,type,
v6_monoid_0: $i > $i > $o ).
thf(v7_monoid_0_decl,type,
v7_monoid_0: $i > $i > $o ).
thf(k9_setwiseo_decl,type,
k9_setwiseo: $i > $i ).
thf(k3_card_fil_decl,type,
k3_card_fil: $i > $i > $i > $i ).
thf(k3_funcsdom_decl,type,
k3_funcsdom: $i > $i > $i > $i ).
thf(v6_ordinal1_decl,type,
v6_ordinal1: $i > $o ).
thf(k19_pralg_1_decl,type,
k19_pralg_1: $i > $i > $i > $i ).
thf(k12_binop_2_decl,type,
k12_binop_2: $i > $i > $i ).
thf(k1_orders_1_decl,type,
k1_orders_1: $i > $i ).
thf(k1_isocat_2_decl,type,
k1_isocat_2: $i > $i > $i > $i > $i ).
thf(k16_funct_3_decl,type,
k16_funct_3: $i > $i > $i > $i > $i > $i > $i ).
thf(k1_funct_5_decl,type,
k1_funct_5: $i > $i ).
thf(k3_subset_1_decl,type,
k3_subset_1: $i > $i > $i ).
thf(r4_nattra_1_decl,type,
r4_nattra_1: $i > $i > $i > $i > $i > $i > $o ).
thf(k2_funct_2_decl,type,
k2_funct_2: $i > $i > $i > $i > $i ).
thf(k1_enumset1_decl,type,
k1_enumset1: $i > $i > $i > $i ).
thf(k6_domain_1_decl,type,
k6_domain_1: $i > $i > $i ).
thf(k5_relset_1_decl,type,
k5_relset_1: $i > $i > $i > $i ).
thf(k13_funct_3_decl,type,
k13_funct_3: $i > $i > $i ).
thf(r5_binop_1_decl,type,
r5_binop_1: $i > $i > $i > $o ).
thf(k7_filter_1_decl,type,
k7_filter_1: $i > $i > $i > $i > $i ).
thf(k4_zfmisc_1_decl,type,
k4_zfmisc_1: $i > $i > $i > $i > $i ).
thf(k3_zfmisc_1_decl,type,
k3_zfmisc_1: $i > $i > $i > $i ).
thf(r2_binop_1_decl,type,
r2_binop_1: $i > $i > $i > $o ).
thf(m1_nat_lat_decl,type,
m1_nat_lat: $i > $i > $i > $i > $o ).
thf(k5_enumset1_decl,type,
k5_enumset1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k4_enumset1_decl,type,
k4_enumset1: $i > $i > $i > $i > $i > $i > $i ).
thf(a_1_0_lattice5_decl,type,
a_1_0_lattice5: $i > $i ).
thf(k5_setfam_1_decl,type,
k5_setfam_1: $i > $i > $i ).
thf(a_3_0_relset_2_decl,type,
a_3_0_relset_2: $i > $i > $i > $i ).
thf(r6_binop_1_decl,type,
r6_binop_1: $i > $i > $i > $o ).
thf(r4_binop_1_decl,type,
r4_binop_1: $i > $i > $i > $o ).
thf(k3_enumset1_decl,type,
k3_enumset1: $i > $i > $i > $i > $i > $i ).
thf(k6_enumset1_decl,type,
k6_enumset1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k3_setwiseo_decl,type,
k3_setwiseo: $i > $i > $i > $i ).
thf(k3_relset_2_decl,type,
k3_relset_2: $i > $i > $i > $i > $i ).
thf(k11_relset_1_decl,type,
k11_relset_1: $i > $i > $i > $i > $i ).
thf(k1_relset_2_decl,type,
k1_relset_2: $i > $i > $i > $i ).
thf(k18_pralg_1_decl,type,
k18_pralg_1: $i > $i > $i > $i ).
thf(k3_funct_2_decl,type,
k3_funct_2: $i > $i > $i > $i > $i ).
thf(k5_relset_2_decl,type,
k5_relset_2: $i > $i > $i ).
thf(k3_funct_4_decl,type,
k3_funct_4: $i > $i > $i ).
thf(k6_pralg_1_decl,type,
k6_pralg_1: $i > $i > $i ).
thf(k8_setwiseo_decl,type,
k8_setwiseo: $i > $i > $i > $i > $i ).
thf(k8_binop_2_decl,type,
k8_binop_2: $i > $i ).
thf(r6_pboole_decl,type,
r6_pboole: $i > $i > $i > $o ).
thf(k6_funcop_1_decl,type,
k6_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(a_6_0_domain_1_decl,type,
a_6_0_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k4_domain_1_decl,type,
k4_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k18_group_2_decl,type,
k18_group_2: $i > $i > $i ).
thf(k2_mcart_1_decl,type,
k2_mcart_1: $i > $i ).
thf(k2_borsuk_1_decl,type,
k2_borsuk_1: $i > $i > $i ).
thf(k12_mcart_1_decl,type,
k12_mcart_1: $i > $i > $i > $i > $i ).
thf(k9_funct_3_decl,type,
k9_funct_3: $i > $i > $i ).
thf(k10_funct_3_decl,type,
k10_funct_3: $i > $i > $i ).
thf(k5_domain_1_decl,type,
k5_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k4_setwiseo_decl,type,
k4_setwiseo: $i > $i > $i > $i > $i ).
thf(k2_ens_1_decl,type,
k2_ens_1: $i > $i ).
thf(k12_funct_3_decl,type,
k12_funct_3: $i > $i ).
thf(v2_setfam_1_decl,type,
v2_setfam_1: $i > $o ).
thf(k10_relset_1_decl,type,
k10_relset_1: $i > $i > $i > $i > $i ).
thf(m1_functor0_decl,type,
m1_functor0: $i > $i > $i > $i > $i > $i > $o ).
thf(k4_urysohn1_decl,type,
k4_urysohn1: $i ).
thf(k4_funct_2_decl,type,
k4_funct_2: $i > $i > $i > $i ).
thf(k1_realset1_decl,type,
k1_realset1: $i > $i > $i ).
thf(m1_realset1_decl,type,
m1_realset1: $i > $i > $i > $o ).
thf(r1_filter_2_decl,type,
r1_filter_2: $i > $i > $i > $o ).
thf(a_3_1_pua2mss1_decl,type,
a_3_1_pua2mss1: $i > $i > $i > $i ).
thf(r2_wellord1_decl,type,
r2_wellord1: $i > $i > $o ).
thf(k36_binop_2_decl,type,
k36_binop_2: $i ).
thf(k13_pboole_decl,type,
k13_pboole: $i > $i > $i ).
thf(k2_yellow_3_decl,type,
k2_yellow_3: $i > $i > $i > $i > $i > $i > $i ).
thf(k1_yellow_3_decl,type,
k1_yellow_3: $i > $i > $i ).
thf(k7_funcop_1_decl,type,
k7_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k1_binop_1_decl,type,
k1_binop_1: $i > $i > $i > $i ).
thf(m1_filter_1_decl,type,
m1_filter_1: $i > $i > $i > $o ).
thf(k1_metric_1_decl,type,
k1_metric_1: $i > $i > $i > $i > $i > $i ).
thf(k7_metric_1_decl,type,
k7_metric_1: $i ).
thf(a_2_0_lattice5_decl,type,
a_2_0_lattice5: $i > $i > $i ).
thf(k8_funcop_1_decl,type,
k8_funcop_1: $i > $i > $i > $i > $i > $i ).
thf(k9_cat_2_decl,type,
k9_cat_2: $i > $i > $i > $i > $i > $i > $i ).
thf(k4_qc_lang1_decl,type,
k4_qc_lang1: $i ).
thf(k1_qc_lang1_decl,type,
k1_qc_lang1: $i ).
thf(k8_eqrel_1_decl,type,
k8_eqrel_1: $i > $i > $i ).
thf(k9_funcop_1_decl,type,
k9_funcop_1: $i > $i > $i > $i > $i ).
thf(k2_nattra_1_decl,type,
k2_nattra_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k10_cat_2_decl,type,
k10_cat_2: $i > $i > $i > $i > $i ).
thf(k11_setwiseo_decl,type,
k11_setwiseo: $i > $i ).
thf(k14_funct_3_decl,type,
k14_funct_3: $i > $i > $i > $i > $i > $i ).
thf(k7_binop_2_decl,type,
k7_binop_2: $i > $i ).
thf(k5_subset_1_decl,type,
k5_subset_1: $i > $i > $i > $i ).
thf(r1_zfrefle1_decl,type,
r1_zfrefle1: $i > $i > $o ).
thf(k1_subset_1_decl,type,
k1_subset_1: $i > $i ).
thf(k9_zf_lang_decl,type,
k9_zf_lang: $i ).
thf(k2_cantor_1_decl,type,
k2_cantor_1: $i > $i > $i ).
thf(k1_cantor_1_decl,type,
k1_cantor_1: $i > $i > $i ).
thf(v1_tex_2_decl,type,
v1_tex_2: $i > $i > $o ).
thf(r1_binop_1_decl,type,
r1_binop_1: $i > $i > $i > $o ).
thf(k1_multop_1_decl,type,
k1_multop_1: $i > $i > $i > $i > $i ).
thf(k20_mcart_1_decl,type,
k20_mcart_1: $i > $i ).
thf(a_2_0_domain_1_decl,type,
a_2_0_domain_1: $i > $i > $i ).
thf(k3_multop_1_decl,type,
k3_multop_1: $i > $i > $i > $i > $i > $i ).
thf(r7_relat_2_decl,type,
r7_relat_2: $i > $i > $o ).
thf(k2_subset_1_decl,type,
k2_subset_1: $i > $i ).
thf(k2_relset_2_decl,type,
k2_relset_2: $i > $i > $i > $i > $i ).
thf(k1_ens_1_decl,type,
k1_ens_1: $i > $i ).
thf(k3_cantor_1_decl,type,
k3_cantor_1: $i > $i > $i > $i > $i > $i ).
thf(v4_finsub_1_decl,type,
v4_finsub_1: $i > $o ).
thf(k33_binop_2_decl,type,
k33_binop_2: $i ).
thf(k7_relset_1_decl,type,
k7_relset_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k2_realset1_decl,type,
k2_realset1: $i > $i > $i > $i ).
thf(a_8_0_domain_1_decl,type,
a_8_0_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k35_binop_2_decl,type,
k35_binop_2: $i ).
thf(k2_functor0_decl,type,
k2_functor0: $i > $i > $i > $i > $i > $i > $i ).
thf(k3_altcat_1_decl,type,
k3_altcat_1: $i > $i > $i > $i ).
thf(k17_mcart_1_decl,type,
k17_mcart_1: $i > $i ).
thf(k18_mcart_1_decl,type,
k18_mcart_1: $i > $i ).
thf(k19_mcart_1_decl,type,
k19_mcart_1: $i > $i ).
thf(k10_funcop_1_decl,type,
k10_funcop_1: $i > $i > $i > $i > $i ).
thf(a_4_2_domain_1_decl,type,
a_4_2_domain_1: $i > $i > $i > $i > $i ).
thf(p1_s4_domain_1_decl,type,
p1_s4_domain_1: $i > $i > $i > $i > $o ).
thf(r1_lattice2_decl,type,
r1_lattice2: $i > $i > $i > $o ).
thf(k1_nattra_1_decl,type,
k1_nattra_1: $i > $i > $i > $i > $i ).
thf(m3_realset1_decl,type,
m3_realset1: $i > $i > $i > $o ).
thf(k1_oppcat_1_decl,type,
k1_oppcat_1: $i > $i > $i > $i > $i ).
thf(a_1_1_ens_1_decl,type,
a_1_1_ens_1: $i > $i ).
thf(k4_card_fil_decl,type,
k4_card_fil: $i > $i ).
thf(k1_eqrel_1_decl,type,
k1_eqrel_1: $i > $i ).
thf(r7_binop_1_decl,type,
r7_binop_1: $i > $i > $i > $o ).
thf(k2_altcat_1_decl,type,
k2_altcat_1: $i > $i > $i ).
thf(k34_binop_2_decl,type,
k34_binop_2: $i ).
thf(v1_yellow18_decl,type,
v1_yellow18: $i > $i > $i > $i > $o ).
thf(k8_setfam_1_decl,type,
k8_setfam_1: $i > $i > $i ).
thf(v7_altcat_1_decl,type,
v7_altcat_1: $i > $o ).
thf(m2_realset1_decl,type,
m2_realset1: $i > $i > $i > $o ).
thf(k3_realset1_decl,type,
k3_realset1: $i > $i > $i > $i ).
thf(k5_funcsdom_decl,type,
k5_funcsdom: $i > $i > $i > $i > $i > $i ).
thf(m2_filter_1_decl,type,
m2_filter_1: $i > $i > $i > $o ).
thf(k1_funcsdom_decl,type,
k1_funcsdom: $i > $i > $i > $i > $i > $i ).
thf(a_4_0_relset_2_decl,type,
a_4_0_relset_2: $i > $i > $i > $i > $i ).
thf(k2_funct_3_decl,type,
k2_funct_3: $i > $i > $i > $i ).
thf(k3_metric_1_decl,type,
k3_metric_1: $i ).
thf(a_3_8_domain_1_decl,type,
a_3_8_domain_1: $i > $i > $i > $i ).
thf(p1_s3_domain_1_decl,type,
p1_s3_domain_1: $i > $i > $i > $o ).
thf(a_1_0_domain_1_decl,type,
a_1_0_domain_1: $i > $i ).
thf(k1_borsuk_1_decl,type,
k1_borsuk_1: $i > $i > $i > $i ).
thf(k1_funct_7_decl,type,
k1_funct_7: $i > $i > $i ).
thf(k4_subset_1_decl,type,
k4_subset_1: $i > $i > $i > $i ).
thf(a_0_0_pre_circ_decl,type,
a_0_0_pre_circ: $i ).
thf(g2_vectsp_1_decl,type,
g2_vectsp_1: $i > $i > $i > $i > $i ).
thf(f2_s1_card_fil_decl,type,
f2_s1_card_fil: $i ).
thf(a_0_0_card_fil_decl,type,
a_0_0_card_fil: $i ).
thf(p1_s1_card_fil_decl,type,
p1_s1_card_fil: $i > $o ).
thf(k3_cat_5_decl,type,
k3_cat_5: $i > $i > $i > $i ).
thf(r5_relat_2_decl,type,
r5_relat_2: $i > $i > $o ).
thf(g1_group_1_decl,type,
g1_group_1: $i > $i > $i ).
thf(r4_waybel_4_decl,type,
r4_waybel_4: $i > $i > $i > $o ).
thf(a_1_2_domain_1_decl,type,
a_1_2_domain_1: $i > $i ).
thf(p1_s1_domain_1_decl,type,
p1_s1_domain_1: $i > $o ).
thf(g3_lattices_decl,type,
g3_lattices: $i > $i > $i > $i ).
thf(k11_domain_1_decl,type,
k11_domain_1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k13_mcart_1_decl,type,
k13_mcart_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k7_subset_1_decl,type,
k7_subset_1: $i > $i > $i > $i ).
thf(a_3_6_domain_1_decl,type,
a_3_6_domain_1: $i > $i > $i > $i ).
thf(f1_s1_setwiseo_decl,type,
f1_s1_setwiseo: $i ).
thf(f2_s1_setwiseo_decl,type,
f2_s1_setwiseo: $i ).
thf(p1_s1_setwiseo_decl,type,
p1_s1_setwiseo: $i > $i > $o ).
thf(a_4_2_relset_2_decl,type,
a_4_2_relset_2: $i > $i > $i > $i > $i ).
thf(k8_relset_2_decl,type,
k8_relset_2: $i > $i > $i > $i > $i ).
thf(r1_realset1_decl,type,
r1_realset1: $i > $i > $i > $o ).
thf(a_2_1_domain_1_decl,type,
a_2_1_domain_1: $i > $i > $i ).
thf(k2_qc_lang1_decl,type,
k2_qc_lang1: $i ).
thf(a_2_3_domain_1_decl,type,
a_2_3_domain_1: $i > $i > $i ).
thf(p1_s2_domain_1_decl,type,
p1_s2_domain_1: $i > $i > $o ).
thf(a_0_0_altcat_2_decl,type,
a_0_0_altcat_2: $i ).
thf(g1_cat_1_decl,type,
g1_cat_1: $i > $i > $i > $i > $i > $i > $i ).
thf(r2_relat_2_decl,type,
r2_relat_2: $i > $i > $o ).
thf(g1_lattices_decl,type,
g1_lattices: $i > $i > $i ).
thf(k4_relset_2_decl,type,
k4_relset_2: $i > $i > $i > $i > $i ).
thf(k6_relset_2_decl,type,
k6_relset_2: $i > $i > $i > $i ).
thf(m1_triang_1_decl,type,
m1_triang_1: $i > $i > $i > $o ).
thf(a_0_0_yellow_3_decl,type,
a_0_0_yellow_3: $i ).
thf(f1_s1_yellow_3_decl,type,
f1_s1_yellow_3: $i ).
thf(f2_s1_yellow_3_decl,type,
f2_s1_yellow_3: $i > $i > $i ).
thf(p1_s1_yellow_3_decl,type,
p1_s1_yellow_3: $i > $i > $o ).
thf(k5_metric_1_decl,type,
k5_metric_1: $i > $i ).
thf(a_4_1_relset_2_decl,type,
a_4_1_relset_2: $i > $i > $i > $i > $i ).
thf(a_4_1_yellow_9_decl,type,
a_4_1_yellow_9: $i > $i > $i > $i > $i ).
thf(k6_funct_3_decl,type,
k6_funct_3: $i > $i > $i ).
thf(k2_multop_1_decl,type,
k2_multop_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k5_trees_3_decl,type,
k5_trees_3: $i > $i ).
thf(a_2_0_card_fil_decl,type,
a_2_0_card_fil: $i > $i > $i ).
thf(g2_rlvect_1_decl,type,
g2_rlvect_1: $i > $i > $i > $i > $i ).
thf(k32_binop_2_decl,type,
k32_binop_2: $i ).
thf(f1_s1_binop_2_decl,type,
f1_s1_binop_2: $i ).
thf(f2_s1_binop_2_decl,type,
f2_s1_binop_2: $i ).
thf(f3_s1_binop_2_decl,type,
f3_s1_binop_2: $i > $i ).
thf(a_3_5_domain_1_decl,type,
a_3_5_domain_1: $i > $i > $i > $i ).
thf(k3_qc_lang1_decl,type,
k3_qc_lang1: $i ).
thf(a_4_3_relset_2_decl,type,
a_4_3_relset_2: $i > $i > $i > $i > $i ).
thf(g3_quantal1_decl,type,
g3_quantal1: $i > $i > $i > $i > $i > $i > $i ).
thf(a_3_2_domain_1_decl,type,
a_3_2_domain_1: $i > $i > $i > $i ).
thf(k5_urysohn1_decl,type,
k5_urysohn1: $i ).
thf(a_2_2_domain_1_decl,type,
a_2_2_domain_1: $i > $i > $i ).
thf(k13_domain_1_decl,type,
k13_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(k31_binop_2_decl,type,
k31_binop_2: $i ).
thf(g1_vectsp_1_decl,type,
g1_vectsp_1: $i > $i > $i > $i ).
thf(k8_domain_1_decl,type,
k8_domain_1: $i > $i > $i > $i > $i ).
thf(v2_pre_topc_decl,type,
v2_pre_topc: $i > $o ).
thf(g1_pre_topc_decl,type,
g1_pre_topc: $i > $i > $i ).
thf(a_0_32_fraenkel_decl,type,
a_0_32_fraenkel: $i ).
thf(f2_s17_fraenkel_decl,type,
f2_s17_fraenkel: $i ).
thf(k1_pcomps_1_decl,type,
k1_pcomps_1: $i > $i ).
thf(k2_monoid_0_decl,type,
k2_monoid_0: $i > $i > $i > $i ).
thf(k14_borsuk_1_decl,type,
k14_borsuk_1: $i > $i > $i > $i > $i ).
thf(g1_rlvect_1_decl,type,
g1_rlvect_1: $i > $i > $i > $i ).
thf(a_0_33_fraenkel_decl,type,
a_0_33_fraenkel: $i ).
thf(f2_s18_fraenkel_decl,type,
f2_s18_fraenkel: $i ).
thf(a_3_4_domain_1_decl,type,
a_3_4_domain_1: $i > $i > $i > $i ).
thf(k14_mcart_1_decl,type,
k14_mcart_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(g3_vectsp_1_decl,type,
g3_vectsp_1: $i > $i > $i > $i > $i > $i ).
thf(a_4_0_pua2mss1_decl,type,
a_4_0_pua2mss1: $i > $i > $i > $i > $i ).
thf(a_3_1_domain_1_decl,type,
a_3_1_domain_1: $i > $i > $i > $i ).
thf(k1_cat_5_decl,type,
k1_cat_5: $i > $i > $i > $i > $i ).
thf(r3_relat_2_decl,type,
r3_relat_2: $i > $i > $o ).
thf(f1_s4_funct_2_decl,type,
f1_s4_funct_2: $i ).
thf(f2_s4_funct_2_decl,type,
f2_s4_funct_2: $i ).
thf(f3_s4_funct_2_decl,type,
f3_s4_funct_2: $i > $i ).
thf(a_4_1_domain_1_decl,type,
a_4_1_domain_1: $i > $i > $i > $i > $i ).
thf(k1_urysohn1_decl,type,
k1_urysohn1: $i ).
thf(k2_urysohn1_decl,type,
k2_urysohn1: $i ).
thf(k17_domain_1_decl,type,
k17_domain_1: $i > $i > $i > $i > $i ).
thf(k15_domain_1_decl,type,
k15_domain_1: $i > $i > $i > $i > $i ).
thf(g1_funcsdom_decl,type,
g1_funcsdom: $i > $i > $i > $i > $i > $i > $i ).
thf(k9_domain_1_decl,type,
k9_domain_1: $i > $i > $i > $i > $i > $i ).
thf(m2_cantor_1_decl,type,
m2_cantor_1: $i > $i > $o ).
thf(f2_s21_fraenkel_decl,type,
f2_s21_fraenkel: $i ).
thf(a_0_38_fraenkel_decl,type,
a_0_38_fraenkel: $i ).
thf(g1_quantal1_decl,type,
g1_quantal1: $i > $i > $i > $i > $i ).
thf(f1_s14_funct_2_decl,type,
f1_s14_funct_2: $i ).
thf(f2_s14_funct_2_decl,type,
f2_s14_funct_2: $i ).
thf(p1_s14_funct_2_decl,type,
p1_s14_funct_2: $i > $i > $o ).
thf(r2_waybel_4_decl,type,
r2_waybel_4: $i > $i > $i > $o ).
thf(a_3_3_domain_1_decl,type,
a_3_3_domain_1: $i > $i > $i > $i ).
thf(p1_s1_funct_1_decl,type,
p1_s1_funct_1: $i > $i > $o ).
thf(f1_s1_funct_1_decl,type,
f1_s1_funct_1: $i ).
thf(f1_s12_funct_2_decl,type,
f1_s12_funct_2: $i ).
thf(f3_s12_funct_2_decl,type,
f3_s12_funct_2: $i > $i ).
thf(f2_s12_funct_2_decl,type,
f2_s12_funct_2: $i ).
thf(g2_quantal1_decl,type,
g2_quantal1: $i > $i > $i > $i > $i > $i ).
thf(k10_domain_1_decl,type,
k10_domain_1: $i > $i > $i > $i > $i > $i > $i ).
thf(f1_s13_funct_2_decl,type,
f1_s13_funct_2: $i ).
thf(f3_s13_funct_2_decl,type,
f3_s13_funct_2: $i > $i ).
thf(f2_s13_funct_2_decl,type,
f2_s13_funct_2: $i ).
thf(k14_domain_1_decl,type,
k14_domain_1: $i > $i > $i > $i > $i ).
thf(k7_relset_2_decl,type,
k7_relset_2: $i > $i > $i > $i > $i ).
thf(a_3_7_domain_1_decl,type,
a_3_7_domain_1: $i > $i > $i > $i ).
thf(a_0_18_fraenkel_decl,type,
a_0_18_fraenkel: $i ).
thf(f1_s10_fraenkel_decl,type,
f1_s10_fraenkel: $i ).
thf(m1_cantor_1_decl,type,
m1_cantor_1: $i > $i > $o ).
thf(a_2_0_cantor_1_decl,type,
a_2_0_cantor_1: $i > $i > $i ).
thf(k4_multop_1_decl,type,
k4_multop_1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(g2_lattices_decl,type,
g2_lattices: $i > $i > $i ).
thf(k2_cat_5_decl,type,
k2_cat_5: $i > $i > $i > $i > $i ).
thf(a_2_1_card_fil_decl,type,
a_2_1_card_fil: $i > $i > $i ).
thf(g1_metric_1_decl,type,
g1_metric_1: $i > $i > $i ).
thf(k3_pre_circ_decl,type,
k3_pre_circ: $i > $i > $i > $i ).
thf(k23_qc_lang1_decl,type,
k23_qc_lang1: $i > $i ).
thf(f1_s3_funct_2_decl,type,
f1_s3_funct_2: $i ).
thf(f2_s3_funct_2_decl,type,
f2_s3_funct_2: $i ).
thf(p1_s3_funct_2_decl,type,
p1_s3_funct_2: $i > $i > $o ).
thf(a_2_0_relset_2_decl,type,
a_2_0_relset_2: $i > $i > $i ).
thf(f3_s22_fraenkel_decl,type,
f3_s22_fraenkel: $i ).
thf(f4_s22_fraenkel_decl,type,
f4_s22_fraenkel: $i ).
thf(a_0_39_fraenkel_decl,type,
a_0_39_fraenkel: $i ).
thf(k12_domain_1_decl,type,
k12_domain_1: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(f1_s1_funct_7_decl,type,
f1_s1_funct_7: $i ).
thf(f2_s1_funct_7_decl,type,
f2_s1_funct_7: $i ).
thf(f4_s1_funct_7_decl,type,
f4_s1_funct_7: $i > $i > $i ).
thf(f3_s1_funct_7_decl,type,
f3_s1_funct_7: $i ).
thf(f1_s4_altcat_1_decl,type,
f1_s4_altcat_1: $i ).
thf(f2_s4_altcat_1_decl,type,
f2_s4_altcat_1: $i ).
thf(f3_s4_altcat_1_decl,type,
f3_s4_altcat_1: $i ).
thf(f4_s4_altcat_1_decl,type,
f4_s4_altcat_1: $i > $i > $i > $i ).
thf(f1_s1_altcat_2_decl,type,
f1_s1_altcat_2: $i ).
thf(f2_s1_altcat_2_decl,type,
f2_s1_altcat_2: $i > $i ).
thf(p1_s1_altcat_2_decl,type,
p1_s1_altcat_2: $i > $o ).
thf(a_0_2_domain_1_decl,type,
a_0_2_domain_1: $i ).
thf(f3_s9_domain_1_decl,type,
f3_s9_domain_1: $i ).
thf(a_0_0_domain_1_decl,type,
a_0_0_domain_1: $i ).
thf(f1_s7_domain_1_decl,type,
f1_s7_domain_1: $i ).
thf(f3_s11_funct_2_decl,type,
f3_s11_funct_2: $i ).
thf(f4_s11_funct_2_decl,type,
f4_s11_funct_2: $i ).
thf(f1_s11_funct_2_decl,type,
f1_s11_funct_2: $i ).
thf(f2_s11_funct_2_decl,type,
f2_s11_funct_2: $i ).
thf(f5_s11_funct_2_decl,type,
f5_s11_funct_2: $i ).
thf(f6_s11_funct_2_decl,type,
f6_s11_funct_2: $i ).
thf(f7_s11_funct_2_decl,type,
f7_s11_funct_2: $i > $i ).
thf(k16_domain_1_decl,type,
k16_domain_1: $i > $i > $i > $i > $i ).
thf(p1_s7_domain_1_decl,type,
p1_s7_domain_1: $i > $o ).
thf(k9_relset_2_decl,type,
k9_relset_2: $i > $i > $i > $i > $i > $i ).
thf(f1_s6_filter_1_decl,type,
f1_s6_filter_1: $i ).
thf(f2_s6_filter_1_decl,type,
f2_s6_filter_1: $i ).
thf(p1_s6_filter_1_decl,type,
p1_s6_filter_1: $i > $i > $i > $o ).
thf(f1_s3_subset_1_decl,type,
f1_s3_subset_1: $i ).
thf(p1_s3_subset_1_decl,type,
p1_s3_subset_1: $i > $o ).
thf(f1_s17_fraenkel_decl,type,
f1_s17_fraenkel: $i ).
thf(f3_s17_fraenkel_decl,type,
f3_s17_fraenkel: $i > $i ).
thf(p1_s17_fraenkel_decl,type,
p1_s17_fraenkel: $i > $o ).
thf(f1_s1_pre_circ_decl,type,
f1_s1_pre_circ: $i ).
thf(f2_s1_pre_circ_decl,type,
f2_s1_pre_circ: $i > $i ).
thf(p1_s1_pre_circ_decl,type,
p1_s1_pre_circ: $i > $o ).
thf(k8_subset_1_decl,type,
k8_subset_1: $i > $i ).
thf(f1_s22_fraenkel_decl,type,
f1_s22_fraenkel: $i ).
thf(f2_s22_fraenkel_decl,type,
f2_s22_fraenkel: $i ).
thf(f5_s22_fraenkel_decl,type,
f5_s22_fraenkel: $i > $i > $i ).
thf(a_0_1_domain_1_decl,type,
a_0_1_domain_1: $i ).
thf(f2_s8_domain_1_decl,type,
f2_s8_domain_1: $i ).
thf(g2_struct_0_decl,type,
g2_struct_0: $i > $i > $i ).
thf(f1_s1_card_fil_decl,type,
f1_s1_card_fil: $i ).
thf(f1_s3_filter_1_decl,type,
f1_s3_filter_1: $i ).
thf(p1_s3_filter_1_decl,type,
p1_s3_filter_1: $i > $i > $i > $o ).
thf(k2_filter_1_decl,type,
k2_filter_1: $i > $i > $i > $i ).
thf(f2_s3_filter_1_decl,type,
f2_s3_filter_1: $i ).
thf(f1_s8_domain_1_decl,type,
f1_s8_domain_1: $i ).
thf(f3_s8_domain_1_decl,type,
f3_s8_domain_1: $i > $i ).
thf(p1_s8_domain_1_decl,type,
p1_s8_domain_1: $i > $o ).
thf(f1_s1_subset_1_decl,type,
f1_s1_subset_1: $i ).
thf(p1_s1_subset_1_decl,type,
p1_s1_subset_1: $i > $o ).
thf(f1_s9_domain_1_decl,type,
f1_s9_domain_1: $i ).
thf(f2_s9_domain_1_decl,type,
f2_s9_domain_1: $i ).
thf(f4_s9_domain_1_decl,type,
f4_s9_domain_1: $i > $i > $i ).
thf(p1_s9_domain_1_decl,type,
p1_s9_domain_1: $i > $i > $o ).
thf(a_0_0_group_5_decl,type,
a_0_0_group_5: $i ).
thf(f1_s1_group_5_decl,type,
f1_s1_group_5: $i ).
thf(f2_s1_group_5_decl,type,
f2_s1_group_5: $i ).
thf(f3_s1_group_5_decl,type,
f3_s1_group_5: $i ).
thf(f4_s1_group_5_decl,type,
f4_s1_group_5: $i > $i > $i > $i ).
thf(p1_s1_group_5_decl,type,
p1_s1_group_5: $i > $i > $i > $o ).
thf(f1_s4_filter_1_decl,type,
f1_s4_filter_1: $i ).
thf(f2_s4_filter_1_decl,type,
f2_s4_filter_1: $i ).
thf(p1_s4_filter_1_decl,type,
p1_s4_filter_1: $i > $o ).
thf(f1_s1_filter_1_decl,type,
f1_s1_filter_1: $i ).
thf(p1_s1_filter_1_decl,type,
p1_s1_filter_1: $i > $o ).
thf(f2_s1_filter_1_decl,type,
f2_s1_filter_1: $i ).
thf(f1_s2_altcat_1_decl,type,
f1_s2_altcat_1: $i ).
thf(f2_s2_altcat_1_decl,type,
f2_s2_altcat_1: $i ).
thf(f3_s2_altcat_1_decl,type,
f3_s2_altcat_1: $i > $i > $i ).
thf(f1_s18_fraenkel_decl,type,
f1_s18_fraenkel: $i ).
thf(f3_s18_fraenkel_decl,type,
f3_s18_fraenkel: $i > $i ).
thf(p1_s18_fraenkel_decl,type,
p1_s18_fraenkel: $i > $o ).
thf(f1_s21_fraenkel_decl,type,
f1_s21_fraenkel: $i ).
thf(f3_s21_fraenkel_decl,type,
f3_s21_fraenkel: $i > $i ).
thf(f1_s2_filter_1_decl,type,
f1_s2_filter_1: $i ).
thf(p1_s2_filter_1_decl,type,
p1_s2_filter_1: $i > $i > $o ).
thf(f2_s2_filter_1_decl,type,
f2_s2_filter_1: $i ).
thf(f1_s2_subset_1_decl,type,
f1_s2_subset_1: $i ).
thf(p1_s2_subset_1_decl,type,
p1_s2_subset_1: $i > $o ).
thf(f1_s4_subset_1_decl,type,
f1_s4_subset_1: $i ).
thf(f2_s4_subset_1_decl,type,
f2_s4_subset_1: $i ).
thf(p1_s4_subset_1_decl,type,
p1_s4_subset_1: $i > $o ).
thf(f3_s4_subset_1_decl,type,
f3_s4_subset_1: $i ).
thf(k2_zfrefle1_decl,type,
k2_zfrefle1: $i ).
thf(f1_s5_filter_1_decl,type,
f1_s5_filter_1: $i ).
thf(f2_s5_filter_1_decl,type,
f2_s5_filter_1: $i ).
thf(p1_s5_filter_1_decl,type,
p1_s5_filter_1: $i > $i > $o ).
thf(p1_s10_fraenkel_decl,type,
p1_s10_fraenkel: $i > $o ).
thf(f1_s24_fraenkel_decl,type,
f1_s24_fraenkel: $i ).
thf(f2_s24_fraenkel_decl,type,
f2_s24_fraenkel: $i ).
thf(f3_s24_fraenkel_decl,type,
f3_s24_fraenkel: $i ).
thf(f4_s24_fraenkel_decl,type,
f4_s24_fraenkel: $i > $i ).
thf(p1_s24_fraenkel_decl,type,
p1_s24_fraenkel: $i > $i > $o ).
thf(f1_s23_fraenkel_decl,type,
f1_s23_fraenkel: $i ).
thf(p1_s23_fraenkel_decl,type,
p1_s23_fraenkel: $i > $i > $o ).
thf(f2_s23_fraenkel_decl,type,
f2_s23_fraenkel: $i ).
thf(703,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) @ r2_hidden ) )
<=> ( ( H @ ( D @ r2_hidden ) )
& ( G @ ( C @ r2_hidden ) )
& ( F @ ( B @ r2_hidden ) )
& ( E @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_mcart_1) ).
thf(5659,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ ( D @ r2_hidden ) )
& ( G @ ( C @ r2_hidden ) )
& ( F @ ( B @ r2_hidden ) )
& ( E @ ( A @ r2_hidden ) ) )
=> ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) @ r2_hidden ) ) )
& ( ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) @ r2_hidden ) )
=> ( ( H @ ( D @ r2_hidden ) )
& ( G @ ( C @ r2_hidden ) )
& ( F @ ( B @ r2_hidden ) )
& ( E @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(1404,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ k3_tarski )
= ( A @ k3_tarski @ ( B @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_funct_3) ).
thf(9405,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ k3_tarski )
= ( A @ k3_tarski @ ( B @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).
thf(842,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
thf(6387,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(2076,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ a_3_8_domain_1 ) ) @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_domain_1) ).
thf(13199,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ a_3_8_domain_1 ) ) @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2076]) ).
thf(1166,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ k1_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
thf(8114,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ k1_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
=> ( A @ ( D @ m1_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_pboole) ).
thf(2876,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
=> ( A @ ( D @ m1_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_finset_1 )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( B @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_card_1) ).
thf(2463,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_finset_1 )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( B @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(2123,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k6_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( C @ k6_relat_1 @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_sysrel) ).
thf(13405,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k6_relat_1 @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( C @ k6_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ k6_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( C @ k6_relat_1 @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2123]) ).
thf(875,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_funct_4) ).
thf(6566,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(2281,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(14181,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2281]) ).
thf(674,axiom,
( ( k1_numbers @ v2_membered )
& ( k1_numbers @ v1_membered )
& ~ ( k1_numbers @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_membered) ).
thf(5509,plain,
( ( k1_numbers @ v2_membered )
& ( k1_numbers @ v1_membered )
& ~ ( k1_numbers @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(2053,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ a_4_0_relset_2 ) ) ) @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_relset_2) ).
thf(13052,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ a_4_0_relset_2 ) ) ) @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2053]) ).
thf(783,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_eqrel_1 ) )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ v2_funct_1 )
& ( D @ k2_relat_1 @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ m2_pua2mss1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_pua2mss1) ).
thf(6085,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_eqrel_1 ) )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ v2_funct_1 )
& ( D @ k2_relat_1 @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ m2_pua2mss1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(2092,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_7_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_domain_1) ).
thf(13266,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_7_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2092]) ).
thf(1108,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
~ ( ( ( E @ ( D @ k1_funct_1 ) )
= C )
& ( A @ ( E @ r2_hidden ) ) )
& ( ( D @ k2_relat_1 )
= B )
& ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_2) ).
thf(7766,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
~ ( ( ( E @ ( D @ k1_funct_1 ) )
= C )
& ( A @ ( E @ r2_hidden ) ) )
& ( ( D @ k2_relat_1 )
= B )
& ( B @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(2049,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_xboole_0 ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( C @ ( D @ ( A @ k8_setfam_1 ) @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_mssubfam) ).
thf(13024,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_xboole_0 ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( C @ ( D @ ( A @ k8_setfam_1 ) @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2049]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k8_relat_1 ) )
= ( C @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t135_relat_1) ).
thf(4447,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k8_relat_1 ) )
= ( C @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(2106,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( B @ ( A @ k7_setfam_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_setfam_1) ).
thf(13321,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( B @ ( A @ k7_setfam_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2106]) ).
thf(585,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_1) ).
thf(5088,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_tarski ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(535,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k3_funct_3 @ k10_relat_1 ) )
= ( B @ ( A @ k1_funct_3 @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_3) ).
thf(4835,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k3_funct_3 @ k10_relat_1 ) )
= ( B @ ( A @ k1_funct_3 @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(1580,axiom,
! [A: $i] :
( ( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( B @ v1_xboole_0 )
=> ( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_tex_2) ).
thf(10259,plain,
! [A: $i] :
( ( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( B @ v1_xboole_0 )
=> ( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1580]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
<=> ( ( C @ ( B @ ( A @ k5_relset_1 ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relset_1) ).
thf(4450,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_relset_1 ) ) )
= B )
=> ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k5_relset_1 ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(1680,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= A ) )
& ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_setfam_1) ).
thf(10785,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= A ) )
& ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1680]) ).
thf(89,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_1) ).
thf(2778,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) )
& ( ( B @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(2122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( D @ ( J @ m1_subset_1 ) )
& ( C @ ( I @ m1_subset_1 ) )
& ( B @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_relset_1 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ~ ( E @ v1_xboole_0 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_multop_1 ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( H @ ( G @ ( F @ k3_multop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_multop_1) ).
thf(13402,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( D @ ( J @ m1_subset_1 ) )
& ( C @ ( I @ m1_subset_1 ) )
& ( B @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_relset_1 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ~ ( E @ v1_xboole_0 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_multop_1 ) ) ) ) ) ) ) ) ) )
= ( J @ ( I @ ( H @ ( G @ ( F @ k3_multop_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2122]) ).
thf(1757,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ m1_pboole ) )
& ( A @ ( D @ m1_pboole ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ? [F: $i] : ( E @ ( D @ ( C @ ( B @ ( A @ ( F @ m1_functor0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_functor0) ).
thf(11192,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ m1_pboole ) )
& ( A @ ( D @ m1_pboole ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ? [F: $i] : ( E @ ( D @ ( C @ ( B @ ( A @ ( F @ m1_functor0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1757]) ).
thf(1259,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ k6_partfun1 @ ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( D @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funcop_1) ).
thf(8663,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ k6_partfun1 @ ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( D @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(292,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( A @ ( B @ k1_setfam_1 @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_orders_1) ).
thf(3661,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( A @ ( B @ k1_setfam_1 @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(1869,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
<=> ( A @ k1_zfmisc_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finset_1) ).
thf(11895,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_finset_1 )
=> ( A @ v1_finset_1 ) )
& ( ( A @ v1_finset_1 )
=> ( A @ k1_zfmisc_1 @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1869]) ).
thf(1968,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_funct_2) ).
thf(12526,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1968]) ).
thf(1640,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r2_hidden ) )
=> ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_realset1) ).
thf(10577,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r2_hidden ) )
=> ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1640]) ).
thf(2163,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
<=> ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
thf(13643,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( A @ v1_relat_1 ) )
& ( ( A @ v1_relat_1 )
=> ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2163]) ).
thf(512,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ r1_partfun1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_partfun1) ).
thf(4729,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ r1_partfun1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(2042,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_finset_1) ).
thf(12975,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2042]) ).
thf(2367,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k4_subset_1 ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(14574,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k4_subset_1 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2367]) ).
thf(1425,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_zfmisc_1) ).
thf(9485,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
<=> ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ ( C @ ( B @ ( B @ ( A @ ( A @ k16_funct_3 ) ) ) ) ) @ v2_funct_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_functor0) ).
thf(3979,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ ( C @ ( B @ ( B @ ( A @ ( A @ k16_funct_3 ) ) ) ) ) @ v2_funct_2 ) ) )
=> ( B @ ( A @ ( C @ v2_funct_2 ) ) ) )
& ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
=> ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ ( C @ ( B @ ( B @ ( A @ ( A @ k16_funct_3 ) ) ) ) ) @ v2_funct_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(1473,axiom,
~ ( k4_qc_lang1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_qc_lang1) ).
thf(9731,plain,
~ ( k4_qc_lang1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473]) ).
thf(1823,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( F @ ( G @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) )
=> ( D
= ( F @ ( E @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funcop_1) ).
thf(11581,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( F @ ( G @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) )
=> ( D
= ( F @ ( E @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1823]) ).
thf(939,axiom,
! [A: $i] :
( ( A @ k1_tarski @ v1_realset1 )
& ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_realset1) ).
thf(6855,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_realset1 )
& ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(1670,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( C @ ( B @ ( A @ k1_borsuk_1 ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ ( B @ ( A @ k1_borsuk_1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k1_borsuk_1 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_borsuk_1) ).
thf(10743,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( C @ ( B @ ( A @ k1_borsuk_1 ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ ( B @ ( A @ k1_borsuk_1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k1_borsuk_1 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1670]) ).
thf(92,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) @ ( A @ r1_partfun1 ) )
=> ( B @ ( C @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ ( A @ k7_relat_1 ) @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_4) ).
thf(2787,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) @ ( A @ r1_partfun1 ) )
=> ( B @ ( C @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ ( A @ k7_relat_1 ) @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(827,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( F @ ( D @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_funcop_1) ).
thf(6317,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( F @ ( D @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) )
= ( F @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(864,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( G @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_mcart_1) ).
thf(6512,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( G @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_xboole_1) ).
thf(2480,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( A @ ( C @ k4_xboole_0 ) @ ( B @ ( C @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(359,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k10_funct_6 @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k10_funct_6 @ k1_funct_1 ) @ v1_funct_1 )
& ( B @ ( A @ k10_funct_6 @ k1_funct_1 ) @ v1_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_funct_6) ).
thf(3969,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k10_funct_6 @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k10_funct_6 @ k1_funct_1 ) @ v1_funct_1 )
& ( B @ ( A @ k10_funct_6 @ k1_funct_1 ) @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(1916,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ g3_vectsp_1 ) ) ) ) )
= ( J @ ( I @ ( H @ ( G @ ( F @ g3_vectsp_1 ) ) ) ) ) )
=> ( ( E = J )
& ( D = I )
& ( C = H )
& ( B = G )
& ( A = F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_vectsp_1) ).
thf(12148,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ g3_vectsp_1 ) ) ) ) )
= ( J @ ( I @ ( H @ ( G @ ( F @ g3_vectsp_1 ) ) ) ) ) )
=> ( ( E = J )
& ( D = I )
& ( C = H )
& ( B = G )
& ( A = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1916]) ).
thf(1331,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).
thf(9076,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(1706,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_relset_1) ).
thf(10944,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1706]) ).
thf(2267,axiom,
! [A: $i,B: $i] : ( A @ k1_zfmisc_1 @ ( B @ ( A @ k1_card_fil ) @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_card_fil) ).
thf(14139,plain,
! [A: $i,B: $i] : ( A @ k1_zfmisc_1 @ ( B @ ( A @ k1_card_fil ) @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2267]) ).
thf(764,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( A @ k1_fraenkel ) @ ( B @ ( D @ ( C @ ( B @ ( A @ k3_cat_2 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ k1_fraenkel ) @ ( B @ ( D @ ( C @ ( B @ ( A @ k3_cat_2 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k3_cat_2 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_cat_2) ).
thf(5999,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( A @ k1_fraenkel ) @ ( B @ ( D @ ( C @ ( B @ ( A @ k3_cat_2 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ k1_fraenkel ) @ ( B @ ( D @ ( C @ ( B @ ( A @ k3_cat_2 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k3_cat_2 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(1885,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
<=> ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_zfmisc_1) ).
thf(11998,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1885]) ).
thf(1602,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k5_funcsdom ) ) ) ) )
= ( E @ ( D @ ( C @ k5_funcop_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_funcsdom) ).
thf(10363,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k5_funcsdom ) ) ) ) )
= ( E @ ( D @ ( C @ k5_funcop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1602]) ).
thf(1406,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k7_relat_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t187_relat_1) ).
thf(9411,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k7_relat_1 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406]) ).
thf(1291,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k4_card_fil @ ( B @ r2_hidden ) )
<=> ( A @ ( B @ m1_card_fil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_card_fil) ).
thf(8828,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_card_fil ) )
=> ( A @ k4_card_fil @ ( B @ r2_hidden ) ) )
& ( ( A @ k4_card_fil @ ( B @ r2_hidden ) )
=> ( A @ ( B @ m1_card_fil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(767,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( C @ k2_funct_4 @ k1_relat_1 @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funct_4) ).
thf(6014,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_funct_4 @ k1_relat_1 @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( C @ k2_funct_4 @ k1_relat_1 @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( ( A @ ( B @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) )
& ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funct_1) ).
thf(5131,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( ( A @ ( B @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) )
& ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(841,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ~ ( ~ ( D @ ( F @ ( C @ ( B @ k2_funct_2 ) ) ) @ ( F @ ( E @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ ( C @ ( A @ k3_funct_2 ) ) ) @ ( D @ ( E @ ( B @ ( A @ k3_funct_2 ) ) ) @ r1_tarski ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funct_2) ).
thf(6374,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ~ ( ~ ( D @ ( F @ ( C @ ( B @ k2_funct_2 ) ) ) @ ( F @ ( E @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ ( C @ ( A @ k3_funct_2 ) ) ) @ ( D @ ( E @ ( B @ ( A @ k3_funct_2 ) ) ) @ r1_tarski ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(796,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_funct_3) ).
thf(6162,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(619,axiom,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v3_binop_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_setwiseo) ).
thf(5224,plain,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v3_binop_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(1588,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_subset_1) ).
thf(10294,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ~ ( B @ ( D @ r2_hidden ) ) )
& ( ~ ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1588]) ).
thf(2202,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_partfun1) ).
thf(13845,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2202]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k4_relat_1 @ k3_xboole_0 ) @ k2_relat_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k4_relat_1 @ k3_xboole_0 ) @ k1_relat_1 @ r1_xboole_0 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k2_relat_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k1_relat_1 @ r1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_sysrel) ).
thf(3680,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k4_relat_1 @ k3_xboole_0 ) @ k2_relat_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k4_relat_1 @ k3_xboole_0 ) @ k1_relat_1 @ r1_xboole_0 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k2_relat_1 @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k1_relat_1 @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(1958,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C @ ( B @ ( D @ k2_relat_1 @ m2_relset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funcop_1) ).
thf(12500,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C @ ( B @ ( D @ k2_relat_1 @ m2_relset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1958]) ).
thf(2207,axiom,
( ! [A: $i] :
( ( f1_s3_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s3_funct_2 ) )
& ( f2_s3_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_2) ).
thf(13869,plain,
( ! [A: $i] :
( ( f1_s3_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s3_funct_2 ) )
& ( f2_s3_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s3_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s3_funct_2 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s3_funct_2 @ ( f1_s3_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2207]) ).
thf(552,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( C = D ) ) ) )
& ( A @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( A
= ( B @ k2_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_funct_1) ).
thf(4931,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( C = D ) ) ) )
& ( A @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( A
= ( B @ k2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(1071,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_fraenkel) ).
thf(7601,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(1954,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ k3_tarski @ ( C @ k9_relat_1 ) @ ( A @ ( C @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) @ ( B @ k5_setfam_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relset_2) ).
thf(12458,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ k3_tarski @ ( C @ k9_relat_1 ) @ ( A @ ( C @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) @ ( B @ k5_setfam_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1954]) ).
thf(2308,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_relset_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_2) ).
thf(14296,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_relset_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2308]) ).
thf(662,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(5454,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(1144,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_lattice2) ).
thf(8005,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(922,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_relat_1) ).
thf(6791,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(1215,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_xboole_1) ).
thf(8417,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(1984,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( D
!= ( F @ ( E @ k4_tarski ) ) ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
& ( C @ ( D @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_grcat_1) ).
thf(12634,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( D
!= ( F @ ( E @ k4_tarski ) ) ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
& ( C @ ( D @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1984]) ).
thf(509,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( A @ k1_enumset1 ) ) )
= ( B @ ( A @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_enumset1) ).
thf(4714,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( A @ k1_enumset1 ) ) )
= ( B @ ( A @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
=> ( C @ ( A @ k4_xboole_0 ) @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_xboole_1) ).
thf(2512,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
=> ( C @ ( A @ k4_xboole_0 ) @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1893,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( C @ r2_hidden ) )
=> ! [F: $i] :
( ( D @ ( F @ r2_hidden ) )
=> ( F @ k1_tarski @ ( E @ k9_relat_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_relset_2) ).
thf(12030,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( C @ r2_hidden ) )
=> ! [F: $i] :
( ( D @ ( F @ r2_hidden ) )
=> ( F @ k1_tarski @ ( E @ k9_relat_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1893]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(3072,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(1560,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ~ ( C @ v1_xboole_0 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_pua2mss1) ).
thf(10149,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ~ ( C @ v1_xboole_0 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1560]) ).
thf(1483,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
=> ( ( A @ k3_tarski @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ k3_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_3) ).
thf(9791,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
=> ( ( A @ k3_tarski @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ k3_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483]) ).
thf(1170,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( D @ ( B @ r2_hidden ) )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).
thf(8129,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ r2_hidden ) )
& ( A = C ) )
=> ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( B @ r2_hidden ) )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(1153,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k1_funct_3 @ m2_relset_1 ) ) )
& ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k1_funct_3 @ v1_funct_2 ) ) )
& ( A @ k1_funct_3 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_3) ).
thf(8044,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k1_funct_3 @ m2_relset_1 ) ) )
& ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k1_funct_3 @ v1_funct_2 ) ) )
& ( A @ k1_funct_3 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(1015,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_1) ).
thf(7358,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
? [C: $i] :
( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(1831,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_lopclset) ).
thf(11635,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1831]) ).
thf(1022,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( E @ k2_relat_1 )
= C )
& ( ( D @ k2_relat_1 )
= B ) )
=> ( ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funct_2) ).
thf(7409,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( E @ k2_relat_1 )
= C )
& ( ( D @ k2_relat_1 )
= B ) )
=> ( ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(719,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ k15_funct_3 ) @ k10_relat_1 ) )
= ( B @ ( D @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k2_zfmisc_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_funct_3) ).
thf(5718,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ k15_funct_3 ) @ k10_relat_1 ) )
= ( B @ ( D @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k2_zfmisc_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(2047,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ r2_waybel_4 ) ) )
<=> ( ! [D: $i] :
~ ( ( C @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( D != B )
& ( A @ ( D @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d24_waybel_4) ).
thf(13007,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( ! [D: $i] :
~ ( ( C @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( D != B )
& ( A @ ( D @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ r2_waybel_4 ) ) ) )
& ( ( C @ ( B @ ( A @ r2_waybel_4 ) ) )
=> ( ! [D: $i] :
~ ( ( C @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( D != B )
& ( A @ ( D @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2047]) ).
thf(2062,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ g2_quantal1 ) ) ) ) )
= ( J @ ( I @ ( H @ ( G @ ( F @ g2_quantal1 ) ) ) ) ) )
=> ( ( E = J )
& ( D = I )
& ( C = H )
& ( B = G )
& ( A = F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g2_quantal1) ).
thf(13110,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ g2_quantal1 ) ) ) ) )
= ( J @ ( I @ ( H @ ( G @ ( F @ g2_quantal1 ) ) ) ) ) )
=> ( ( E = J )
& ( D = I )
& ( C = H )
& ( B = G )
& ( A = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2062]) ).
thf(942,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k1_tarski @ v1_fraenkel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_fraenkel) ).
thf(6868,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k1_tarski @ v1_fraenkel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(315,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k1_relat_1 )
= ( A @ k2_funct_1 @ k2_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( A @ k2_funct_1 @ k1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
thf(3762,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k1_relat_1 )
= ( A @ k2_funct_1 @ k2_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( A @ k2_funct_1 @ k1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(2071,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_realset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_realset1) ).
thf(13177,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2071]) ).
thf(2114,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(13351,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2114]) ).
thf(1159,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
<=> ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
& ( C @ ( B @ ( A @ r4_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_binop_1) ).
thf(8082,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
& ( C @ ( B @ ( A @ r4_binop_1 ) ) ) )
=> ( C @ ( B @ ( A @ r6_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
=> ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
& ( C @ ( B @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(1990,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ k1_tarski @ ( B @ r2_hidden ) ) )
=> ( A @ k1_tarski @ ( C @ r2_hidden ) ) )
& ( ( ( A @ k1_tarski @ ( C @ r2_hidden ) )
& ( A @ k1_tarski @ ( B @ r2_hidden ) ) )
=> ( A @ k1_tarski @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ r2_hidden ) ) ) ) ) )
& ~ ( A @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_card_fil) ).
thf(12666,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( ( C @ ( B @ r1_tarski ) )
& ( A @ k1_tarski @ ( B @ r2_hidden ) ) )
=> ( A @ k1_tarski @ ( C @ r2_hidden ) ) )
& ( ( ( A @ k1_tarski @ ( C @ r2_hidden ) )
& ( A @ k1_tarski @ ( B @ r2_hidden ) ) )
=> ( A @ k1_tarski @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ r2_hidden ) ) ) ) ) )
& ~ ( A @ k1_tarski @ ( k1_xboole_0 @ r2_hidden ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1990]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( C @ k5_funct_5 @ k1_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k3_funct_5 @ k1_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_funct_5) ).
thf(3230,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( C @ k5_funct_5 @ k1_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k3_funct_5 @ k1_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(1445,axiom,
( ( k1_xboole_0 @ ( k1_xboole_0 @ k1_funct_2 ) )
= ( k1_xboole_0 @ k6_relat_1 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_altcat_1) ).
thf(9604,plain,
( ( k1_xboole_0 @ ( k1_xboole_0 @ k1_funct_2 ) )
= ( k1_xboole_0 @ k6_relat_1 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445]) ).
thf(1657,axiom,
! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) )
& ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( ( D @ ( C @ k4_tarski ) )
!= B )
& ( A @ ( B @ r2_hidden ) ) ) )
=> ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funct_1) ).
thf(10673,plain,
! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) )
& ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( ( D @ ( C @ k4_tarski ) )
!= B )
& ( A @ ( B @ r2_hidden ) ) ) )
=> ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1657]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_cat_2 ) ) ) )
= ( D @ k5_funct_5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_cat_2) ).
thf(3549,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_cat_2 ) ) ) )
= ( D @ k5_funct_5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(855,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( A @ ( B @ r1_tarski ) )
& ( A @ ( C @ r7_relat_2 ) ) )
=> ( B @ ( C @ r7_relat_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_orders_1) ).
thf(6463,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( A @ ( B @ r1_tarski ) )
& ( A @ ( C @ r7_relat_2 ) ) )
=> ( B @ ( C @ r7_relat_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(243,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( B @ ( k5_numbers @ ( D @ m2_relset_1 ) ) )
& ( B @ ( k5_numbers @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C
= ( A @ k2_finseq_1 @ ( D @ ( B @ ( k5_numbers @ k2_partfun1 ) ) ) ) )
=> ( ( C @ k3_finseq_1 )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_finseq_2) ).
thf(3417,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( B @ ( k5_numbers @ ( D @ m2_relset_1 ) ) )
& ( B @ ( k5_numbers @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C
= ( A @ k2_finseq_1 @ ( D @ ( B @ ( k5_numbers @ k2_partfun1 ) ) ) ) )
=> ( ( C @ k3_finseq_1 )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ ( B @ ( A @ k5_partfun1 ) ) )
= ( B @ ( A @ k1_funct_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_funct_2) ).
thf(3509,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ ( B @ ( A @ k5_partfun1 ) ) )
= ( B @ ( A @ k1_funct_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(890,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k5_funcop_1 ) ) )
= ( A @ ( C @ ( B @ ( C @ k1_relat_1 @ k2_funcop_1 ) @ k13_funct_3 ) @ k5_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funcop_1) ).
thf(6619,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k5_funcop_1 ) ) )
= ( A @ ( C @ ( B @ ( C @ k1_relat_1 @ k2_funcop_1 ) @ k13_funct_3 ) @ k5_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(1637,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k5_subset_1 ) ) @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_subset_1) ).
thf(10567,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k5_subset_1 ) ) @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1637]) ).
thf(1506,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( A @ k2_tarski ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k1_funct_1 ) @ ( A @ ( C @ k1_funct_1 ) @ k2_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_funct_1) ).
thf(9901,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( A @ k2_tarski ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k1_funct_1 ) @ ( A @ ( C @ k1_funct_1 ) @ k2_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1506]) ).
thf(928,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k6_domain_1 ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_domain_1) ).
thf(6813,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k6_domain_1 ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( ( k1_numbers @ ( B @ m1_subset_1 ) )
& ( k1_numbers @ ( A @ m1_subset_1 ) ) )
=> ( k1_numbers @ ( B @ ( A @ k9_binop_2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_binop_2) ).
thf(3153,plain,
! [A: $i,B: $i] :
( ( ( k1_numbers @ ( B @ m1_subset_1 ) )
& ( k1_numbers @ ( A @ m1_subset_1 ) ) )
=> ( k1_numbers @ ( B @ ( A @ k9_binop_2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc37_membered) ).
thf(2590,plain,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(2365,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_subset_1) ).
thf(14570,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k7_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2365]) ).
thf(1264,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) @ k2_relat_1 )
= ( A @ ( B @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_relat_1) ).
thf(8682,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) @ k2_relat_1 )
= ( A @ ( B @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(133,axiom,
( ( k1_xboole_0 @ k4_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_relat_1) ).
thf(2947,plain,
( ( k1_xboole_0 @ k4_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v4_finsub_1 )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ m1_subset_1 ) )
& ( C @ ( A @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ k3_xboole_0 ) @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finsub_1) ).
thf(6796,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v4_finsub_1 )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ m1_subset_1 ) )
& ( C @ ( A @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ k3_xboole_0 ) @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(2142,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( A @ r6_binop_1 ) ) )
& ( F
= ( B @ ( D @ k1_realset1 ) ) )
& ( E
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( F @ ( E @ ( B @ r6_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_filter_2) ).
thf(13548,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( A @ r6_binop_1 ) ) )
& ( F
= ( B @ ( D @ k1_realset1 ) ) )
& ( E
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( F @ ( E @ ( B @ r6_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2142]) ).
thf(346,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( ( B @ k4_finseq_1 @ ( B @ k4_finseq_1 @ ( C @ m2_relset_1 ) ) )
& ( B @ k4_finseq_1 @ ( B @ k4_finseq_1 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ ( B @ ( C @ ( A @ ( k5_numbers @ ( B @ k4_finseq_1 @ ( B @ k4_finseq_1 @ k1_partfun1 ) ) ) ) ) @ m2_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_finseq_2) ).
thf(3912,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
=> ! [C: $i] :
( ( ( B @ k4_finseq_1 @ ( B @ k4_finseq_1 @ ( C @ m2_relset_1 ) ) )
& ( B @ k4_finseq_1 @ ( B @ k4_finseq_1 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ ( B @ ( C @ ( A @ ( k5_numbers @ ( B @ k4_finseq_1 @ ( B @ k4_finseq_1 @ k1_partfun1 ) ) ) ) ) @ m2_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(161,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( A @ k2_funct_1 @ k2_funct_1 )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funct_1) ).
thf(3098,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( A @ k2_funct_1 @ k2_funct_1 )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(1542,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_subset_1) ).
thf(10061,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1542]) ).
thf(1660,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_zfmisc_1) ).
thf(10705,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1660]) ).
thf(745,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != C )
& ( A != B )
& ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_zfmisc_1) ).
thf(5878,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != C )
& ( A != B )
& ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(925,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ r2_hidden ) )
=> ( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funcop_1) ).
thf(6798,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ r2_hidden ) )
=> ( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(829,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ~ ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ! [B: $i] :
( ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ m1_orders_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( C @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_orders_1) ).
thf(6323,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ~ ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ! [B: $i] :
( ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( C @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( A @ ( B @ m1_orders_1 ) ) )
& ( ( A @ ( B @ m1_orders_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( C @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(1016,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m1_nat_lat ) ) ) )
<=> ( C @ ( D @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_nat_lat) ).
thf(7368,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( C @ ( D @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ ( D @ m1_nat_lat ) ) ) ) )
& ( ( C @ ( B @ ( A @ ( D @ m1_nat_lat ) ) ) )
=> ( C @ ( D @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(1000,axiom,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfmisc_1) ).
thf(7253,plain,
( ( k1_xboole_0 @ k3_tarski )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(1578,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v2_setfam_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_triang_1) ).
thf(10244,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v2_setfam_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1578]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_mcart_1) ).
thf(4711,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(933,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= ( F @ ( E @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funcop_1) ).
thf(6830,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= ( F @ ( E @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(760,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v6_monoid_0 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_monoid_0) ).
thf(5982,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) )
=> ( D = E ) ) ) ) )
=> ( A @ ( B @ v6_monoid_0 ) ) )
& ( ( A @ ( B @ v6_monoid_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(147,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( B @ k4_relat_1 @ ( A @ r1_tarski ) )
=> ( B @ ( A @ k4_relat_1 @ r1_tarski ) ) )
& ( ( B @ ( A @ k4_relat_1 @ r1_tarski ) )
=> ( B @ k4_relat_1 @ ( A @ r1_tarski ) ) )
& ( ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_waybel10) ).
thf(3012,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( B @ k4_relat_1 @ ( A @ r1_tarski ) )
=> ( B @ ( A @ k4_relat_1 @ r1_tarski ) ) )
& ( ( B @ ( A @ k4_relat_1 @ r1_tarski ) )
=> ( B @ k4_relat_1 @ ( A @ r1_tarski ) ) )
& ( ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(2190,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(13796,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2190]) ).
thf(2151,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_cantor_1 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_cantor_1) ).
thf(13586,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_cantor_1 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2151]) ).
thf(628,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_membered) ).
thf(5265,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(415,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v3_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_binop_1) ).
thf(4215,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= C ) )
=> ( A @ ( B @ v3_binop_1 ) ) )
& ( ( A @ ( B @ v3_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(884,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k10_relat_1 ) @ v1_finset_1 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finset_1) ).
thf(6602,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k10_relat_1 ) @ v1_finset_1 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(1319,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( A @ ( B @ k8_funct_2 ) ) ) @ k1_tarski @ ( C @ ( A @ ( B @ k3_funct_2 ) ) ) @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_setwiseo) ).
thf(8988,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( A @ ( B @ k8_funct_2 ) ) ) @ k1_tarski @ ( C @ ( A @ ( B @ k3_funct_2 ) ) ) @ ( D @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(1616,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
<=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(10463,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1616]) ).
thf(2255,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ a_4_1_domain_1 ) ) ) @ ( A @ r2_hidden ) )
<=> ? [F: $i,G: $i] :
( ( E @ ( G @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_1_domain_1) ).
thf(14078,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [F: $i,G: $i] :
( ( E @ ( G @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( C @ ( B @ a_4_1_domain_1 ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( E @ ( D @ ( C @ ( B @ a_4_1_domain_1 ) ) ) @ ( A @ r2_hidden ) )
=> ? [F: $i,G: $i] :
( ( E @ ( G @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2255]) ).
thf(1868,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_subset_1) ).
thf(11881,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k6_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1868]) ).
thf(1732,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k5_finsub_1 )
= ( A @ k1_zfmisc_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finsub_1) ).
thf(11080,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ( ( A @ k5_finsub_1 )
= ( A @ k1_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1732]) ).
thf(463,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_relset_1) ).
thf(4479,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(1119,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(7813,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(1518,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).
thf(9950,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1518]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k8_relat_1 ) @ k2_relat_1 @ ( A @ r2_hidden ) )
<=> ( ( C @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
thf(4105,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( ( C @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k8_relat_1 ) @ k2_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k8_relat_1 ) @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( ( C @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_2) ).
thf(4090,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ ( B @ ( A @ k1_tarski @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(1062,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( E @ ( B @ k2_setwiseo ) @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_setwiseo) ).
thf(7573,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( E @ ( B @ k2_setwiseo ) @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(714,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k1_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_setwiseo) ).
thf(5701,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k1_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(775,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( C @ k2_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_funct_2) ).
thf(6046,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( C @ k2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(475,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ? [B: $i] :
( ( ( B @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funct_1) ).
thf(4543,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ? [B: $i] :
( ( ( B @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(682,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) )
= ( B @ k3_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(5550,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) )
= ( B @ k3_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(1520,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k1_funct_4 ) )
= ( C @ ( A @ k1_funct_4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_funct_4) ).
thf(9956,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k1_funct_4 ) )
= ( C @ ( A @ k1_funct_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1520]) ).
thf(594,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( B @ v1_realset1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_tex_2) ).
thf(5120,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( B @ v1_realset1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(1513,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( E @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_partfun1) ).
thf(9933,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( E @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1513]) ).
thf(1677,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
thf(10775,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1677]) ).
thf(1353,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v7_altcat_1 )
<=> ! [B: $i] :
~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ~ ( ( ( B @ ( A @ k1_funct_1 ) )
= ( D @ ( C @ k5_relat_1 ) ) )
& ( B
= ( C @ ( D @ k4_tarski ) ) ) ) ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_altcat_1) ).
thf(9184,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i] :
~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ~ ( ( ( B @ ( A @ k1_funct_1 ) )
= ( D @ ( C @ k5_relat_1 ) ) )
& ( B
= ( C @ ( D @ k4_tarski ) ) ) ) ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ v7_altcat_1 ) )
& ( ( A @ v7_altcat_1 )
=> ! [B: $i] :
~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ~ ( ( ( B @ ( A @ k1_funct_1 ) )
= ( D @ ( C @ k5_relat_1 ) ) )
& ( B
= ( C @ ( D @ k4_tarski ) ) ) ) ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).
thf(1180,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ k2_funct_5 )
= ( D @ ( B @ k2_tarski ) ) )
& ( ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ k1_funct_5 )
= ( C @ ( A @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_5) ).
thf(8182,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ k2_funct_5 )
= ( D @ ( B @ k2_tarski ) ) )
& ( ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ k1_funct_5 )
= ( C @ ( A @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(1455,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A
= ( A @ a_1_0_domain_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_domain_1) ).
thf(9644,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A
= ( A @ a_1_0_domain_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455]) ).
thf(2379,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_cantor_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_cantor_1) ).
thf(14602,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k2_cantor_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2379]) ).
thf(246,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k4_finseq_1 @ ( B @ r2_hidden ) )
=> ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finseq_3) ).
thf(3429,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k4_finseq_1 @ ( B @ r2_hidden ) )
=> ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1200,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_relat_1 @ ( C @ m1_eqrel_1 ) )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_1_pua2mss1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( A
= ( D @ ( B @ k7_relat_1 ) ) )
& ( C @ ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_pua2mss1) ).
thf(8335,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_relat_1 @ ( C @ m1_eqrel_1 ) )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ( A
= ( D @ ( B @ k7_relat_1 ) ) )
& ( C @ ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) ) )
=> ( C @ ( B @ a_2_1_pua2mss1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_1_pua2mss1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( A
= ( D @ ( B @ k7_relat_1 ) ) )
& ( C @ ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(686,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_filter_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_filter_1) ).
thf(5565,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_filter_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(1241,axiom,
( ( k1_xboole_0 @ k2_funct_4 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funct_5) ).
thf(8551,plain,
( ( k1_xboole_0 @ k2_funct_4 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(1980,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( ( A
= ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_domain_1) ).
thf(12590,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( ( ! [E: $i] :
( ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) )
=> ( A @ ( E @ r2_hidden ) ) )
& ( ( A @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) )
=> ( A
= ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) ) )
& ( ( A
= ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) )
=> ! [E: $i] :
( ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) )
=> ( A @ ( E @ r2_hidden ) ) )
& ( ( A @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1980]) ).
thf(1729,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( ( C @ ( E @ ( D @ k5_relat_1 ) @ k1_funct_1 ) )
= ( C @ ( D @ k1_funct_1 ) @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_2) ).
thf(11072,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( ( C @ ( E @ ( D @ k5_relat_1 ) @ k1_funct_1 ) )
= ( C @ ( D @ k1_funct_1 ) @ ( E @ k1_funct_1 ) ) )
| ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1729]) ).
thf(691,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k3_pua2mss1 )
= ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_relset_2) ).
thf(5589,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k3_pua2mss1 )
= ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(40,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m2_finseq_1 ) )
=> ( C @ ( F @ ( D @ ( E @ k5_funcop_1 ) ) @ m2_finseq_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_finseq_2) ).
thf(2607,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m2_finseq_1 ) )
=> ( C @ ( F @ ( D @ ( E @ k5_funcop_1 ) ) @ m2_finseq_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1524,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k15_funct_3 ) @ k2_relat_1 )
= ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_zfmisc_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_funct_3) ).
thf(9978,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k15_funct_3 ) @ k2_relat_1 )
= ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_zfmisc_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1524]) ).
thf(1255,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
<=> ( C = k1_xboole_0 ) )
| ( A = k1_xboole_0 ) ) )
& ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
<=> ( A
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).
thf(8635,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B = k1_xboole_0 )
=> ( ( ( ( C = k1_xboole_0 )
=> ( B @ ( A @ ( C @ v1_funct_2 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
=> ( C = k1_xboole_0 ) ) )
| ( A = k1_xboole_0 ) ) )
& ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ( A
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) )
=> ( B @ ( A @ ( C @ v1_funct_2 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
=> ( A
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(2104,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_cantor_1 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_yellow_9) ).
thf(13317,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_cantor_1 ) )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2104]) ).
thf(2264,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(14124,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2264]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_funct_1) ).
thf(4647,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(813,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r1_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_binop_1) ).
thf(6246,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r1_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r1_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(289,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_sysrel) ).
thf(3648,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(1244,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k5_finsub_1 @ ( F @ m1_subset_1 ) )
=> ~ ( ( ( D @ ( F @ ( E @ ( B @ k5_setwiseo ) ) @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
!= ( D @ ( F @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( D @ ( E @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) )
& ( F != k1_xboole_0 )
& ( E != k1_xboole_0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_setwiseo) ).
thf(8568,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k5_finsub_1 @ ( F @ m1_subset_1 ) )
=> ~ ( ( ( D @ ( F @ ( E @ ( B @ k5_setwiseo ) ) @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
!= ( D @ ( F @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( D @ ( E @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) )
& ( F != k1_xboole_0 )
& ( E != k1_xboole_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(369,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) )
<=> ( ( A @ k4_finseq_1 )
= ( B @ k4_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_finseq_3) ).
thf(4011,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( A @ k4_finseq_1 )
= ( B @ k4_finseq_1 ) )
=> ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) )
& ( ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) )
=> ( ( A @ k4_finseq_1 )
= ( B @ k4_finseq_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(2131,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_fraenkel )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_fraenkel) ).
thf(13457,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_fraenkel )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ! [D: $i] :
( ( C @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) )
=> ( B @ ( A @ ( C @ m1_fraenkel ) ) ) )
& ( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
=> ! [D: $i] :
( ( C @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2131]) ).
thf(544,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_enumset1 ) ) )
= ( B @ ( C @ ( A @ k1_enumset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_enumset1) ).
thf(4870,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_enumset1 ) ) )
= ( B @ ( C @ ( A @ k1_enumset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(901,axiom,
! [A: $i,B: $i] :
( ( B @ k3_pua2mss1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A
= ( C @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_relset_2) ).
thf(6665,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A
= ( C @ k1_tarski ) ) )
=> ( B @ k3_pua2mss1 @ ( A @ r2_hidden ) ) )
& ( ( B @ k3_pua2mss1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A
= ( C @ k1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(1601,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k3_realset1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k3_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k3_realset1 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_realset1) ).
thf(10358,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k3_realset1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k3_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k3_realset1 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1601]) ).
thf(1253,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
<=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
thf(8622,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( B = C ) )
=> ( A @ v2_funct_1 ) )
& ( ( A @ v2_funct_1 )
=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(373,axiom,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) ) )
=> ( A @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_grcat_1) ).
thf(4026,plain,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) ) )
=> ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(1048,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k9_funcop_1 ) ) ) )
= ( D @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_funcop_1) ).
thf(7524,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k9_funcop_1 ) ) ) )
= ( D @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(1717,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i,H: $i] :
( ( A @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
<=> ( D @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) ) )
& ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_zfmisc_1) ).
thf(11014,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i,H: $i] :
( ( ( D @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) ) ) )
& ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1717]) ).
thf(2059,axiom,
( ! [A: $i] :
( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s12_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s12_funct_2 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s12_funct_2) ).
thf(13095,plain,
( ! [A: $i] :
( ( f1_s12_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s12_funct_2 @ ( A @ f3_s12_funct_2 @ r2_hidden ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s12_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s12_funct_2 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s12_funct_2 @ ( f1_s12_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2059]) ).
thf(390,axiom,
k1_numbers @ ( k5_numbers @ r1_tarski ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_numbers) ).
thf(4110,plain,
k1_numbers @ ( k5_numbers @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(1274,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_partfun1) ).
thf(8747,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(1412,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funct_2) ).
thf(9428,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( A @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412]) ).
thf(1438,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ k7_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funcop_1) ).
thf(9565,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ k7_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1438]) ).
thf(1874,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( C @ ( B @ k1_funct_2 ) @ ( E @ r2_hidden ) )
& ( B @ ( A @ k1_funct_2 ) @ ( D @ r2_hidden ) ) )
=> ( C @ ( A @ k1_funct_2 ) @ ( E @ ( D @ k5_relat_1 ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_altcat_1) ).
thf(11917,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( C @ ( B @ k1_funct_2 ) @ ( E @ r2_hidden ) )
& ( B @ ( A @ k1_funct_2 ) @ ( D @ r2_hidden ) ) )
=> ( C @ ( A @ k1_funct_2 ) @ ( E @ ( D @ k5_relat_1 ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1874]) ).
thf(1489,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v2_funct_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( C @ k2_funct_1 @ ( D @ ( C @ k5_relat_1 ) @ k5_relat_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( D @ ( B @ ( C @ k1_funct_1 ) @ ( A @ ( C @ k1_funct_1 ) @ k4_tarski ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow21) ).
thf(9813,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v2_funct_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( ( D @ ( B @ ( C @ k1_funct_1 ) @ ( A @ ( C @ k1_funct_1 ) @ k4_tarski ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( C @ k2_funct_1 @ ( D @ ( C @ k5_relat_1 ) @ k5_relat_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ k2_funct_1 @ ( D @ ( C @ k5_relat_1 ) @ k5_relat_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( B @ ( C @ k1_funct_1 ) @ ( A @ ( C @ k1_funct_1 ) @ k4_tarski ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489]) ).
thf(910,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( A @ ( B @ k2_zfmisc_1 ) @ ( C @ k2_funct_4 @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_4) ).
thf(6727,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( A @ ( B @ k2_zfmisc_1 ) @ ( C @ k2_funct_4 @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(1557,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_group_1 ) )
= ( D @ ( C @ g1_group_1 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_group_1) ).
thf(10138,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_group_1 ) )
= ( D @ ( C @ g1_group_1 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1557]) ).
thf(639,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_1_pua2mss1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ~ ( C @ ( E @ r1_xboole_0 ) )
& ( A
= ( C @ ( E @ k3_xboole_0 ) ) )
& ( D @ ( B @ k1_zfmisc_1 @ ( E @ m2_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_pua2mss1) ).
thf(5316,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ~ ( C @ ( E @ r1_xboole_0 ) )
& ( A
= ( C @ ( E @ k3_xboole_0 ) ) )
& ( D @ ( B @ k1_zfmisc_1 @ ( E @ m2_subset_1 ) ) ) )
=> ( D @ ( C @ ( B @ a_3_1_pua2mss1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_1_pua2mss1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ~ ( C @ ( E @ r1_xboole_0 ) )
& ( A
= ( C @ ( E @ k3_xboole_0 ) ) )
& ( D @ ( B @ k1_zfmisc_1 @ ( E @ m2_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(897,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( D @ ( B @ r1_partfun1 ) ) )
=> ( C @ ( B @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t152_funct_2) ).
thf(6655,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( D @ ( B @ r1_partfun1 ) ) )
=> ( C @ ( B @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1730,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_trees_3 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_pre_circ) ).
thf(11075,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_trees_3 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1730]) ).
thf(1011,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
<=> ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relset_2) ).
thf(7345,plain,
! [A: $i,B: $i] :
( ( ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(1966,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_pboole) ).
thf(12522,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1966]) ).
thf(320,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) )
& ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_1) ).
thf(3781,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) )
& ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(458,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C
= ( B @ ( A @ ( D @ k5_funcop_1 ) ) ) )
& ( D @ k1_relat_1 @ ( B @ k2_relat_1 @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( ( C @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_finseq_2) ).
thf(4440,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C
= ( B @ ( A @ ( D @ k5_funcop_1 ) ) ) )
& ( D @ k1_relat_1 @ ( B @ k2_relat_1 @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( ( C @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(1962,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i,G: $i] :
( ( ( E @ ( G @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) ) )
=> ( ( F @ ( G @ ( C @ k1_binop_1 ) ) )
= ( F @ ( G @ ( D @ ( E @ ( A @ ( B @ k12_mcart_1 ) ) ) @ ( C @ k7_relat_1 ) @ k1_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_altcat_1) ).
thf(12511,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i,G: $i] :
( ( ( E @ ( G @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) ) )
=> ( ( F @ ( G @ ( C @ k1_binop_1 ) ) )
= ( F @ ( G @ ( D @ ( E @ ( A @ ( B @ k12_mcart_1 ) ) ) @ ( C @ k7_relat_1 ) @ k1_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1962]) ).
thf(1361,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( B @ ( A @ r1_filter_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_filter_2) ).
thf(9218,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( B @ ( A @ r1_filter_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).
thf(604,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( A @ k2_funct_4 @ v2_funct_1 )
& ( A @ k2_funct_4 @ v1_funct_1 )
& ( A @ k2_funct_4 @ v1_relat_1 )
& ( A @ k2_funct_4 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_functor0) ).
thf(5163,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( A @ k2_funct_4 @ v2_funct_1 )
& ( A @ k2_funct_4 @ v1_funct_1 )
& ( A @ k2_funct_4 @ v1_relat_1 )
& ( A @ k2_funct_4 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(493,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ k1_tarski ) )
=> ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_zfmisc_1) ).
thf(4650,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ k1_tarski ) )
=> ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(1207,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(8370,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(706,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k2_funct_4 @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B @ ( A @ k4_tarski ) @ ( C @ k2_funct_4 @ k1_funct_1 ) )
= ( A @ ( B @ k4_tarski ) @ ( C @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_4) ).
thf(5674,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k2_funct_4 @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B @ ( A @ k4_tarski ) @ ( C @ k2_funct_4 @ k1_funct_1 ) )
= ( A @ ( B @ k4_tarski ) @ ( C @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(1308,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) )
= ( B @ k2_relat_1 @ ( A @ k2_zfmisc_1 ) @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_relat_1) ).
thf(8947,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) )
= ( B @ k2_relat_1 @ ( A @ k2_zfmisc_1 ) @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).
thf(1184,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= B ) )
=> ( A
= ( B @ ( A @ k1_relat_1 @ k2_funcop_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funcop_1) ).
thf(8210,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= B ) )
=> ( A
= ( B @ ( A @ k1_relat_1 @ k2_funcop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(1946,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ a_4_1_domain_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_domain_1) ).
thf(12421,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ a_4_1_domain_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1946]) ).
thf(991,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( A @ ( E @ m2_relset_1 ) ) )
& ( D @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( E @ ( D @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( C @ ( B @ ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_cat_1) ).
thf(7188,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( A @ ( E @ m2_relset_1 ) ) )
& ( D @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( E @ ( D @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( C @ ( B @ ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( B @ ( E @ ( D @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(2354,axiom,
! [A: $i] :
( ( a_0_33_fraenkel @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ~ ( f2_s18_fraenkel @ ( B @ f3_s18_fraenkel @ r2_hidden ) )
& ( B @ p1_s18_fraenkel )
& ( A
= ( B @ f3_s18_fraenkel ) )
& ( f1_s18_fraenkel @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_33_fraenkel) ).
thf(14478,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( f2_s18_fraenkel @ ( B @ f3_s18_fraenkel @ r2_hidden ) )
& ( B @ p1_s18_fraenkel )
& ( A
= ( B @ f3_s18_fraenkel ) )
& ( f1_s18_fraenkel @ ( B @ m1_subset_1 ) ) )
=> ( a_0_33_fraenkel @ ( A @ r2_hidden ) ) )
& ( ( a_0_33_fraenkel @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ~ ( f2_s18_fraenkel @ ( B @ f3_s18_fraenkel @ r2_hidden ) )
& ( B @ p1_s18_fraenkel )
& ( A
= ( B @ f3_s18_fraenkel ) )
& ( f1_s18_fraenkel @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2354]) ).
thf(919,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B
= ( C @ k1_relat_1 ) ) ) )
& ~ ( ( B != k1_xboole_0 )
& ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_1) ).
thf(6759,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B
= ( C @ k1_relat_1 ) ) ) )
& ~ ( ( B != k1_xboole_0 )
& ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_partfun1) ).
thf(2901,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(1130,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_relat_1) ).
thf(7871,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(1029,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( C @ v1_setwiseo ) )
& ( B @ ( C @ v3_binop_1 ) )
& ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) ) )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( D @ ( D @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( D @ ( D @ ( D @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( E @ v1_setwiseo ) )
& ( D @ ( E @ v3_binop_1 ) )
& ( D @ ( E @ v2_binop_1 ) )
& ( D @ ( E @ v1_binop_1 ) ) )
=> ! [F: $i] :
( ( ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( D @ ( B @ ( G @ m2_relset_1 ) ) )
& ( D @ ( B @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( B @ ( I @ m1_subset_1 ) )
=> ( ( I @ ( H @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) )
= ( I @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) @ ( H @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( D @ ( D @ k2_binop_1 ) ) ) ) ) ) ) ) )
& ( ( C @ ( B @ k3_binop_1 ) @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( D @ k3_binop_1 ) ) ) )
=> ! [H: $i] :
( ( A @ k5_finsub_1 @ ( H @ m1_subset_1 ) )
=> ( ( F @ ( H @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) )
= ( G @ ( F @ ( D @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( H @ ( E @ ( D @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_setwiseo) ).
thf(7452,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( C @ v1_setwiseo ) )
& ( B @ ( C @ v3_binop_1 ) )
& ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) ) )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( D @ ( D @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( D @ ( D @ ( D @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( E @ v1_setwiseo ) )
& ( D @ ( E @ v3_binop_1 ) )
& ( D @ ( E @ v2_binop_1 ) )
& ( D @ ( E @ v1_binop_1 ) ) )
=> ! [F: $i] :
( ( ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( D @ ( B @ ( G @ m2_relset_1 ) ) )
& ( D @ ( B @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( B @ ( I @ m1_subset_1 ) )
=> ( ( I @ ( H @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) )
= ( I @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) @ ( H @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( D @ ( D @ k2_binop_1 ) ) ) ) ) ) ) ) )
& ( ( C @ ( B @ k3_binop_1 ) @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( D @ k3_binop_1 ) ) ) )
=> ! [H: $i] :
( ( A @ k5_finsub_1 @ ( H @ m1_subset_1 ) )
=> ( ( F @ ( H @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) )
= ( G @ ( F @ ( D @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( H @ ( E @ ( D @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(1486,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finseq_1) ).
thf(9801,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486]) ).
thf(788,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(6117,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(2144,axiom,
! [A: $i] :
( ( A @ k6_relat_1 @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= ( A @ k6_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_sysrel) ).
thf(13557,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= ( A @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2144]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k3_funct_3 @ k10_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_funct_3) ).
thf(2844,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k3_funct_3 @ k10_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1725,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( C @ ( B @ r1_tarski ) )
& ( ( C @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( A @ ( C @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_zfmisc_1) ).
thf(11055,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( C @ ( B @ r1_tarski ) )
& ( ( C @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( A @ ( C @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1725]) ).
thf(456,axiom,
! [A: $i] :
( ( A @ k6_partfun1 )
= ( A @ k6_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(4435,plain,
! [A: $i] :
( ( A @ k6_partfun1 )
= ( A @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(2242,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k7_setfam_1 ) )
= ( B @ ( A @ a_2_1_card_fil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_card_fil) ).
thf(14025,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k7_setfam_1 ) )
= ( B @ ( A @ a_2_1_card_fil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2242]) ).
thf(1183,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_pboole) ).
thf(8204,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(2310,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_relset_2) ).
thf(14301,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2310]) ).
thf(2183,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( k1_xboole_0 @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_partfun1) ).
thf(13764,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( k1_xboole_0 @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2183]) ).
thf(1105,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_partfun1 @ ( A @ ( A @ k3_funct_2 ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_borsuk_1) ).
thf(7748,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_partfun1 @ ( A @ ( A @ k3_funct_2 ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(1852,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( B @ r2_binop_1 ) ) )
& ( E @ ( C @ ( A @ r2_binop_1 ) ) ) )
<=> ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r2_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_filter_1) ).
thf(11786,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r2_binop_1 ) ) )
=> ( ( F @ ( D @ ( B @ r2_binop_1 ) ) )
& ( E @ ( C @ ( A @ r2_binop_1 ) ) ) ) )
& ( ( ( F @ ( D @ ( B @ r2_binop_1 ) ) )
& ( E @ ( C @ ( A @ r2_binop_1 ) ) ) )
=> ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r2_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1852]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_partfun1) ).
thf(3717,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(611,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_funcop_1 ) @ v1_funct_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funcop_1) ).
thf(5192,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_funcop_1 ) @ v1_funct_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(896,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ~ ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( C
= ( B @ ( A @ k1_funct_1 ) ) )
<=> ( C = k1_xboole_0 ) ) )
& ( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( C
= ( B @ ( A @ k1_funct_1 ) ) )
<=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
thf(6640,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ~ ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( ( C = k1_xboole_0 )
=> ( C
= ( B @ ( A @ k1_funct_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_funct_1 ) ) )
=> ( C = k1_xboole_0 ) ) ) )
& ( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( C
= ( B @ ( A @ k1_funct_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_funct_1 ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(1434,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k4_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_mcart_1) ).
thf(9540,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k4_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1434]) ).
thf(994,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_relset_1) ).
thf(7220,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(1799,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( C @ ( A @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).
thf(11449,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( C @ ( A @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) ) )
& ( ( B @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( C @ ( A @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1799]) ).
thf(1237,axiom,
k5_numbers != k1_numbers,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_numbers) ).
thf(8539,plain,
k5_numbers != k1_numbers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(946,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ k2_tarski ) @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_subset_1) ).
thf(6887,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ k2_tarski ) @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(2007,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(12763,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ k3_subset_1 ) @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2007]) ).
thf(2004,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k1_relset_2 ) ) @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ ( B @ ( A @ k8_setfam_1 ) @ ( A @ k5_subset_1 ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_relset_2) ).
thf(12757,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k1_relset_2 ) ) @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ ( B @ ( A @ k8_setfam_1 ) @ ( A @ k5_subset_1 ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2004]) ).
thf(1694,axiom,
! [A: $i] : ( A @ ( A @ ( A @ k6_relat_1 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_relset_1) ).
thf(10854,plain,
! [A: $i] : ( A @ ( A @ ( A @ k6_relat_1 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1694]) ).
thf(1886,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(12009,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1886]) ).
thf(831,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( ( A @ v1_realset1 )
& ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ v1_tex_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_tex_2) ).
thf(6342,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( ( A @ v1_realset1 )
& ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ v1_tex_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(1187,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k7_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(8224,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k7_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(1341,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( C @ k7_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_relat_1) ).
thf(9116,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( B @ ( A @ k3_xboole_0 ) @ ( C @ k7_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341]) ).
thf(1600,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
= D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_binop_1) ).
thf(10351,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
= D ) )
=> ( C @ ( B @ ( A @ r1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ k1_binop_1 ) ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1600]) ).
thf(1891,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( B @ ( A @ k2_cantor_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_cantor_1) ).
thf(12026,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( B @ ( A @ k2_cantor_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1891]) ).
thf(1952,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_binop_1) ).
thf(12447,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r5_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1952]) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r2_wellord2 ) ) )
& ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( C @ k4_card_3 @ ( B @ k4_card_3 @ r2_wellord2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_funct_6) ).
thf(3103,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ r2_wellord2 ) ) )
& ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( C @ k4_card_3 @ ( B @ k4_card_3 @ r2_wellord2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1295,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ ( E @ ( B @ k3_setwiseo ) ) @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_setwiseo) ).
thf(8851,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ ( E @ ( B @ k3_setwiseo ) ) @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295]) ).
thf(1595,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_funct_1) ).
thf(10336,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1595]) ).
thf(1574,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_mcart_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ a_6_0_domain_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_domain_1) ).
thf(10230,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_mcart_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ a_6_0_domain_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1574]) ).
thf(1424,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ k1_funct_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
& ( B @ ( A @ k1_funct_1 ) @ ( D @ r2_hidden ) ) )
=> ( ( ( E @ ( C @ ( A @ k3_pralg_3 ) @ k10_relat_1 ) @ ( D @ k1_tarski @ ( B @ ( A @ k3_pralg_3 ) @ k10_relat_1 ) @ r1_tarski ) )
<=> ( ( E @ ( D @ r2_hidden ) )
& ( B = C ) ) )
| ( E
= ( C @ ( A @ k1_funct_1 ) ) )
| ( ( A @ k4_card_3 )
= k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_yellow17) ).
thf(9476,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( A @ k1_funct_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
& ( B @ ( A @ k1_funct_1 ) @ ( D @ r2_hidden ) ) )
=> ( ( ( ( ( E @ ( D @ r2_hidden ) )
& ( B = C ) )
=> ( E @ ( C @ ( A @ k3_pralg_3 ) @ k10_relat_1 ) @ ( D @ k1_tarski @ ( B @ ( A @ k3_pralg_3 ) @ k10_relat_1 ) @ r1_tarski ) ) )
& ( ( E @ ( C @ ( A @ k3_pralg_3 ) @ k10_relat_1 ) @ ( D @ k1_tarski @ ( B @ ( A @ k3_pralg_3 ) @ k10_relat_1 ) @ r1_tarski ) )
=> ( ( E @ ( D @ r2_hidden ) )
& ( B = C ) ) ) )
| ( E
= ( C @ ( A @ k1_funct_1 ) ) )
| ( ( A @ k4_card_3 )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424]) ).
thf(1294,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_relat_1) ).
thf(8848,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).
thf(724,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
<=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_funct_2) ).
thf(5740,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) )
=> ( B @ v2_funct_1 ) )
& ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ v1_funct_1 )
& ( F @ v1_relat_1 ) )
=> ( ( E @ ( D @ k2_zfmisc_1 ) @ ( F @ k1_relat_1 @ r1_tarski ) )
=> ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k1_funct_2 ) @ ( F @ r2_hidden ) )
| ( ~ ( C @ ( A @ k1_funct_2 ) @ ( B @ k1_funct_2 ) @ ( F @ k5_funct_5 @ r2_hidden ) )
& ~ ( C @ ( B @ k1_funct_2 ) @ ( A @ k1_funct_2 ) @ ( F @ k3_funct_5 @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_6) ).
thf(3545,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ v1_funct_1 )
& ( F @ v1_relat_1 ) )
=> ( ( E @ ( D @ k2_zfmisc_1 ) @ ( F @ k1_relat_1 @ r1_tarski ) )
=> ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k1_funct_2 ) @ ( F @ r2_hidden ) )
| ( ~ ( C @ ( A @ k1_funct_2 ) @ ( B @ k1_funct_2 ) @ ( F @ k5_funct_5 @ r2_hidden ) )
& ~ ( C @ ( B @ k1_funct_2 ) @ ( A @ k1_funct_2 ) @ ( F @ k3_funct_5 @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(73,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) )
& ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).
thf(2723,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ ( A @ k2_funct_1 @ k5_relat_1 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) )
& ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(2160,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_tex_2) ).
thf(13626,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2160]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k10_relat_1 ) @ ( B @ k4_relat_1 @ k10_relat_1 ) @ ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t183_relat_1) ).
thf(2972,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k10_relat_1 ) @ ( B @ k4_relat_1 @ k10_relat_1 ) @ ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(284,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funct_1) ).
thf(3634,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k5_relat_1 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(758,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k11_setwiseo @ ( B @ ( A @ ( A @ k10_setwiseo ) ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_setwiseo) ).
thf(5977,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k11_setwiseo @ ( B @ ( A @ ( A @ k10_setwiseo ) ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(977,axiom,
! [A: $i,B: $i] :
( ( B @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(7064,plain,
! [A: $i,B: $i] :
( ( B @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_pua2mss1 ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_pua2mss1) ).
thf(2432,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_pua2mss1 ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1381,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v3_binop_1 ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k5_finsub_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ r1_tarski ) )
=> ( ( ( D @ ( F @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( D @ ( E @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( D @ ( F @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) ) )
| ( E = k1_xboole_0 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_setwiseo) ).
thf(9292,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v3_binop_1 ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k5_finsub_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ r1_tarski ) )
=> ( ( ( D @ ( F @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( D @ ( E @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( D @ ( F @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) ) )
| ( E = k1_xboole_0 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381]) ).
thf(1496,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_funct_2) ).
thf(9845,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496]) ).
thf(255,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k3_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_funct_3) ).
thf(3502,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k3_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1771,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(11260,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i] :
~ ( ! [D: $i,E: $i] :
( C
!= ( E @ ( D @ k4_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1771]) ).
thf(2230,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_filter_2) ).
thf(13970,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( C @ ( B @ ( A @ r1_filter_2 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2230]) ).
thf(1699,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r1_xboole_0 ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( D @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_subset_1) ).
thf(10908,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r1_xboole_0 ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( D @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1699]) ).
thf(595,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ v1_relat_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_relat_1) ).
thf(5123,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(2215,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_filter_1 ) ) )
=> ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_filter_1) ).
thf(13915,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_filter_1 ) ) )
=> ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2215]) ).
thf(1647,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_mssubfam) ).
thf(10599,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1647]) ).
thf(2072,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_1_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_1_domain_1) ).
thf(13179,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_1_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_1_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2072]) ).
thf(2143,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k2_funcop_1 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_funcop_1) ).
thf(13552,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k2_funcop_1 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2143]) ).
thf(395,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B
= ( A @ k2_funct_4 ) )
<=> ( ! [C: $i,D: $i] :
( ( A @ k1_relat_1 @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( D @ k4_tarski ) @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k4_tarski ) @ ( A @ k1_funct_1 ) ) ) )
& ! [C: $i] :
( ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
<=> ? [D: $i,E: $i] :
( ( A @ k1_relat_1 @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( C
= ( D @ ( E @ k4_tarski ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funct_4) ).
thf(4124,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i,D: $i] :
( ( A @ k1_relat_1 @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( D @ k4_tarski ) @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k4_tarski ) @ ( A @ k1_funct_1 ) ) ) )
& ! [C: $i] :
( ( ? [D: $i,E: $i] :
( ( A @ k1_relat_1 @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( C
= ( D @ ( E @ k4_tarski ) ) ) )
=> ( B @ k1_relat_1 @ ( C @ r2_hidden ) ) )
& ( ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ? [D: $i,E: $i] :
( ( A @ k1_relat_1 @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( C
= ( D @ ( E @ k4_tarski ) ) ) ) ) ) )
=> ( B
= ( A @ k2_funct_4 ) ) )
& ( ( B
= ( A @ k2_funct_4 ) )
=> ( ! [C: $i,D: $i] :
( ( A @ k1_relat_1 @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( D @ k4_tarski ) @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k4_tarski ) @ ( A @ k1_funct_1 ) ) ) )
& ! [C: $i] :
( ( ? [D: $i,E: $i] :
( ( A @ k1_relat_1 @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( C
= ( D @ ( E @ k4_tarski ) ) ) )
=> ( B @ k1_relat_1 @ ( C @ r2_hidden ) ) )
& ( ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ? [D: $i,E: $i] :
( ( A @ k1_relat_1 @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( C
= ( D @ ( E @ k4_tarski ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(356,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ k1_tarski @ ( A @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ k1_tarski @ ( B @ v9_monoid_0 ) )
& ( A @ k1_tarski @ ( B @ v8_monoid_0 ) )
& ( A @ k1_tarski @ ( B @ v5_monoid_0 ) )
& ( A @ k1_tarski @ ( B @ v3_binop_1 ) )
& ( A @ k1_tarski @ ( B @ v2_binop_1 ) )
& ( A @ k1_tarski @ ( B @ v1_binop_1 ) )
& ( A @ k1_tarski @ ( B @ v1_setwiseo ) )
& ( B
= ( A @ ( A @ ( A @ k4_tarski ) @ k1_tarski @ k2_funcop_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_monoid_0) ).
thf(3947,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_tarski @ ( A @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ k1_tarski @ ( A @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ k1_tarski @ ( B @ v9_monoid_0 ) )
& ( A @ k1_tarski @ ( B @ v8_monoid_0 ) )
& ( A @ k1_tarski @ ( B @ v5_monoid_0 ) )
& ( A @ k1_tarski @ ( B @ v3_binop_1 ) )
& ( A @ k1_tarski @ ( B @ v2_binop_1 ) )
& ( A @ k1_tarski @ ( B @ v1_binop_1 ) )
& ( A @ k1_tarski @ ( B @ v1_setwiseo ) )
& ( B
= ( A @ ( A @ ( A @ k4_tarski ) @ k1_tarski @ k2_funcop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(1545,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
<=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_subset_1) ).
thf(10071,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) )
& ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1545]) ).
thf(736,axiom,
k1_qc_lang1 @ k1_zfmisc_1 @ ( k4_qc_lang1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_qc_lang1) ).
thf(5825,plain,
k1_qc_lang1 @ k1_zfmisc_1 @ ( k4_qc_lang1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(730,axiom,
! [A: $i,B: $i] :
~ ( ~ ( ( ( B @ ( A @ k2_zfmisc_1 ) @ k2_relat_1 )
= B )
& ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_relat_1 )
= A ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_sysrel) ).
thf(5770,plain,
! [A: $i,B: $i] :
~ ( ~ ( ( ( B @ ( A @ k2_zfmisc_1 ) @ k2_relat_1 )
= B )
& ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_relat_1 )
= A ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(2009,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k5_relat_1 ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
<=> ? [F: $i] :
( ( B @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( F @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
thf(12770,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( B @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( F @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ? [F: $i] :
( ( B @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( F @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k5_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k5_relat_1 ) ) )
=> ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( B @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( F @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ? [F: $i] :
( ( B @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( F @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2009]) ).
thf(1010,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_subset_1) ).
thf(7343,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_tarski @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(2389,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s24_fraenkel @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
<=> ? [C: $i] :
( ( C @ ( B @ p1_s24_fraenkel ) )
& ( B
= ( C @ f4_s24_fraenkel ) )
& ( f3_s24_fraenkel @ ( C @ r2_hidden ) )
& ( f2_s24_fraenkel @ ( C @ m1_subset_1 ) ) ) ) )
& ( f1_s24_fraenkel @ k5_finsub_1 @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s24_fraenkel) ).
thf(14644,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s24_fraenkel @ ( B @ m1_subset_1 ) )
=> ( ( ? [C: $i] :
( ( C @ ( B @ p1_s24_fraenkel ) )
& ( B
= ( C @ f4_s24_fraenkel ) )
& ( f3_s24_fraenkel @ ( C @ r2_hidden ) )
& ( f2_s24_fraenkel @ ( C @ m1_subset_1 ) ) )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ? [C: $i] :
( ( C @ ( B @ p1_s24_fraenkel ) )
& ( B
= ( C @ f4_s24_fraenkel ) )
& ( f3_s24_fraenkel @ ( C @ r2_hidden ) )
& ( f2_s24_fraenkel @ ( C @ m1_subset_1 ) ) ) ) ) )
& ( f1_s24_fraenkel @ k5_finsub_1 @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2389]) ).
thf(518,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_relat_1) ).
thf(4760,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(498,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k6_partfun1 @ ( A @ k6_partfun1 @ ( C @ ( C @ ( B @ ( B @ ( A @ ( A @ k16_funct_3 ) ) ) ) ) @ ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ ( A @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_functor0) ).
thf(4665,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k6_partfun1 @ ( A @ k6_partfun1 @ ( C @ ( C @ ( B @ ( B @ ( A @ ( A @ k16_funct_3 ) ) ) ) ) @ ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ ( A @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(2082,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_funcop_1) ).
thf(13223,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2082]) ).
thf(2284,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(14188,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2284]) ).
thf(397,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) @ ( C @ ( A @ k7_relat_1 ) @ k1_funct_4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_funct_4) ).
thf(4156,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) @ ( C @ ( A @ k7_relat_1 ) @ k1_funct_4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(725,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( B
!= ( E @ k1_tarski ) )
& ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_funct_2) ).
thf(5750,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( B
!= ( E @ k1_tarski ) )
& ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(2046,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(13003,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k2_zfmisc_1 ) @ r1_tarski ) )
| ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( D @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2046]) ).
thf(1402,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( A @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ k1_relat_1 @ ( B @ ( A @ k9_funct_7 ) @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ k9_funct_7 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funct_7) ).
thf(9394,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( A @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ k1_relat_1 @ ( B @ ( A @ k9_funct_7 ) @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ k9_funct_7 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402]) ).
thf(295,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k3_pralg_3 ) @ v1_funct_1 )
& ( B @ ( A @ k3_pralg_3 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_pralg_3) ).
thf(3688,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k3_pralg_3 ) @ v1_funct_1 )
& ( B @ ( A @ k3_pralg_3 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(1077,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ k13_funct_3 ) @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) @ ( A @ k13_funct_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funcop_1) ).
thf(7628,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ k13_funct_3 ) @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) @ ( A @ k13_funct_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(472,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) @ ( B @ ( A @ ( A @ k3_funct_2 ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funct_2) ).
thf(4511,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) @ ( B @ ( A @ ( A @ k3_funct_2 ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(575,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_setfam_1) ).
thf(5024,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(419,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_binop_1) ).
thf(4249,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r2_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1248,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k4_card_fil @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ v6_ordinal1 )
=> ( A @ ( B @ k3_tarski @ m1_card_fil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_card_fil) ).
thf(8610,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k4_card_fil @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ v6_ordinal1 )
=> ( A @ ( B @ k3_tarski @ m1_card_fil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_xboole_1) ).
thf(3976,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(245,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B
= ( C @ ( A @ k5_relat_1 ) ) )
& ( C @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) ) )
=> ( ( B @ k3_finseq_1 )
= ( A @ k3_finseq_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_finseq_2) ).
thf(3425,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B
= ( C @ ( A @ k5_relat_1 ) ) )
& ( C @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) ) )
=> ( ( B @ k3_finseq_1 )
= ( A @ k3_finseq_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(523,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( B @ k6_subset_1 ) ) @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) )
=> ( F @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( E @ ( A @ k6_subset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_7) ).
thf(4778,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( B @ k6_subset_1 ) ) @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) )
=> ( F @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( E @ ( A @ k6_subset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(1158,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( E @ v1_xboole_0 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ a_4_2_domain_1 ) ) ) @ ( A @ r2_hidden ) )
<=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( I @ ( H @ ( G @ ( F @ p1_s4_domain_1 ) ) ) )
& ( A
= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
& ( E @ ( I @ m1_subset_1 ) )
& ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_2_domain_1) ).
thf(8069,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( E @ v1_xboole_0 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [F: $i,G: $i,H: $i,I: $i] :
( ( I @ ( H @ ( G @ ( F @ p1_s4_domain_1 ) ) ) )
& ( A
= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
& ( E @ ( I @ m1_subset_1 ) )
& ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( C @ ( B @ a_4_2_domain_1 ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( E @ ( D @ ( C @ ( B @ a_4_2_domain_1 ) ) ) @ ( A @ r2_hidden ) )
=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( I @ ( H @ ( G @ ( F @ p1_s4_domain_1 ) ) ) )
& ( A
= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
& ( E @ ( I @ m1_subset_1 ) )
& ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(3820,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) @ k2_funct_1 )
= ( A @ ( B @ ( C @ k2_funct_1 @ k3_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_partfun1) ).
thf(3891,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) @ k2_funct_1 )
= ( A @ ( B @ ( C @ k2_funct_1 @ k3_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(683,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k1_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_3) ).
thf(5553,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k1_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(1796,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v1_fraenkel )
& ( B @ ( A @ k2_tarski ) @ v1_finset_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_closure2) ).
thf(11426,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v1_fraenkel )
& ( B @ ( A @ k2_tarski ) @ v1_finset_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1796]) ).
thf(728,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( B @ ( A @ k1_funct_2 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_fraenkel) ).
thf(5765,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( B @ ( A @ k1_funct_2 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(1652,axiom,
~ ( k1_qc_lang1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_qc_lang1) ).
thf(10619,plain,
~ ( k1_qc_lang1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1652]) ).
thf(1594,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_0_domain_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i,E: $i] :
( ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_domain_1) ).
thf(10326,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i,E: $i] :
( ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_domain_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_domain_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i,E: $i] :
( ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1594]) ).
thf(476,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_mcart_1) ).
thf(4546,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(1554,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r5_relat_2 ) )
<=> ! [C: $i,D: $i] :
~ ( ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_2) ).
thf(10121,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
~ ( ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r5_relat_2 ) ) )
& ( ( B @ ( A @ r5_relat_2 ) )
=> ! [C: $i,D: $i] :
~ ( ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1554]) ).
thf(1879,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g1_rlvect_1 ) ) )
= ( F @ ( E @ ( D @ g1_rlvect_1 ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_rlvect_1) ).
thf(11949,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g1_rlvect_1 ) ) )
= ( F @ ( E @ ( D @ g1_rlvect_1 ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1879]) ).
thf(1585,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t152_relat_1) ).
thf(10286,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1585]) ).
thf(655,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_funct_4) ).
thf(5429,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(185,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m2_pua2mss1 ) )
=> ( ( B @ v2_funct_1 )
& ( B @ v2_relat_1 )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_pua2mss1) ).
thf(3195,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m2_pua2mss1 ) )
=> ( ( B @ v2_funct_1 )
& ( B @ v2_relat_1 )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(2351,axiom,
k1_qc_lang1 @ k1_zfmisc_1 @ ( k3_qc_lang1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_qc_lang1) ).
thf(14474,plain,
k1_qc_lang1 @ k1_zfmisc_1 @ ( k3_qc_lang1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2351]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funct_2) ).
thf(4348,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ ( A @ ( A @ k2_funct_2 ) ) ) )
= ( B @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(1379,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k2_realset1 ) ) )
= ( C @ ( B @ k1_realset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_realset1) ).
thf(9287,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k2_realset1 ) ) )
= ( C @ ( B @ k1_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379]) ).
thf(1862,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_ens_1 @ ( B @ r2_hidden ) )
<=> ? [C: $i] :
( ? [D: $i] :
( ( D @ ( C @ ( B @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( A @ ( D @ m1_subset_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_ens_1) ).
thf(11844,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ? [C: $i] :
( ? [D: $i] :
( ( D @ ( C @ ( B @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( A @ ( D @ m1_subset_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) )
=> ( A @ k1_ens_1 @ ( B @ r2_hidden ) ) )
& ( ( A @ k1_ens_1 @ ( B @ r2_hidden ) )
=> ? [C: $i] :
( ? [D: $i] :
( ( D @ ( C @ ( B @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( A @ ( D @ m1_subset_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1862]) ).
thf(75,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v1_setwiseo ) )
<=> ( B @ ( B @ ( A @ k3_binop_1 ) @ ( A @ r3_binop_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_setwiseo) ).
thf(2735,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ ( B @ ( A @ k3_binop_1 ) @ ( A @ r3_binop_1 ) ) )
=> ( A @ ( B @ v1_setwiseo ) ) )
& ( ( A @ ( B @ v1_setwiseo ) )
=> ( B @ ( B @ ( A @ k3_binop_1 ) @ ( A @ r3_binop_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(207,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( B @ ( A @ r2_wellord2 ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_card_1) ).
thf(3275,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( B @ ( A @ r2_wellord2 ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(1329,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ k6_partfun1 @ ( B @ k9_relat_1 ) )
= ( A @ k6_partfun1 @ ( B @ k2_funct_4 @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_functor0) ).
thf(9067,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ k6_partfun1 @ ( B @ k9_relat_1 ) )
= ( A @ k6_partfun1 @ ( B @ k2_funct_4 @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329]) ).
thf(2174,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ ( D @ m1_relset_1 ) ) )
& ( C @ k1_zfmisc_1 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ ( A @ k3_cantor_1 ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_cantor_1) ).
thf(13696,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ ( D @ m1_relset_1 ) ) )
& ( C @ k1_zfmisc_1 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ ( A @ k3_cantor_1 ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2174]) ).
thf(1094,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A != B )
& ( C @ ( B @ r2_hidden ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_zfmisc_1) ).
thf(7696,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A != B )
& ( C @ ( B @ r2_hidden ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(1493,axiom,
! [A: $i] :
( ( k1_numbers @ ( A @ m1_subset_1 ) )
=> ( k1_numbers @ ( A @ k7_binop_2 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_binop_2) ).
thf(9828,plain,
! [A: $i] :
( ( k1_numbers @ ( A @ m1_subset_1 ) )
=> ( k1_numbers @ ( A @ k7_binop_2 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1493]) ).
thf(1025,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( A @ ( F @ r2_hidden ) )
<=> ? [G: $i,H: $i,I: $i,J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ r2_hidden ) )
& ( D @ ( I @ r2_hidden ) )
& ( C @ ( H @ r2_hidden ) )
& ( B @ ( G @ r2_hidden ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_mcart_1) ).
thf(7418,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( ? [G: $i,H: $i,I: $i,J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ r2_hidden ) )
& ( D @ ( I @ r2_hidden ) )
& ( C @ ( H @ r2_hidden ) )
& ( B @ ( G @ r2_hidden ) ) )
=> ( A @ ( F @ r2_hidden ) ) )
& ( ( A @ ( F @ r2_hidden ) )
=> ? [G: $i,H: $i,I: $i,J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ r2_hidden ) )
& ( D @ ( I @ r2_hidden ) )
& ( C @ ( H @ r2_hidden ) )
& ( B @ ( G @ r2_hidden ) ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(869,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ r1_tarski ) )
=> ( A
= ( A @ k1_relat_1 @ k6_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_sysrel) ).
thf(6538,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ r1_tarski ) )
=> ( A
= ( A @ k1_relat_1 @ k6_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(1760,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ ( B @ ( A @ k6_funct_3 ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( B @ ( A @ k6_funct_3 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k6_funct_3 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_funct_3) ).
thf(11203,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ ( B @ ( A @ k6_funct_3 ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( B @ ( A @ k6_funct_3 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k6_funct_3 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1760]) ).
thf(384,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A )
& ( A
= ( B @ k2_relat_1 ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_funct_1) ).
thf(4070,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( B @ k5_relat_1 ) )
= ( D @ ( B @ k5_relat_1 ) ) )
& ( ( D @ k1_relat_1 )
= A )
& ( ( C @ k1_relat_1 )
= A )
& ( A
= ( B @ k2_relat_1 ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(165,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k1_setfam_1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_setfam_1) ).
thf(3116,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_setfam_1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1021,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( ( B @ ( C @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( A != C )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_zfmisc_1) ).
thf(7401,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( ( B @ ( C @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( ( A != C )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(2127,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m2_relset_1 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( G @ m2_relset_1 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( B @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( C @ ( J @ m1_subset_1 ) )
=> ! [K: $i] :
( ( D @ ( K @ m1_subset_1 ) )
=> ( ( K @ ( J @ ( I @ ( H @ ( D @ ( C @ ( B @ ( A @ k5_domain_1 ) ) ) ) ) ) ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ k8_funct_2 ) ) ) )
= ( K @ ( J @ ( I @ ( H @ ( D @ ( C @ ( B @ ( A @ k5_domain_1 ) ) ) ) ) ) ) @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ k8_funct_2 ) ) ) ) ) ) ) ) )
=> ( F = G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_multop_1) ).
thf(13429,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m2_relset_1 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( G @ m2_relset_1 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( B @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( C @ ( J @ m1_subset_1 ) )
=> ! [K: $i] :
( ( D @ ( K @ m1_subset_1 ) )
=> ( ( K @ ( J @ ( I @ ( H @ ( D @ ( C @ ( B @ ( A @ k5_domain_1 ) ) ) ) ) ) ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ k8_funct_2 ) ) ) )
= ( K @ ( J @ ( I @ ( H @ ( D @ ( C @ ( B @ ( A @ k5_domain_1 ) ) ) ) ) ) ) @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ k8_funct_2 ) ) ) ) ) ) ) ) )
=> ( F = G ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2127]) ).
thf(871,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_relset_2 ) ) ) )
= ( D @ k1_tarski @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_2) ).
thf(6547,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_relset_2 ) ) ) )
= ( D @ k1_tarski @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(819,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( B @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
thf(6274,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( B @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(632,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_zfmisc_1) ).
thf(5284,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( B @ ( C @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(1718,axiom,
( ( ( k1_xboole_0 @ k2_funct_5 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_funct_5 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_funct_5) ).
thf(11025,plain,
( ( ( k1_xboole_0 @ k2_funct_5 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_funct_5 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1718]) ).
thf(1360,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k2_relat_1 @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_funct_3) ).
thf(9216,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k2_relat_1 @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).
thf(1540,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( C @ ( D @ r1_tarski ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( E @ ( D @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_partfun1) ).
thf(10053,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( C @ ( D @ r1_tarski ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( E @ ( D @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540]) ).
thf(1334,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
| ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(9084,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
| ( B @ ( A @ r1_xboole_0 ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).
thf(82,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_xboole_1) ).
thf(2755,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(1393,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ ( A @ k6_enumset1 ) ) ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_enumset1) ).
thf(9332,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ ( A @ k6_enumset1 ) ) ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393]) ).
thf(1092,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) ) )
=> ( ( D @ ( C @ k8_relat_1 ) )
= ( C @ ( A @ k2_zfmisc_1 ) @ ( D @ k3_xboole_0 ) ) ) )
& ( ( ( A @ ( C @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) ) )
=> ( ( C @ ( D @ k7_relat_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( D @ k3_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_sysrel) ).
thf(7683,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) ) )
=> ( ( D @ ( C @ k8_relat_1 ) )
= ( C @ ( A @ k2_zfmisc_1 ) @ ( D @ k3_xboole_0 ) ) ) )
& ( ( ( A @ ( C @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ r1_tarski ) ) )
=> ( ( C @ ( D @ k7_relat_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( D @ k3_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(2355,axiom,
! [A: $i] :
( ( a_0_38_fraenkel @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ( f2_s21_fraenkel @ ( B @ r2_hidden ) )
& ( A
= ( B @ f3_s21_fraenkel ) )
& ( f1_s21_fraenkel @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_38_fraenkel) ).
thf(14489,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( f2_s21_fraenkel @ ( B @ r2_hidden ) )
& ( A
= ( B @ f3_s21_fraenkel ) )
& ( f1_s21_fraenkel @ ( B @ m1_subset_1 ) ) )
=> ( a_0_38_fraenkel @ ( A @ r2_hidden ) ) )
& ( ( a_0_38_fraenkel @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ( f2_s21_fraenkel @ ( B @ r2_hidden ) )
& ( A
= ( B @ f3_s21_fraenkel ) )
& ( f1_s21_fraenkel @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2355]) ).
thf(1797,axiom,
! [A: $i] :
( ( k1_numbers @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( ( A @ v2_membered )
& ( A @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_membered) ).
thf(11431,plain,
! [A: $i] :
( ( k1_numbers @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( ( A @ v2_membered )
& ( A @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1797]) ).
thf(1463,axiom,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v2_membered ) )
=> ( A @ k3_tarski @ v2_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_membered) ).
thf(9693,plain,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v2_membered ) )
=> ( A @ k3_tarski @ v2_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463]) ).
thf(1775,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ~ ( ( C @ ( E @ r2_hidden ) )
<=> ( D @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k7_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_subset_1) ).
thf(11299,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k7_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1775]) ).
thf(584,axiom,
! [A: $i] :
( ( k1_numbers @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( ( A = k4_urysohn1 )
<=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
<=> ? [C: $i] :
( ( C @ k3_urysohn1 @ ( B @ r2_hidden ) )
& ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_urysohn1) ).
thf(5064,plain,
! [A: $i] :
( ( k1_numbers @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( ( ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ( ( ? [C: $i] :
( ( C @ k3_urysohn1 @ ( B @ r2_hidden ) )
& ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) ) )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ? [C: $i] :
( ( C @ k3_urysohn1 @ ( B @ r2_hidden ) )
& ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) ) ) ) ) )
=> ( A = k4_urysohn1 ) )
& ( ( A = k4_urysohn1 )
=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ( ( ? [C: $i] :
( ( C @ k3_urysohn1 @ ( B @ r2_hidden ) )
& ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) ) )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ? [C: $i] :
( ( C @ k3_urysohn1 @ ( B @ r2_hidden ) )
& ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(1878,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ m2_relset_1 ) ) )
& ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k5_relset_2 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relset_2) ).
thf(11944,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ m2_relset_1 ) ) )
& ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k5_relset_2 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1878]) ).
thf(291,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r2_wellord2 ) )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_card_1) ).
thf(3653,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( k1_xboole_0 @ ( A @ r2_wellord2 ) ) )
& ( ( k1_xboole_0 @ ( A @ r2_wellord2 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1663,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_borsuk_1) ).
thf(10719,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663]) ).
thf(2248,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k12_domain_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_enumset1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k12_domain_1) ).
thf(14039,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k12_domain_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_enumset1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2248]) ).
thf(1292,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k7_relat_1 ) @ v1_finset_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_rfinseq) ).
thf(8834,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k7_relat_1 ) @ v1_finset_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).
thf(862,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(6506,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(2268,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( B @ ( A @ a_2_3_domain_1 ) @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_domain_1) ).
thf(14141,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( B @ ( A @ a_2_3_domain_1 ) @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2268]) ).
thf(2344,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k7_relset_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_relset_2) ).
thf(14440,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k7_relset_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2344]) ).
thf(62,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k3_funct_3 )
= ( A @ k3_funct_3 @ ( B @ k3_funct_3 @ k5_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_3) ).
thf(2682,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k3_funct_3 )
= ( A @ k3_funct_3 @ ( B @ k3_funct_3 @ k5_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1233,axiom,
! [A: $i] :
( ( k1_numbers @ ( A @ m1_subset_1 ) )
=> ( k1_numbers @ ( A @ k8_binop_2 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_binop_2) ).
thf(8522,plain,
! [A: $i] :
( ( k1_numbers @ ( A @ m1_subset_1 ) )
=> ( k1_numbers @ ( A @ k8_binop_2 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(1740,axiom,
! [A: $i,B: $i] :
( ( B @ v1_membered )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_membered) ).
thf(11111,plain,
! [A: $i,B: $i] :
( ( B @ v1_membered )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1740]) ).
thf(1387,axiom,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v2_binop_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_setwiseo) ).
thf(9315,plain,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v2_binop_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387]) ).
thf(1128,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_3) ).
thf(7867,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(1531,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ( A @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k18_pralg_1 ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k18_pralg_1) ).
thf(10010,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ( A @ ( B @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k18_pralg_1 ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1531]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ( ( C @ k2_relat_1 @ ( A @ k1_funct_2 ) @ ( C @ k5_funct_5 @ k2_relat_1 @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( B @ k1_funct_2 ) @ ( C @ k3_funct_5 @ k2_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_funct_5) ).
thf(3749,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ( ( C @ k2_relat_1 @ ( A @ k1_funct_2 ) @ ( C @ k5_funct_5 @ k2_relat_1 @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( B @ k1_funct_2 ) @ ( C @ k3_funct_5 @ k2_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(1173,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_enumset1 ) ) )
= ( C @ ( A @ ( B @ k1_enumset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_enumset1) ).
thf(8146,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_enumset1 ) ) )
= ( C @ ( A @ ( B @ k1_enumset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(900,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( B @ k4_card_3 @ ( A @ r2_hidden ) )
=> ( C @ ( B @ k7_relat_1 ) @ k4_card_3 @ ( C @ ( A @ k7_relat_1 ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_pralg_3) ).
thf(6662,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( B @ k4_card_3 @ ( A @ r2_hidden ) )
=> ( C @ ( B @ k7_relat_1 ) @ k4_card_3 @ ( C @ ( A @ k7_relat_1 ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(310,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m1_orders_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_orders_1) ).
thf(3744,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m1_orders_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(718,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
<=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_partfun1) ).
thf(5712,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) )
=> ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(865,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v4_monoid_0 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( ( E @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D )
& ( A @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_monoid_0) ).
thf(6519,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( ( E @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D )
& ( A @ ( E @ m1_subset_1 ) ) ) ) )
=> ( A @ ( B @ v4_monoid_0 ) ) )
& ( ( A @ ( B @ v4_monoid_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( ( E @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D )
& ( A @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(966,axiom,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(7000,plain,
! [A: $i] :
( ( A @ ( A @ k2_tarski ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(1724,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k4_card_fil @ m1_subset_1 ) )
& ~ ( A @ k4_card_fil @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_card_fil) ).
thf(11051,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k4_card_fil @ m1_subset_1 ) )
& ~ ( A @ k4_card_fil @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1724]) ).
thf(2094,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( E @ ( D @ ( C @ k1_enumset1 ) ) @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_qc_lang1) ).
thf(13273,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( E @ ( D @ ( C @ k1_enumset1 ) ) @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2094]) ).
thf(2095,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_partfun1) ).
thf(13275,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2095]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( ( B @ ( A @ k2_tarski ) )
= ( C @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_zfmisc_1) ).
thf(4766,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( ( B @ ( A @ k2_tarski ) )
= ( C @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(1103,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_functor0 ) ) ) )
= ( D @ k2_funct_4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_functor0) ).
thf(7743,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_functor0 ) ) ) )
= ( D @ k2_funct_4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(808,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ k1_tarski ) )
=> ( ( ( C @ ( A @ k1_cantor_1 ) )
= ( k1_xboole_0 @ ( B @ k2_tarski ) ) )
& ( ( C @ ( A @ k2_cantor_1 ) )
= ( A @ ( B @ k2_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_yellow_9) ).
thf(6208,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ k1_tarski ) )
=> ( ( ( C @ ( A @ k1_cantor_1 ) )
= ( k1_xboole_0 @ ( B @ k2_tarski ) ) )
& ( ( C @ ( A @ k2_cantor_1 ) )
= ( A @ ( B @ k2_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(1617,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_partfun1) ).
thf(10469,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1617]) ).
thf(2292,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_cantor_1 ) @ ( A @ k1_cantor_1 ) )
= ( B @ ( A @ k1_cantor_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_yellow_9) ).
thf(14228,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_cantor_1 ) @ ( A @ k1_cantor_1 ) )
= ( B @ ( A @ k1_cantor_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2292]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k3_funct_5 )
= ( D @ k3_funct_5 ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funct_5) ).
thf(2745,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k3_funct_5 )
= ( D @ k3_funct_5 ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(2238,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k15_funct_3 ) @ m2_relset_1 ) ) )
& ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k15_funct_3 ) @ v1_funct_2 ) ) )
& ( F @ ( E @ k15_funct_3 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_funct_3) ).
thf(14007,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k15_funct_3 ) @ m2_relset_1 ) ) )
& ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ k15_funct_3 ) @ v1_funct_2 ) ) )
& ( F @ ( E @ k15_funct_3 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2238]) ).
thf(793,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( k9_zf_lang @ k1_subset_1 @ ( A @ r1_zfrefle1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfrefle1) ).
thf(6130,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( k9_zf_lang @ k1_subset_1 @ ( A @ r1_zfrefle1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(70,axiom,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( A @ ( E @ ( D @ ( C @ ( B @ k4_mcart_1 ) ) ) @ m1_subset_1 ) )
& ( A @ ( D @ ( C @ ( B @ k3_mcart_1 ) ) @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_grcat_1) ).
thf(2703,plain,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( A @ ( E @ ( D @ ( C @ ( B @ k4_mcart_1 ) ) ) @ m1_subset_1 ) )
& ( A @ ( D @ ( C @ ( B @ k3_mcart_1 ) ) @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(2318,axiom,
f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s8_domain_1) ).
thf(14331,plain,
f2_s8_domain_1 @ k1_zfmisc_1 @ ( a_0_1_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2318]) ).
thf(2383,axiom,
( ! [A: $i] :
( ( f1_s5_filter_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s5_filter_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s5_filter_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f2_s5_filter_1 @ ( D @ m1_subset_1 ) )
=> ( D @ ( B @ ( f2_s5_filter_1 @ ( f1_s5_filter_1 @ k1_domain_1 ) ) ) @ ( C @ ( A @ ( f2_s5_filter_1 @ ( f1_s5_filter_1 @ k1_domain_1 ) ) ) @ p1_s5_filter_1 ) ) ) ) ) )
=> ! [A: $i] :
( ( f2_s5_filter_1 @ ( f1_s5_filter_1 @ k2_zfmisc_1 ) @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f2_s5_filter_1 @ ( f1_s5_filter_1 @ k2_zfmisc_1 ) @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ p1_s5_filter_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s5_filter_1) ).
thf(14611,plain,
( ! [A: $i] :
( ( f1_s5_filter_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s5_filter_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s5_filter_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f2_s5_filter_1 @ ( D @ m1_subset_1 ) )
=> ( D @ ( B @ ( f2_s5_filter_1 @ ( f1_s5_filter_1 @ k1_domain_1 ) ) ) @ ( C @ ( A @ ( f2_s5_filter_1 @ ( f1_s5_filter_1 @ k1_domain_1 ) ) ) @ p1_s5_filter_1 ) ) ) ) ) )
=> ! [A: $i] :
( ( f2_s5_filter_1 @ ( f1_s5_filter_1 @ k2_zfmisc_1 ) @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f2_s5_filter_1 @ ( f1_s5_filter_1 @ k2_zfmisc_1 ) @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ p1_s5_filter_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2383]) ).
thf(443,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_orders_1 @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_orders_1) ).
thf(4358,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_orders_1 @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(1245,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_4 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_4) ).
thf(8571,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_4 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(1638,axiom,
( ( a_0_0_altcat_2 @ v1_funct_1 )
& ( a_0_0_altcat_2 @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_altcat_2) ).
thf(10570,plain,
( ( a_0_0_altcat_2 @ v1_funct_1 )
& ( a_0_0_altcat_2 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1638]) ).
thf(462,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( ! [B: $i] :
? [C: $i] :
( ! [D: $i] :
( ( C @ ( B @ k3_xboole_0 ) )
!= ( D @ k1_tarski ) )
& ( A @ ( C @ r2_hidden ) ) )
& ! [B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( ( C @ ( B @ r1_xboole_0 ) )
| ( B = C ) ) )
& ! [B: $i] :
~ ( ( B = k1_xboole_0 )
& ( A @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_wellord2) ).
thf(4460,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( ! [B: $i] :
? [C: $i] :
( ! [D: $i] :
( ( C @ ( B @ k3_xboole_0 ) )
!= ( D @ k1_tarski ) )
& ( A @ ( C @ r2_hidden ) ) )
& ! [B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( ( C @ ( B @ r1_xboole_0 ) )
| ( B = C ) ) )
& ! [B: $i] :
~ ( ( B = k1_xboole_0 )
& ( A @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(1169,axiom,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc27_membered) ).
thf(8126,plain,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(586,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= A )
& ( ( B @ k2_relat_1 )
= A ) )
=> ( ( C @ ( B @ ( A @ k4_funct_2 ) ) @ k2_relat_1 )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_2) ).
thf(5091,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= A )
& ( ( B @ k2_relat_1 )
= A ) )
=> ( ( C @ ( B @ ( A @ k4_funct_2 ) ) @ k2_relat_1 )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(1045,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(7509,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(780,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( D @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
& ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_zfmisc_1) ).
thf(6071,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( D @ k2_zfmisc_1 ) @ ( A @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ r1_xboole_0 ) )
& ( D @ ( B @ k1_tarski @ k2_zfmisc_1 ) @ ( C @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(1280,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) )
=> ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( B @ ( A @ k2_altcat_1 ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_altcat_1) ).
thf(8770,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) )
=> ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( B @ ( A @ k2_altcat_1 ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_finset_1) ).
thf(2420,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(643,axiom,
! [A: $i] :
( ( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( A = k36_binop_2 )
<=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k1_numbers @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k12_binop_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_binop_2) ).
thf(5338,plain,
! [A: $i] :
( ( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k1_numbers @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k12_binop_2 ) ) ) ) )
=> ( A = k36_binop_2 ) )
& ( ( A = k36_binop_2 )
=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k1_numbers @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k12_binop_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(815,axiom,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finsub_1) ).
thf(6253,plain,
( ( k1_xboole_0 @ k5_finsub_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(249,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C
= ( B @ ( A @ k3_pralg_3 ) ) )
<=> ( ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( B @ ( D @ k1_funct_1 ) ) ) ) )
& ( ( C @ k1_relat_1 )
= ( A @ k4_card_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_pralg_3) ).
thf(3463,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( B @ ( D @ k1_funct_1 ) ) ) ) )
& ( ( C @ k1_relat_1 )
= ( A @ k4_card_3 ) ) )
=> ( C
= ( B @ ( A @ k3_pralg_3 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_pralg_3 ) ) )
=> ( ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( B @ ( D @ k1_funct_1 ) ) ) ) )
& ( ( C @ k1_relat_1 )
= ( A @ k4_card_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(2033,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_relset_1) ).
thf(12920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2033]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_zfmisc_1) ).
thf(4353,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(2102,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B
= ( D @ ( C @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( D @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_mssubfam) ).
thf(13307,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B
= ( D @ ( C @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( D @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2102]) ).
thf(858,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_funct_1) ).
thf(6470,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(696,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) @ ( A @ r1_partfun1 ) )
=> ( C @ ( A @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_funct_4) ).
thf(5605,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) @ ( A @ r1_partfun1 ) )
=> ( C @ ( A @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(2208,axiom,
( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k33_binop_2 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k33_binop_2 @ v1_funct_2 ) ) )
& ( k33_binop_2 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k33_binop_2) ).
thf(13878,plain,
( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k33_binop_2 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k33_binop_2 @ v1_funct_2 ) ) )
& ( k33_binop_2 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2208]) ).
thf(542,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( A @ ( B @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( B @ k7_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t101_relat_1) ).
thf(4862,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( A @ ( B @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( B @ k7_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(2330,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k15_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_domain_1) ).
thf(14376,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k15_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2330]) ).
thf(1529,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_funct_7 ) )
= ( C @ ( A @ k1_funct_7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_funct_7) ).
thf(10003,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_funct_7 ) )
= ( C @ ( A @ k1_funct_7 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1529]) ).
thf(952,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t175_partfun1) ).
thf(6905,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(2346,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_finsub_1) ).
thf(14455,plain,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2346]) ).
thf(993,axiom,
! [A: $i] :
( ~ ( ! [B: $i] :
~ ( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) )
& ( ( A @ k3_tarski )
!= k1_xboole_0 ) )
& ~ ( ( ( A @ k3_tarski )
= k1_xboole_0 )
& ? [B: $i] :
( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_orders_1) ).
thf(7209,plain,
! [A: $i] :
( ~ ( ! [B: $i] :
~ ( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) )
& ( ( A @ k3_tarski )
!= k1_xboole_0 ) )
& ~ ( ( ( A @ k3_tarski )
= k1_xboole_0 )
& ? [B: $i] :
( ( A @ ( B @ r2_hidden ) )
& ( B != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(1115,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( C @ k1_funct_4 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_7) ).
thf(7803,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( C @ k1_funct_4 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(1289,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_binop_1) ).
thf(8819,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(1225,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( B @ ( A @ k8_relat_1 ) @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_funct_1) ).
thf(8468,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( B @ ( A @ k8_relat_1 ) @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(1769,axiom,
! [A: $i] :
( ( k1_qc_lang1 @ ( A @ r2_hidden ) )
<=> ~ ( ~ ( k2_qc_lang1 @ ( A @ r2_hidden ) )
& ~ ( k4_qc_lang1 @ ( A @ r2_hidden ) )
& ~ ( k3_qc_lang1 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_cqc_lang) ).
thf(11247,plain,
! [A: $i] :
( ( ~ ( ~ ( k2_qc_lang1 @ ( A @ r2_hidden ) )
& ~ ( k4_qc_lang1 @ ( A @ r2_hidden ) )
& ~ ( k3_qc_lang1 @ ( A @ r2_hidden ) ) )
=> ( k1_qc_lang1 @ ( A @ r2_hidden ) ) )
& ( ( k1_qc_lang1 @ ( A @ r2_hidden ) )
=> ~ ( ~ ( k2_qc_lang1 @ ( A @ r2_hidden ) )
& ~ ( k4_qc_lang1 @ ( A @ r2_hidden ) )
& ~ ( k3_qc_lang1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1769]) ).
thf(2260,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(14109,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2260]) ).
thf(2320,axiom,
! [A: $i] :
( ( k2_qc_lang1 @ ( A @ m1_subset_1 ) )
=> ( k2_qc_lang1 @ k1_zfmisc_1 @ ( A @ k23_qc_lang1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k23_qc_lang1) ).
thf(14334,plain,
! [A: $i] :
( ( k2_qc_lang1 @ ( A @ m1_subset_1 ) )
=> ( k2_qc_lang1 @ k1_zfmisc_1 @ ( A @ k23_qc_lang1 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2320]) ).
thf(1951,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ( ( C = D )
=> ( ( C @ ( A @ k6_funct_3 ) )
= ( B @ ( A @ k6_funct_3 ) @ ( D @ ( B @ k6_funct_3 ) @ ( A @ ( B @ ( D @ k7_funct_2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_functor1) ).
thf(12443,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ( ( C = D )
=> ( ( C @ ( A @ k6_funct_3 ) )
= ( B @ ( A @ k6_funct_3 ) @ ( D @ ( B @ k6_funct_3 ) @ ( A @ ( B @ ( D @ k7_funct_2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1951]) ).
thf(551,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_tarski ) @ k3_mcart_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_mcart_1) ).
thf(4928,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_tarski ) @ k3_mcart_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(1788,axiom,
( ( k5_urysohn1 @ v2_membered )
& ( k5_urysohn1 @ v1_membered )
& ~ ( k5_urysohn1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_urysohn1) ).
thf(11378,plain,
( ( k5_urysohn1 @ v2_membered )
& ( k5_urysohn1 @ v1_membered )
& ~ ( k5_urysohn1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1788]) ).
thf(1855,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_setwiseo) ).
thf(11802,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1855]) ).
thf(1742,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) ) )
=> ( ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_mcart_1) ).
thf(11115,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) ) )
=> ( ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) )
| ( D = k1_xboole_0 )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1742]) ).
thf(581,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k11_relset_1 ) ) ) )
= ( C @ ( A @ ( B @ k4_relset_1 ) ) ) )
& ( ( A @ ( C @ ( A @ ( B @ k11_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) )
= ( C @ ( A @ ( B @ k5_relset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_relset_1) ).
thf(5052,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k11_relset_1 ) ) ) )
= ( C @ ( A @ ( B @ k4_relset_1 ) ) ) )
& ( ( A @ ( C @ ( A @ ( B @ k11_relset_1 ) ) ) @ ( C @ ( A @ ( B @ k10_relset_1 ) ) ) )
= ( C @ ( A @ ( B @ k5_relset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(1842,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_funct_2) ).
thf(11741,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1842]) ).
thf(1354,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ k7_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funcop_1) ).
thf(9199,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ k7_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354]) ).
thf(1922,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_eqrel_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_eqrel_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ a_4_0_pua2mss1 ) ) ) @ m1_eqrel_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_pua2mss1) ).
thf(12180,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_eqrel_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_eqrel_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ a_4_0_pua2mss1 ) ) ) @ m1_eqrel_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1922]) ).
thf(2119,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
<=> ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_realset1) ).
thf(13393,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m2_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2119]) ).
thf(216,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r2_wellord2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r2_wellord2) ).
thf(3312,plain,
! [A: $i] : ( A @ ( A @ r2_wellord2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(738,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_funct_2) ).
thf(5829,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ m2_relset_1 ) ) )
& ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(1211,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ k5_funcop_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_funcop_1) ).
thf(8384,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ k5_funcop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(331,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k5_funct_5 @ v1_funct_1 )
& ( A @ k5_funct_5 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_funct_5) ).
thf(3835,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k5_funct_5 @ v1_funct_1 )
& ( A @ k5_funct_5 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(721,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( D @ ( C @ ( B @ k3_mcart_1 ) ) @ ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_mcart_1) ).
thf(5727,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( D @ ( C @ ( B @ k3_mcart_1 ) ) @ ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(1254,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k3_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_funct_1) ).
thf(8632,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k3_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(574,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) )
=> ( ( C @ ( E @ ( A @ ( D @ k4_funcop_1 ) ) @ k7_relat_1 ) )
= ( C @ ( E @ ( B @ ( D @ k4_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_funcop_1) ).
thf(5020,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) )
=> ( ( C @ ( E @ ( A @ ( D @ k4_funcop_1 ) ) @ k7_relat_1 ) )
= ( C @ ( E @ ( B @ ( D @ k4_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(1150,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relset_1) ).
thf(8037,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(672,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t154_relat_1) ).
thf(5493,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(912,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ k3_enumset1 ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_subset_1) ).
thf(6734,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ k3_enumset1 ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(1587,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_binop_1) ).
thf(10292,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1587]) ).
thf(1881,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(11959,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1881]) ).
thf(1784,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( E @ ( D @ ( C @ ( A @ k5_subset_1 ) ) @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( B @ k4_subset_1 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_relset_2) ).
thf(11363,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( E @ ( D @ ( C @ ( A @ k5_subset_1 ) ) @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( B @ k4_subset_1 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1784]) ).
thf(1793,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( A @ ( C @ k10_relset_1 ) ) ) @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_relset_1) ).
thf(11404,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( C @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) )
=> ( B @ ( D @ ( A @ ( C @ k10_relset_1 ) ) ) @ ( E @ r2_hidden ) ) )
& ( ( B @ ( D @ ( A @ ( C @ k10_relset_1 ) ) ) @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( E @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1793]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_zfmisc_1) ).
thf(4302,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B = D )
& ( A = C ) )
=> ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ k1_tarski @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_tarski ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( D = B )
| ( D = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(4514,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ k2_tarski ) ) ) )
& ( ( C
= ( B @ ( A @ k2_tarski ) ) )
=> ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(1745,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(11139,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1745]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_funct_2) ).
thf(4253,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 )
= A ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(1042,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r5_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_binop_1) ).
thf(7500,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r5_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r6_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r5_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(1964,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( E @ ( C @ ( B @ ( A @ k18_pralg_1 ) ) @ k1_binop_1 ) ) )
= ( E @ ( D @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_altcat_2) ).
thf(12517,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( E @ ( C @ ( B @ ( A @ k18_pralg_1 ) ) @ k1_binop_1 ) ) )
= ( E @ ( D @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1964]) ).
thf(1478,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( C @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( B @ k1_relat_1 )
= A ) ) )
& ! [B: $i] :
~ ( ( B = k1_xboole_0 )
& ( A @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_wellord2) ).
thf(9768,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( C @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( B @ k1_relat_1 )
= A ) ) )
& ! [B: $i] :
~ ( ( B = k1_xboole_0 )
& ( A @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478]) ).
thf(2022,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r2_hidden ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_setfam_1) ).
thf(12875,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r2_hidden ) ) )
=> ( C @ ( A @ k8_setfam_1 ) @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r2_hidden ) )
=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2022]) ).
thf(1299,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(8870,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( A @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(1443,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_8_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ p1_s3_domain_1 ) ) )
& ( A
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
& ( D @ ( G @ m1_subset_1 ) )
& ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_8_domain_1) ).
thf(9580,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ p1_s3_domain_1 ) ) )
& ( A
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
& ( D @ ( G @ m1_subset_1 ) )
& ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_8_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_8_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ p1_s3_domain_1 ) ) )
& ( A
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
& ( D @ ( G @ m1_subset_1 ) )
& ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443]) ).
thf(996,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k2_relat_1 @ v1_relat_1 )
& ( A @ k2_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(7226,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k2_relat_1 @ v1_relat_1 )
& ( A @ k2_relat_1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(2148,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ k2_zfmisc_1 ) @ ( A @ ( C @ ( B @ k13_funct_3 ) @ k9_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funct_3) ).
thf(13575,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ k2_zfmisc_1 ) @ ( A @ ( C @ ( B @ k13_funct_3 ) @ k9_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2148]) ).
thf(104,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ~ ( B @ k2_relat_1 @ k3_tarski @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_pre_circ) ).
thf(2829,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ~ ( B @ k2_relat_1 @ k3_tarski @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(757,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k5_relat_1 ) )
= ( B @ k2_relat_1 @ ( A @ k7_relat_1 ) @ ( B @ k5_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funct_4) ).
thf(5974,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k5_relat_1 ) )
= ( B @ k2_relat_1 @ ( A @ k7_relat_1 ) @ ( B @ k5_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(1411,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ r2_binop_1 ) ) )
& ( B @ ( C @ ( A @ r1_binop_1 ) ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_binop_1) ).
thf(9425,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ r2_binop_1 ) ) )
& ( B @ ( C @ ( A @ r1_binop_1 ) ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411]) ).
thf(1751,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( A @ ( k1_numbers @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( A @ ( A @ ( k1_numbers @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( B @ m1_subset_1 ) ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ g2_rlvect_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ g2_rlvect_1 ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g2_rlvect_1) ).
thf(11163,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( A @ ( k1_numbers @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( A @ ( A @ ( k1_numbers @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( B @ m1_subset_1 ) ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ g2_rlvect_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ g2_rlvect_1 ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1751]) ).
thf(1311,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v1_setwiseo ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( E @ ( F @ ( B @ k2_setwiseo ) @ ( D @ ( B @ k5_setwiseo ) ) @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= ( F @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_setwiseo) ).
thf(8956,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v1_setwiseo ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( E @ ( F @ ( B @ k2_setwiseo ) @ ( D @ ( B @ k5_setwiseo ) ) @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= ( F @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311]) ).
thf(237,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) )
& ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_finseq_2) ).
thf(3393,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) )
& ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1809,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_funct_2) ).
thf(11500,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k4_funct_2 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1809]) ).
thf(1733,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ k4_subset_1 ) ) @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( B @ k5_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_relset_2) ).
thf(11083,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ k4_subset_1 ) ) @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( B @ k5_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1733]) ).
thf(935,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ k4_funcop_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_funcop_1) ).
thf(6841,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ k4_funcop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(873,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r5_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_binop_1) ).
thf(6559,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r4_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r5_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r5_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_xboole_1) ).
thf(4432,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(1002,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) )
& ( ( A @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( C @ ( B @ ( A @ k5_relset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_relset_1) ).
thf(7258,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) )
& ( ( A @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( C @ ( B @ ( A @ k5_relset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(1613,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc15_finset_1) ).
thf(10454,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1613]) ).
thf(2246,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_relat_1) ).
thf(14034,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2246]) ).
thf(2322,axiom,
k1_numbers @ k1_zfmisc_1 @ ( k4_urysohn1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_urysohn1) ).
thf(14339,plain,
k1_numbers @ k1_zfmisc_1 @ ( k4_urysohn1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2322]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ m1_pboole ) )
<=> ( ( B @ k1_relat_1 )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pboole) ).
thf(4696,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k1_relat_1 )
= A )
=> ( A @ ( B @ m1_pboole ) ) )
& ( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ k1_relat_1 )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(2186,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k7_setfam_1 ) ) )
<=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
<=> ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
thf(13771,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k7_setfam_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k7_setfam_1 ) ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2186]) ).
thf(657,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( B @ ( A @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ k6_partfun1 @ ( A @ k5_relat_1 ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funct_7) ).
thf(5433,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( B @ ( A @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ k6_partfun1 @ ( A @ k5_relat_1 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(1498,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k7_relat_1 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_relat_1) ).
thf(9854,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k7_relat_1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498]) ).
thf(412,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ~ ( ( A @ k2_relat_1 @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ~ ( A @ k1_relat_1 @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_frechet2) ).
thf(4205,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ~ ( ( A @ k2_relat_1 @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ~ ( A @ k1_relat_1 @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(1859,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_finsub_1) ).
thf(11821,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1859]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v2_relat_1 )
<=> ! [C: $i] :
~ ( ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_pboole) ).
thf(3322,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( ! [C: $i] :
~ ( ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ v2_relat_1 ) )
& ( ( B @ v2_relat_1 )
=> ! [C: $i] :
~ ( ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(1181,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_xboole_0 ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t186_partfun1) ).
thf(8190,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_xboole_0 ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(247,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B
= ( A @ k2_funct_1 ) )
<=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
thf(3431,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) )
=> ( B
= ( A @ k2_funct_1 ) ) )
& ( ( B
= ( A @ k2_funct_1 ) )
=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) ) )
& ( ( ( D
= ( C @ ( B @ k1_funct_1 ) ) )
& ( A @ k2_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(2205,axiom,
? [A: $i] :
( ( A @ v1_fraenkel )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_fraenkel) ).
thf(13863,plain,
? [A: $i] :
( ( A @ v1_fraenkel )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2205]) ).
thf(1593,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(10324,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1593]) ).
thf(1112,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v2_funct_1 )
& ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v1_funct_1 )
& ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v1_relat_1 )
& ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funcop_1) ).
thf(7786,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v2_funct_1 )
& ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v1_funct_1 )
& ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v1_relat_1 )
& ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(1004,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B @ ( A @ ( A @ k5_partfun1 ) ) @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_funct_2) ).
thf(7273,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B @ ( A @ ( A @ k5_partfun1 ) ) @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(748,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( H
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) ) )
<=> ! [I: $i] :
( ( H @ ( I @ r2_hidden ) )
<=> ~ ( ( I != G )
& ( I != F )
& ( I != E )
& ( I != D )
& ( I != C )
& ( I != B )
& ( I != A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_enumset1) ).
thf(5892,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i] :
( ( ~ ( ( I != G )
& ( I != F )
& ( I != E )
& ( I != D )
& ( I != C )
& ( I != B )
& ( I != A ) )
=> ( H @ ( I @ r2_hidden ) ) )
& ( ( H @ ( I @ r2_hidden ) )
=> ~ ( ( I != G )
& ( I != F )
& ( I != E )
& ( I != D )
& ( I != C )
& ( I != B )
& ( I != A ) ) ) )
=> ( H
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) ) ) )
& ( ( H
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) ) )
=> ! [I: $i] :
( ( ~ ( ( I != G )
& ( I != F )
& ( I != E )
& ( I != D )
& ( I != C )
& ( I != B )
& ( I != A ) )
=> ( H @ ( I @ r2_hidden ) ) )
& ( ( H @ ( I @ r2_hidden ) )
=> ~ ( ( I != G )
& ( I != F )
& ( I != E )
& ( I != D )
& ( I != C )
& ( I != B )
& ( I != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(2035,axiom,
! [A: $i,B: $i] :
( ( B @ v4_finsub_1 )
=> ( ( B
= ( A @ k5_finsub_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( ( C @ v1_finset_1 )
& ( A @ ( C @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_finsub_1) ).
thf(12924,plain,
! [A: $i,B: $i] :
( ( B @ v4_finsub_1 )
=> ( ( ! [C: $i] :
( ( ( ( C @ v1_finset_1 )
& ( A @ ( C @ r1_tarski ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( ( C @ v1_finset_1 )
& ( A @ ( C @ r1_tarski ) ) ) ) )
=> ( B
= ( A @ k5_finsub_1 ) ) )
& ( ( B
= ( A @ k5_finsub_1 ) )
=> ! [C: $i] :
( ( ( ( C @ v1_finset_1 )
& ( A @ ( C @ r1_tarski ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( ( C @ v1_finset_1 )
& ( A @ ( C @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2035]) ).
thf(1039,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ ( A @ k8_relat_1 ) @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t126_funct_1) ).
thf(7492,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ ( A @ k8_relat_1 ) @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(1849,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_sysrel) ).
thf(11778,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1849]) ).
thf(1209,axiom,
! [A: $i] :
( ( ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finsub_1) ).
thf(8379,plain,
! [A: $i] :
( ( ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(1727,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finset_1 )
& ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_setwiseo) ).
thf(11064,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finset_1 )
& ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1727]) ).
thf(811,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k2_funct_4 @ ( A @ k2_funct_4 @ r1_tarski ) )
& ( A @ k1_relat_1 @ v1_relat_1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_yellow20) ).
thf(6227,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k2_funct_4 @ ( A @ k2_funct_4 @ r1_tarski ) )
& ( A @ k1_relat_1 @ v1_relat_1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1889,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( D @ ( C @ k9_relat_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_waybel_2) ).
thf(12023,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( D @ ( C @ k9_relat_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1889]) ).
thf(2233,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_tex_2) ).
thf(13987,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2233]) ).
thf(1781,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ g3_quantal1 ) ) ) ) ) )
= ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ g3_quantal1 ) ) ) ) ) ) )
=> ( ( F = L )
& ( E = K )
& ( D = J )
& ( C = I )
& ( B = H )
& ( A = G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_quantal1) ).
thf(11344,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ g3_quantal1 ) ) ) ) ) )
= ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ g3_quantal1 ) ) ) ) ) ) )
=> ( ( F = L )
& ( E = K )
& ( D = J )
& ( C = I )
& ( B = H )
& ( A = G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1781]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k4_relat_1 )
= ( A @ ( B @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_sysrel) ).
thf(3075,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k4_relat_1 )
= ( A @ ( B @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(694,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_relat_1) ).
thf(5597,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(144,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( B
= ( A @ k3_finseq_1 ) )
<=> ( ( B @ k2_finseq_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_finseq_1) ).
thf(2996,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( ( ( B @ k2_finseq_1 )
= ( A @ k1_relat_1 ) )
=> ( B
= ( A @ k3_finseq_1 ) ) )
& ( ( B
= ( A @ k3_finseq_1 ) )
=> ( ( B @ k2_finseq_1 )
= ( A @ k1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1335,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_funct_3 @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_funct_3) ).
thf(9088,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k1_funct_3 @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).
thf(2017,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k6_setfam_1 ) )
= ( B @ ( A @ k5_setfam_1 ) @ ( A @ k3_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_tops_2) ).
thf(12828,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k6_setfam_1 ) )
= ( B @ ( A @ k5_setfam_1 ) @ ( A @ k3_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2017]) ).
thf(898,axiom,
! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_zfmisc_1) ).
thf(6657,plain,
! [A: $i,B: $i] : ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k3_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(2108,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ r1_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
=> ( ! [E: $i] :
( ( D @ ( C @ k1_funct_2 ) @ ( E @ m1_subset_1 ) )
=> ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) )
| ( ( D @ ( C @ k1_funct_2 ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_fraenkel) ).
thf(13325,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ r1_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
=> ( ! [E: $i] :
( ( D @ ( C @ k1_funct_2 ) @ ( E @ m1_subset_1 ) )
=> ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) )
| ( ( D @ ( C @ k1_funct_2 ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2108]) ).
thf(1177,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ ( C @ ( A @ k1_funct_1 ) @ r1_tarski ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( B @ k4_card_3 @ ( A @ k4_card_3 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_card_3) ).
thf(8158,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ ( C @ ( A @ k1_funct_1 ) @ r1_tarski ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( B @ k4_card_3 @ ( A @ k4_card_3 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(1120,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( A @ k2_funcop_1 ) @ ( B @ k6_partfun1 @ k1_funct_4 ) @ k2_relat_1 @ ( A @ r1_xboole_0 ) )
=> ( A @ ( C @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_funct_7) ).
thf(7818,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( A @ k2_funcop_1 ) @ ( B @ k6_partfun1 @ k1_funct_4 ) @ k2_relat_1 @ ( A @ r1_xboole_0 ) )
=> ( A @ ( C @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(2371,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_domain_1) ).
thf(14584,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2371]) ).
thf(1583,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s1_setwiseo @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s1_setwiseo @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f1_s1_setwiseo @ k5_finsub_1 @ ( f1_s1_setwiseo @ k8_funct_2 ) ) ) @ ( C @ r2_hidden ) )
<=> ( ( B @ ( C @ p1_s1_setwiseo ) )
& ( f2_s1_setwiseo @ ( C @ r2_hidden ) ) ) ) ) )
& ( f1_s1_setwiseo @ k5_finsub_1 @ ( f1_s1_setwiseo @ ( A @ m2_relset_1 ) ) )
& ( f1_s1_setwiseo @ k5_finsub_1 @ ( f1_s1_setwiseo @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_setwiseo) ).
thf(10271,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s1_setwiseo @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s1_setwiseo @ ( C @ m1_subset_1 ) )
=> ( ( ( ( B @ ( C @ p1_s1_setwiseo ) )
& ( f2_s1_setwiseo @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ ( f1_s1_setwiseo @ k5_finsub_1 @ ( f1_s1_setwiseo @ k8_funct_2 ) ) ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ ( f1_s1_setwiseo @ k5_finsub_1 @ ( f1_s1_setwiseo @ k8_funct_2 ) ) ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ p1_s1_setwiseo ) )
& ( f2_s1_setwiseo @ ( C @ r2_hidden ) ) ) ) ) ) )
& ( f1_s1_setwiseo @ k5_finsub_1 @ ( f1_s1_setwiseo @ ( A @ m2_relset_1 ) ) )
& ( f1_s1_setwiseo @ k5_finsub_1 @ ( f1_s1_setwiseo @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1583]) ).
thf(2361,axiom,
( ( ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( f3_s4_subset_1 @ ( A @ r2_hidden ) )
<=> ( A @ p1_s4_subset_1 ) ) )
& ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( f2_s4_subset_1 @ ( A @ r2_hidden ) )
<=> ( A @ p1_s4_subset_1 ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_subset_1) ).
thf(14532,plain,
( ( ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( ( A @ p1_s4_subset_1 )
=> ( f3_s4_subset_1 @ ( A @ r2_hidden ) ) )
& ( ( f3_s4_subset_1 @ ( A @ r2_hidden ) )
=> ( A @ p1_s4_subset_1 ) ) ) )
& ! [A: $i] :
( ( f1_s4_subset_1 @ ( A @ m1_subset_1 ) )
=> ( ( ( A @ p1_s4_subset_1 )
=> ( f2_s4_subset_1 @ ( A @ r2_hidden ) ) )
& ( ( f2_s4_subset_1 @ ( A @ r2_hidden ) )
=> ( A @ p1_s4_subset_1 ) ) ) ) )
=> ( f2_s4_subset_1 = f3_s4_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2361]) ).
thf(2252,axiom,
( ! [A: $i] :
( ( f1_s1_funct_7 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f2_s1_funct_7 @ ( B @ m1_subset_1 ) )
=> ( f3_s1_funct_7 @ ( B @ ( A @ f4_s1_funct_7 ) @ r2_hidden ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_funct_7 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s1_funct_7 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( f2_s1_funct_7 @ ( f1_s1_funct_7 @ k1_domain_1 ) ) ) @ ( A @ ( f3_s1_funct_7 @ ( f2_s1_funct_7 @ ( f1_s1_funct_7 @ k2_zfmisc_1 ) @ k8_funct_2 ) ) ) )
= ( C @ ( B @ f4_s1_funct_7 ) ) ) ) )
& ( f3_s1_funct_7 @ ( f2_s1_funct_7 @ ( f1_s1_funct_7 @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( f3_s1_funct_7 @ ( f2_s1_funct_7 @ ( f1_s1_funct_7 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_7) ).
thf(14061,plain,
( ! [A: $i] :
( ( f1_s1_funct_7 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f2_s1_funct_7 @ ( B @ m1_subset_1 ) )
=> ( f3_s1_funct_7 @ ( B @ ( A @ f4_s1_funct_7 ) @ r2_hidden ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s1_funct_7 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s1_funct_7 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( f2_s1_funct_7 @ ( f1_s1_funct_7 @ k1_domain_1 ) ) ) @ ( A @ ( f3_s1_funct_7 @ ( f2_s1_funct_7 @ ( f1_s1_funct_7 @ k2_zfmisc_1 ) @ k8_funct_2 ) ) ) )
= ( C @ ( B @ f4_s1_funct_7 ) ) ) ) )
& ( f3_s1_funct_7 @ ( f2_s1_funct_7 @ ( f1_s1_funct_7 @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( f3_s1_funct_7 @ ( f2_s1_funct_7 @ ( f1_s1_funct_7 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2252]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ k4_card_3 @ v1_fraenkel )
& ~ ( B @ k4_card_3 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_pralg_1) ).
thf(2451,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ k4_card_3 @ v1_fraenkel )
& ~ ( B @ k4_card_3 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
& ( C @ v2_funct_1 ) )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_funct_2) ).
thf(3527,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
& ( C @ v2_funct_1 ) )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ k2_funct_1 @ v1_funct_2 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(1109,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ k6_relat_1 @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
<=> ( ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_1) ).
thf(7775,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ k6_relat_1 @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) ) )
& ( ( A @ k6_relat_1 @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(363,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i,D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B @ ( D @ v1_setwiseo ) )
& ( B @ ( D @ v3_binop_1 ) )
& ( B @ ( D @ v2_binop_1 ) )
& ( B @ ( D @ v1_binop_1 ) ) )
=> ! [E: $i] :
( ( ( C @ k5_finsub_1 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ k5_finsub_1 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( C @ k5_finsub_1 @ ( F @ m2_relset_1 ) ) )
& ( B @ ( C @ k5_finsub_1 @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ! [G: $i] :
( ( C @ k5_finsub_1 @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ k5_finsub_1 @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( G @ ( C @ k5_setwiseo ) ) @ ( F @ ( B @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( H @ ( F @ ( B @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( G @ ( F @ ( B @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) ) ) ) )
& ( ( C @ k1_setwiseo @ ( F @ ( B @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( D @ ( B @ k3_binop_1 ) ) ) )
=> ! [G: $i] :
( ( A @ k5_finsub_1 @ ( G @ m1_subset_1 ) )
=> ( ( E @ ( G @ ( C @ ( A @ k10_setwiseo ) ) ) @ ( F @ ( B @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( F @ ( E @ ( B @ ( C @ k5_finsub_1 @ ( A @ k7_funct_2 ) ) ) ) @ ( G @ ( D @ ( B @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_setwiseo) ).
thf(3983,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i,D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B @ ( D @ v1_setwiseo ) )
& ( B @ ( D @ v3_binop_1 ) )
& ( B @ ( D @ v2_binop_1 ) )
& ( B @ ( D @ v1_binop_1 ) ) )
=> ! [E: $i] :
( ( ( C @ k5_finsub_1 @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ k5_finsub_1 @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( C @ k5_finsub_1 @ ( F @ m2_relset_1 ) ) )
& ( B @ ( C @ k5_finsub_1 @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ! [G: $i] :
( ( C @ k5_finsub_1 @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ k5_finsub_1 @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( G @ ( C @ k5_setwiseo ) ) @ ( F @ ( B @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( H @ ( F @ ( B @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( G @ ( F @ ( B @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) ) ) ) )
& ( ( C @ k1_setwiseo @ ( F @ ( B @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( D @ ( B @ k3_binop_1 ) ) ) )
=> ! [G: $i] :
( ( A @ k5_finsub_1 @ ( G @ m1_subset_1 ) )
=> ( ( E @ ( G @ ( C @ ( A @ k10_setwiseo ) ) ) @ ( F @ ( B @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( F @ ( E @ ( B @ ( C @ k5_finsub_1 @ ( A @ k7_funct_2 ) ) ) ) @ ( G @ ( D @ ( B @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(802,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( A @ ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t152_funct_1) ).
thf(6189,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( A @ ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(795,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ k10_relat_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
thf(6135,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k10_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k10_relat_1 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(1495,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( D @ r1_tarski ) ) )
=> ( A @ ( D @ r1_tarski ) ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_xboole_1) ).
thf(9837,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( D @ r1_tarski ) ) )
=> ( A @ ( D @ r1_tarski ) ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1495]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( B @ ( C @ ( E @ ( D @ k5_relat_1 ) @ k3_partfun1 ) ) @ ( B @ ( A @ ( E @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( A @ ( C @ k1_partfun1 ) ) ) ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_partfun1) ).
thf(3525,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( B @ ( C @ ( E @ ( D @ k5_relat_1 ) @ k3_partfun1 ) ) @ ( B @ ( A @ ( E @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( A @ ( C @ k1_partfun1 ) ) ) ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(801,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k1_relat_1 @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_relset_1) ).
thf(6187,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( D @ k1_relat_1 @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(2339,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ k14_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_domain_1) ).
thf(14408,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ k14_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2339]) ).
thf(1763,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
thf(11215,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1763]) ).
thf(1500,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_lattice2) ).
thf(9860,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1500]) ).
thf(2324,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( B @ ( C @ ( A @ k5_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(14346,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( B @ ( C @ ( A @ k5_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2324]) ).
thf(964,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_2) ).
thf(6964,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_2 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(360,axiom,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ~ ( A @ ( B @ r2_hidden ) )
& ( A != B )
& ~ ( B @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_classes2) ).
thf(3973,plain,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ~ ( ~ ( A @ ( B @ r2_hidden ) )
& ( A != B )
& ~ ( B @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(1836,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_funct_3) ).
thf(11691,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1836]) ).
thf(1258,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_xboole_0 ) ) )
=> ( B @ ( A @ k3_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_zfmisc_1) ).
thf(8659,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_xboole_0 ) ) )
=> ( B @ ( A @ k3_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(1948,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k5_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) @ ( A @ k2_subset_1 @ ( A @ k6_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).
thf(12436,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k5_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) @ ( A @ k2_subset_1 @ ( A @ k6_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1948]) ).
thf(2125,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k5_finsub_1 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k5_finsub_1 @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k11_setwiseo ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k2_setwiseo ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_setwiseo) ).
thf(13414,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k5_finsub_1 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k5_finsub_1 @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k2_setwiseo ) ) ) )
=> ( B
= ( A @ k11_setwiseo ) ) )
& ( ( B
= ( A @ k11_setwiseo ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( A @ k2_setwiseo ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2125]) ).
thf(1843,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k9_relat_1 ) )
= ( A @ ( B @ k9_relat_1 ) @ ( C @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t159_relat_1) ).
thf(11748,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k9_relat_1 ) )
= ( A @ ( B @ k9_relat_1 ) @ ( C @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1843]) ).
thf(578,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( C @ v2_funct_1 )
<=> ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_funct_2) ).
thf(5032,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) )
=> ( C @ v2_funct_1 ) )
& ( ( C @ v2_funct_1 )
=> ! [D: $i,E: $i] :
( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ( ( ( ( C @ k5_funct_5 @ k1_relat_1 )
= B )
& ( ( C @ k3_funct_5 @ k1_relat_1 )
= A ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_funct_5) ).
thf(3290,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ( ( ( ( C @ k5_funct_5 @ k1_relat_1 )
= B )
& ( ( C @ k3_funct_5 @ k1_relat_1 )
= A ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(931,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_enumset1 ) ) )
= ( A @ ( B @ ( C @ k1_enumset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_enumset1) ).
thf(6823,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_enumset1 ) ) )
= ( A @ ( B @ ( C @ k1_enumset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(393,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( ( A @ ( B @ k1_funct_4 ) )
= B )
& ( ( B @ ( A @ k1_funct_4 ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funct_4) ).
thf(4115,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( ( A @ ( B @ k1_funct_4 ) )
= B )
& ( ( B @ ( A @ k1_funct_4 ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(2141,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ ( B @ ( A @ k2_borsuk_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( B @ ( A @ k2_borsuk_1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k2_borsuk_1 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_borsuk_1) ).
thf(13543,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ ( B @ ( A @ k2_borsuk_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( B @ ( A @ k2_borsuk_1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k2_borsuk_1 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2141]) ).
thf(2099,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
thf(13290,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2099]) ).
thf(980,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ ( A @ ( B @ k1_partfun1 ) ) ) ) ) )
= ( B @ k6_partfun1 ) )
=> ( ( C @ k2_relat_1 )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_funct_2) ).
thf(7139,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ ( A @ ( B @ k1_partfun1 ) ) ) ) ) )
= ( B @ k6_partfun1 ) )
=> ( ( C @ k2_relat_1 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(663,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( A @ r6_binop_1 ) ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( A @ ( B @ ( F @ m2_relset_1 ) ) )
& ( A @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( E @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( D @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( G @ ( F @ ( D @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ ( E @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_setwiseo) ).
thf(5457,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( A @ r6_binop_1 ) ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( A @ ( B @ ( F @ m2_relset_1 ) ) )
& ( A @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( E @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( D @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( G @ ( F @ ( D @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ ( E @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(525,axiom,
! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ ( A @ k6_relat_1 @ r2_hidden ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_altcat_1) ).
thf(4783,plain,
! [A: $i] : ( A @ ( A @ k1_funct_2 ) @ ( A @ k6_relat_1 @ r2_hidden ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ ( D @ ( C @ k4_tarski ) @ k1_tarski @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_relset_1) ).
thf(4556,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ ( D @ ( C @ k4_tarski ) @ k1_tarski @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(1389,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( B @ ( C @ ( A @ k2_tarski ) @ r1_xboole_0 ) )
& ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_zfmisc_1) ).
thf(9319,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( B @ ( C @ ( A @ k2_tarski ) @ r1_xboole_0 ) )
& ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389]) ).
thf(1479,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k5_finsub_1 )
= ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finsub_1) ).
thf(9779,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k5_finsub_1 )
= ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1479]) ).
thf(532,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ k4_tarski ) ) )
=> ! [B: $i] :
( ( B
= ( A @ k2_mcart_1 ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ k4_tarski ) ) )
=> ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_mcart_1) ).
thf(4810,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( C @ ( B @ k4_tarski ) ) )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ k4_tarski ) ) )
=> ( B = D ) )
=> ( B
= ( A @ k2_mcart_1 ) ) )
& ( ( B
= ( A @ k2_mcart_1 ) )
=> ! [C: $i,D: $i] :
( ( A
= ( D @ ( C @ k4_tarski ) ) )
=> ( B = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(806,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_zfmisc_1) ).
thf(6204,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(335,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_setfam_1 @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r2_hidden ) )
& ( B @ ( A @ k1_zfmisc_1 @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_classes2) ).
thf(3851,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_setfam_1 @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r2_hidden ) )
& ( B @ ( A @ k1_zfmisc_1 @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(2287,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k16_domain_1 ) ) ) )
= ( D @ k19_mcart_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k16_domain_1) ).
thf(14209,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k16_domain_1 ) ) ) )
= ( D @ k19_mcart_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2287]) ).
thf(1386,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( B @ ( D @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( D @ k1_relat_1 ) ) )
=> ( ( ( B @ ( A @ k10_funct_3 ) @ ( D @ ( C @ k13_funct_3 ) @ k5_relat_1 ) )
= D )
& ( ( B @ ( A @ k9_funct_3 ) @ ( D @ ( C @ k13_funct_3 ) @ k5_relat_1 ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_3) ).
thf(9309,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( B @ ( D @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( D @ k1_relat_1 ) ) )
=> ( ( ( B @ ( A @ k10_funct_3 ) @ ( D @ ( C @ k13_funct_3 ) @ k5_relat_1 ) )
= D )
& ( ( B @ ( A @ k9_funct_3 ) @ ( D @ ( C @ k13_funct_3 ) @ k5_relat_1 ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386]) ).
thf(739,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k6_pralg_1 ) @ ( A @ ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ k9_funcop_1 ) ) ) )
= ( A @ ( B @ k2_zfmisc_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_pralg_1) ).
thf(5834,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k6_pralg_1 ) @ ( A @ ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ k9_funcop_1 ) ) ) )
= ( A @ ( B @ k2_zfmisc_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(1815,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( A @ ( F @ m2_relset_1 ) ) )
& ( C @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( C @ ( A @ ( G @ m2_relset_1 ) ) )
& ( C @ ( A @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ k13_funct_3 ) )
= ( G @ ( E @ k13_funct_3 ) ) )
=> ( ( ( F = G )
& ( D = E ) )
| ( ( A != k1_xboole_0 )
& ( C = k1_xboole_0 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_funct_3) ).
thf(11523,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( A @ ( F @ m2_relset_1 ) ) )
& ( C @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( C @ ( A @ ( G @ m2_relset_1 ) ) )
& ( C @ ( A @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ k13_funct_3 ) )
= ( G @ ( E @ k13_funct_3 ) ) )
=> ( ( ( F = G )
& ( D = E ) )
| ( ( A != k1_xboole_0 )
& ( C = k1_xboole_0 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1815]) ).
thf(1191,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ k4_card_3 )
= k1_xboole_0 )
<=> ( A @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_card_3) ).
thf(8274,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( A @ k4_card_3 )
= k1_xboole_0 ) )
& ( ( ( A @ k4_card_3 )
= k1_xboole_0 )
=> ( A @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(1764,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(11218,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1764]) ).
thf(894,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_tarski @ v1_realset1 )
& ( A @ k1_tarski @ v1_fraenkel )
& ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_altcat_1) ).
thf(6631,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_tarski @ v1_realset1 )
& ( A @ k1_tarski @ v1_fraenkel )
& ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(183,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_finseq_1 )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m2_finseq_1 ) )
=> ( ( E
= ( D @ ( G @ ( F @ k4_funcop_1 ) ) ) )
=> ( ( E @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_finseq_2) ).
thf(3189,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_finseq_1 )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m2_finseq_1 ) )
=> ( ( E
= ( D @ ( G @ ( F @ k4_funcop_1 ) ) ) )
=> ( ( E @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
=> ( ( A @ ( k5_numbers @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_finseq_1) ).
thf(3712,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
=> ( ( A @ ( k5_numbers @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(1084,axiom,
( ( k1_numbers @ ( k35_binop_2 @ v2_binop_1 ) )
& ( k1_numbers @ ( k35_binop_2 @ v1_binop_1 ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k35_binop_2 @ v1_funct_2 ) ) )
& ( k35_binop_2 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_binop_2) ).
thf(7645,plain,
( ( k1_numbers @ ( k35_binop_2 @ v2_binop_1 ) )
& ( k1_numbers @ ( k35_binop_2 @ v1_binop_1 ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k35_binop_2 @ v1_funct_2 ) ) )
& ( k35_binop_2 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(605,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).
thf(5169,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(1023,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( B @ k1_relat_1 @ ( C @ r1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= ( C @ ( A @ k7_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funct_4) ).
thf(7413,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( B @ k1_relat_1 @ ( C @ r1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= ( C @ ( A @ k7_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(1902,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_partfun1) ).
thf(12090,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1902]) ).
thf(1033,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k15_funct_3 ) @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) @ ( C @ ( A @ k1_funct_1 ) @ k4_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_funct_3) ).
thf(7473,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k15_funct_3 ) @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) @ ( C @ ( A @ k1_funct_1 ) @ k4_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(1960,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relset_1) ).
thf(12504,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
& ( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1960]) ).
thf(1604,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
& ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_binop_1) ).
thf(10404,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
& ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r6_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r6_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( ( F @ ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) )
& ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1604]) ).
thf(381,axiom,
! [A: $i,B: $i] :
( ( B @ k6_partfun1 @ ( A @ k6_partfun1 @ r1_tarski ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_4) ).
thf(4055,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k6_partfun1 @ ( A @ k6_partfun1 @ r1_tarski ) ) )
& ( ( B @ k6_partfun1 @ ( A @ k6_partfun1 @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(1612,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( ( ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( F @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
& ( D @ ( E @ r2_hidden ) ) )
=> ( D @ ( F @ r2_hidden ) ) ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_t_0topsp) ).
thf(10442,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( ( ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( F @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
& ( D @ ( E @ r2_hidden ) ) )
=> ( D @ ( F @ r2_hidden ) ) ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1612]) ).
thf(660,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k2_ens_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_ens_1 ) ) @ ( D @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_2 ) @ ( D @ k2_mcart_1 @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_ens_1) ).
thf(5448,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k2_ens_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_ens_1 ) ) @ ( D @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_2 ) @ ( D @ k2_mcart_1 @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(1449,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_relat_1) ).
thf(9616,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k3_xboole_0 ) @ ( C @ ( B @ k3_xboole_0 ) @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449]) ).
thf(244,axiom,
! [A: $i] :
( ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k4_relat_1 @ v1_funct_1 )
& ( A @ k4_relat_1 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funct_1) ).
thf(3421,plain,
! [A: $i] :
( ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k4_relat_1 @ v1_funct_1 )
& ( A @ k4_relat_1 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(914,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( A @ ( A @ ( A @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( B @ ( A @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_enumset1) ).
thf(6740,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( A @ ( A @ ( A @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( B @ ( A @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_card_fil ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_card_fil ) )
= ( B @ ( A @ k7_setfam_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_card_fil) ).
thf(2483,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_card_fil ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_card_fil ) )
= ( B @ ( A @ k7_setfam_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1288,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ k3_xboole_0 ) @ ( C @ ( B @ ( A @ k3_xboole_0 ) @ k5_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_relset_2) ).
thf(8817,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ k3_xboole_0 ) @ ( C @ ( B @ ( A @ k3_xboole_0 ) @ k5_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(1419,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_mcart_1) ).
thf(9452,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419]) ).
thf(2340,axiom,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
<=> ( ( B @ p1_s1_subset_1 )
& ( f1_s1_subset_1 @ ( B @ r2_hidden ) ) ) )
& ( f1_s1_subset_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_subset_1) ).
thf(14410,plain,
? [A: $i] :
( ! [B: $i] :
( ( ( ( B @ p1_s1_subset_1 )
& ( f1_s1_subset_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ p1_s1_subset_1 )
& ( f1_s1_subset_1 @ ( B @ r2_hidden ) ) ) ) )
& ( f1_s1_subset_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2340]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_classes2 )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( B @ ( A @ k2_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_classes2) ).
thf(3808,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_classes2 )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( B @ ( A @ k2_tarski ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(1345,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_relat_1) ).
thf(9140,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).
thf(446,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_relset_1) ).
thf(4364,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(1935,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_pboole ) )
=> ( ( D
= ( C @ ( B @ ( A @ k3_altcat_1 ) ) ) )
<=> ! [E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( ( G @ ( F @ ( E @ ( D @ k1_multop_1 ) ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( G @ ( F @ ( C @ k1_binop_1 ) ) @ k2_zfmisc_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_altcat_1) ).
thf(12315,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( D @ m1_pboole ) )
=> ( ( ! [E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( ( G @ ( F @ ( E @ ( D @ k1_multop_1 ) ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( G @ ( F @ ( C @ k1_binop_1 ) ) @ k2_zfmisc_1 ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k3_altcat_1 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k3_altcat_1 ) ) ) )
=> ! [E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( ( G @ ( F @ ( E @ ( D @ k1_multop_1 ) ) ) )
= ( F @ ( E @ ( B @ k1_binop_1 ) ) @ ( G @ ( F @ ( C @ k1_binop_1 ) ) @ k2_zfmisc_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1935]) ).
thf(1139,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ k1_funct_1 ) )
= ( B @ ( C @ ( A @ k6_relat_1 @ k5_relat_1 ) @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_1) ).
thf(7909,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ k1_funct_1 ) )
= ( B @ ( C @ ( A @ k6_relat_1 @ k5_relat_1 ) @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(2253,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( A @ k11_setwiseo @ ( A @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r2_hidden ) )
& ( D @ ( A @ k11_setwiseo @ ( A @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( B @ r2_hidden ) ) )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_setwiseo) ).
thf(14071,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( A @ k11_setwiseo @ ( A @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( C @ r2_hidden ) )
& ( D @ ( A @ k11_setwiseo @ ( A @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( B @ r2_hidden ) ) )
=> ( B = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2253]) ).
thf(2056,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_setfam_1) ).
thf(13072,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k7_setfam_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r2_hidden ) ) )
& ( ( B @ ( A @ k7_setfam_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2056]) ).
thf(1905,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_mcart_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ a_8_0_domain_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_domain_1) ).
thf(12101,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_mcart_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ a_8_0_domain_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1905]) ).
thf(2391,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k1_relset_2 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relset_2) ).
thf(14658,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k1_relset_2 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2391]) ).
thf(906,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ~ ( ( ( C @ ( B @ k10_funct_3 ) @ ( E @ ( D @ k13_funct_3 ) @ k5_relat_1 ) )
= E )
& ( ( C @ ( B @ k9_funct_3 ) @ ( E @ ( D @ k13_funct_3 ) @ k5_relat_1 ) )
= D ) )
& ( ( C = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_funct_3) ).
thf(6702,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ~ ( ( ( C @ ( B @ k10_funct_3 ) @ ( E @ ( D @ k13_funct_3 ) @ k5_relat_1 ) )
= E )
& ( ( C @ ( B @ k9_funct_3 ) @ ( E @ ( D @ k13_funct_3 ) @ k5_relat_1 ) )
= D ) )
& ( ( C = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(534,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
<=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_lattice2) ).
thf(4825,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) ) ) )
& ( ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k2_partfun1 ) ) ) ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(940,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ k8_relat_1 ) @ ( B @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_relat_1) ).
thf(6863,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ k8_relat_1 ) @ ( B @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(905,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_funct_1) ).
thf(6700,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(2385,axiom,
! [A: $i] :
( ( a_0_18_fraenkel @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ( B @ p1_s10_fraenkel )
& ( A = B )
& ( f1_s10_fraenkel @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_18_fraenkel) ).
thf(14622,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ p1_s10_fraenkel )
& ( A = B )
& ( f1_s10_fraenkel @ ( B @ m1_subset_1 ) ) )
=> ( a_0_18_fraenkel @ ( A @ r2_hidden ) ) )
& ( ( a_0_18_fraenkel @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ( B @ p1_s10_fraenkel )
& ( A = B )
& ( f1_s10_fraenkel @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2385]) ).
thf(769,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) )
= ( E @ ( D @ k13_funct_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k14_funct_3) ).
thf(6021,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) )
= ( E @ ( D @ k13_funct_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(1684,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( G @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ! [H: $i] :
( ( ( F @ ( E @ ( D @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( F @ ( E @ ( D @ k2_zfmisc_1 ) @ ( H @ v1_funct_2 ) ) )
& ( H @ v1_funct_1 ) )
=> ~ ( ~ ( ( F @ ( C @ k2_zfmisc_1 ) @ ( E @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( H @ ( G @ k3_funct_4 ) @ m2_relset_1 ) ) )
& ( F @ ( C @ k2_zfmisc_1 ) @ ( E @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( H @ ( G @ k3_funct_4 ) @ v1_funct_2 ) ) )
& ( H @ ( G @ k3_funct_4 ) @ v1_funct_1 ) )
& ( F != k1_xboole_0 )
& ( C != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funct_4) ).
thf(10801,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( G @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ! [H: $i] :
( ( ( F @ ( E @ ( D @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( F @ ( E @ ( D @ k2_zfmisc_1 ) @ ( H @ v1_funct_2 ) ) )
& ( H @ v1_funct_1 ) )
=> ~ ( ~ ( ( F @ ( C @ k2_zfmisc_1 ) @ ( E @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( H @ ( G @ k3_funct_4 ) @ m2_relset_1 ) ) )
& ( F @ ( C @ k2_zfmisc_1 ) @ ( E @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( H @ ( G @ k3_funct_4 ) @ v1_funct_2 ) ) )
& ( H @ ( G @ k3_funct_4 ) @ v1_funct_1 ) )
& ( F != k1_xboole_0 )
& ( C != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1684]) ).
thf(1398,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) )
& ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
<=> ( ( B @ k1_relat_1 @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k5_relat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funct_1) ).
thf(9368,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) )
& ! [D: $i] :
( ( ( ( B @ k1_relat_1 @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( B @ k1_relat_1 @ ( D @ ( A @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) )
=> ( C
= ( B @ ( A @ k5_relat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398]) ).
thf(1432,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k1_funct_4 ) )
= ( C @ ( B @ k1_funct_4 ) @ ( A @ k1_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_4) ).
thf(9533,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k1_funct_4 ) )
= ( C @ ( B @ k1_funct_4 ) @ ( A @ k1_funct_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432]) ).
thf(1367,axiom,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ( A @ k1_tarski @ v1_realset1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_tex_2) ).
thf(9236,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ( A @ k1_tarski @ v1_realset1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).
thf(1851,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( A @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( D @ ( F @ m2_relset_1 ) ) )
& ( B @ ( D @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ~ ( G @ v1_xboole_0 ) )
=> ! [H: $i] :
( ( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
& ~ ( H @ v1_xboole_0 ) )
=> ( ( H @ ( G @ ( D @ ( C @ k12_mcart_1 ) ) ) @ ( F @ ( E @ ( B @ ( A @ ( D @ ( C @ k9_cat_2 ) ) ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ k2_zfmisc_1 ) @ k1_nattra_1 ) ) ) )
= ( H @ ( F @ ( B @ ( D @ k1_nattra_1 ) ) ) @ ( G @ ( E @ ( A @ ( C @ k1_nattra_1 ) ) ) @ ( B @ ( A @ ( H @ ( G @ k9_cat_2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_nattra_1) ).
thf(11783,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( A @ ( C @ ( E @ m2_relset_1 ) ) )
& ( A @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( D @ ( F @ m2_relset_1 ) ) )
& ( B @ ( D @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ~ ( G @ v1_xboole_0 ) )
=> ! [H: $i] :
( ( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
& ~ ( H @ v1_xboole_0 ) )
=> ( ( H @ ( G @ ( D @ ( C @ k12_mcart_1 ) ) ) @ ( F @ ( E @ ( B @ ( A @ ( D @ ( C @ k9_cat_2 ) ) ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ k2_zfmisc_1 ) @ k1_nattra_1 ) ) ) )
= ( H @ ( F @ ( B @ ( D @ k1_nattra_1 ) ) ) @ ( G @ ( E @ ( A @ ( C @ k1_nattra_1 ) ) ) @ ( B @ ( A @ ( H @ ( G @ k9_cat_2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1851]) ).
thf(80,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_finseq_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_finseq_1) ).
thf(2750,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_finseq_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1575,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_6_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_domain_1) ).
thf(10233,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_6_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1575]) ).
thf(1639,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_2) ).
thf(10574,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k2_funct_2 ) ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1639]) ).
thf(2388,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
<=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tex_2) ).
thf(14637,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B != A )
=> ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) ) )
& ( ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
=> ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2388]) ).
thf(1810,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A @ ( I @ m1_subset_1 ) )
& ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) )
= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k6_enumset1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k13_domain_1) ).
thf(11505,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A @ ( I @ m1_subset_1 ) )
& ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) )
= ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k6_enumset1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1810]) ).
thf(599,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
=> ( ( B @ k3_tarski @ ( D @ ( C @ ( A @ k2_funct_2 ) ) ) )
= ( B @ ( D @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_3) ).
thf(5137,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
=> ( ( B @ k3_tarski @ ( D @ ( C @ ( A @ k2_funct_2 ) ) ) )
= ( B @ ( D @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(889,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_tarski ) )
= ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(6616,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_tarski ) )
= ( A @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(1615,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k2_funct_5 @ ( B @ r2_hidden ) )
& ( C @ k1_funct_5 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_5) ).
thf(10459,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k2_funct_5 @ ( B @ r2_hidden ) )
& ( C @ k1_funct_5 @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1615]) ).
thf(1325,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k2_ens_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ens_1) ).
thf(9007,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k2_ens_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).
thf(976,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v8_monoid_0 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_monoid_0) ).
thf(7051,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) )
=> ( D = E ) ) ) ) )
=> ( A @ ( B @ v8_monoid_0 ) ) )
& ( ( A @ ( B @ v8_monoid_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(1376,axiom,
? [A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tex_2) ).
thf(9272,plain,
? [A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376]) ).
thf(1030,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( D @ ( B @ k1_funct_1 ) @ ( C @ k1_funct_1 ) @ ( D @ ( A @ k1_funct_1 ) @ r2_wellord2 ) ) )
& ( B @ v2_funct_1 )
& ( ( C @ k1_relat_1 )
= ( B @ k2_relat_1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( C @ k4_card_3 @ ( A @ k4_card_3 @ r2_wellord2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_6) ).
thf(7460,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( D @ ( B @ k1_funct_1 ) @ ( C @ k1_funct_1 ) @ ( D @ ( A @ k1_funct_1 ) @ r2_wellord2 ) ) )
& ( B @ v2_funct_1 )
& ( ( C @ k1_relat_1 )
= ( B @ k2_relat_1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( C @ k4_card_3 @ ( A @ k4_card_3 @ r2_wellord2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(641,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r2_wellord1 ) ) )
=> ( C @ ( A @ r2_wellord1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t187_orders_1) ).
thf(5328,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( ( B @ ( C @ r1_tarski ) )
& ( B @ ( A @ r2_wellord1 ) ) )
=> ( C @ ( A @ r2_wellord1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(1205,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_partfun1) ).
thf(8362,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( D @ k1_funct_1 ) @ k1_tarski @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_xboole_1) ).
thf(2982,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(2199,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k1_cantor_1 ) @ ( B @ ( A @ k1_cantor_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_cantor_1) ).
thf(13838,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k1_cantor_1 ) @ ( B @ ( A @ k1_cantor_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2199]) ).
thf(2087,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_partfun1) ).
thf(13248,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2087]) ).
thf(1534,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_xboole_1) ).
thf(10029,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534]) ).
thf(997,axiom,
! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) )
<=> ( A @ k3_tarski @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finset_1) ).
thf(7230,plain,
! [A: $i] :
( ( ( A @ k3_tarski @ v1_finset_1 )
=> ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) ) )
& ( ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_finset_1 ) )
& ( A @ v1_finset_1 ) )
=> ( A @ k3_tarski @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(713,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( k1_xboole_0 @ ( A @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_partfun1) ).
thf(5695,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( k1_xboole_0 @ ( A @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(1273,axiom,
( ( k1_xboole_0 @ v1_finseq_1 )
& ( k1_xboole_0 @ v1_funct_1 )
& ( k1_xboole_0 @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finseq_1) ).
thf(8742,plain,
( ( k1_xboole_0 @ v1_finseq_1 )
& ( k1_xboole_0 @ v1_funct_1 )
& ( k1_xboole_0 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(2170,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) )
=> ( E @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_funct_7) ).
thf(13683,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) )
=> ( E @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2170]) ).
thf(1972,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(12559,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1972]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_partfun1) ).
thf(2762,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( A @ ( B @ ( C @ k2_funct_1 @ m2_relset_1 ) ) )
& ( C @ k2_funct_1 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(233,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v8_monoid_0 ) )
<=> ( ( A @ ( B @ v7_monoid_0 ) )
& ( A @ ( B @ v6_monoid_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_monoid_0) ).
thf(3378,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( ( A @ ( B @ v7_monoid_0 ) )
& ( A @ ( B @ v6_monoid_0 ) ) )
=> ( A @ ( B @ v8_monoid_0 ) ) )
& ( ( A @ ( B @ v8_monoid_0 ) )
=> ( ( A @ ( B @ v7_monoid_0 ) )
& ( A @ ( B @ v6_monoid_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1491,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( G @ m2_relset_1 ) ) )
& ( G @ v1_funct_1 ) )
=> ! [H: $i] :
( ( ( F @ ( E @ ( D @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( H @ v1_funct_1 ) )
=> ( ( F @ ( C @ k2_zfmisc_1 ) @ ( E @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( H @ ( G @ k3_funct_4 ) @ m2_relset_1 ) ) )
& ( H @ ( G @ k3_funct_4 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_4) ).
thf(9822,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( G @ m2_relset_1 ) ) )
& ( G @ v1_funct_1 ) )
=> ! [H: $i] :
( ( ( F @ ( E @ ( D @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( H @ v1_funct_1 ) )
=> ( ( F @ ( C @ k2_zfmisc_1 ) @ ( E @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( H @ ( G @ k3_funct_4 ) @ m2_relset_1 ) ) )
& ( H @ ( G @ k3_funct_4 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1491]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ m2_relset_1 ) ) )
& ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ k1_funct_1 ) @ v1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_pboole) ).
thf(2473,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ m2_relset_1 ) ) )
& ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ k1_funct_1 ) @ v1_funct_1 ) ) )
=> ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) ) )
& ( ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ m2_relset_1 ) ) )
& ( E @ ( C @ k1_funct_1 ) @ ( E @ ( B @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ k1_funct_1 ) @ v1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1362,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ k3_funcop_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_funcop_1) ).
thf(9221,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ k3_funcop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362]) ).
thf(1853,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C != k1_xboole_0 )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ v1_funct_2 ) ) )
& ( D @ k2_funct_4 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_funct_4) ).
thf(11791,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C != k1_xboole_0 )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ v1_funct_2 ) ) )
& ( D @ k2_funct_4 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1853]) ).
thf(659,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_card_fil ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( C @ ( A @ k7_setfam_1 ) @ ( D @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) ) ) )
& ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( B @ ( A @ k2_card_fil ) @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_card_fil) ).
thf(5443,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_card_fil ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( C @ ( A @ k7_setfam_1 ) @ ( D @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) ) ) )
& ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( B @ ( A @ k2_card_fil ) @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(777,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k6_partfun1 @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funcop_1) ).
thf(6058,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k6_partfun1 @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(1261,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r7_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_funct_1 ) )
= ( E @ ( B @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_binop_1) ).
thf(8668,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_funct_1 ) )
= ( E @ ( B @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ ( C @ k1_binop_1 ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r7_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r7_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ k1_binop_1 ) ) @ ( B @ k1_funct_1 ) )
= ( E @ ( B @ k1_funct_1 ) @ ( D @ ( B @ k1_funct_1 ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(1940,axiom,
! [A: $i] :
( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( ( A @ k2_funct_5 )
= k1_xboole_0 )
& ( ( A @ k1_funct_5 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_5) ).
thf(12365,plain,
! [A: $i] :
( ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( ( A @ k2_funct_5 )
= k1_xboole_0 )
& ( ( A @ k1_funct_5 )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1940]) ).
thf(821,axiom,
! [A: $i] :
( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_1) ).
thf(6282,plain,
! [A: $i] :
( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( B = C ) ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(1275,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k10_relat_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc18_finseq_1) ).
thf(8751,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k10_relat_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(1527,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_zfmisc_1) ).
thf(9997,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ r1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527]) ).
thf(1087,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_partfun1) ).
thf(7657,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(1750,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ k1_tarski ) )
=> ( ( B @ ( A @ k7_setfam_1 ) )
= ( k1_xboole_0 @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_setfam_1) ).
thf(11159,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ k1_tarski ) )
=> ( ( B @ ( A @ k7_setfam_1 ) )
= ( k1_xboole_0 @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1750]) ).
thf(2364,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_setfam_1) ).
thf(14558,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2364]) ).
thf(1510,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( B
= ( A @ ( C @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
thf(9917,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( B
= ( A @ ( C @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B
= ( A @ ( C @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1510]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_partfun1) ).
thf(3899,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( D @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(607,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v3_binop_1 ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( F @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_setwiseo) ).
thf(5174,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v3_binop_1 ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ r2_hidden ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( F @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(2348,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_funct_3 ) )
= ( B @ k6_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_funct_3) ).
thf(14462,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_funct_3 ) )
= ( B @ k6_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2348]) ).
thf(540,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_tarski ) ) )
=> ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_partfun1) ).
thf(4853,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_tarski ) ) )
=> ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(2373,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(14588,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k2_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2373]) ).
thf(2210,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( G @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ! [H: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( H @ v1_funct_2 ) ) )
& ( H @ v1_funct_1 ) )
=> ( ( F @ ( D @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( H @ ( G @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( H @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( G @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ k1_domain_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_filter_1) ).
thf(13885,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( G @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ! [H: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( H @ v1_funct_2 ) ) )
& ( H @ v1_funct_1 ) )
=> ( ( F @ ( D @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( H @ ( G @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( H @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( G @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ k1_domain_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2210]) ).
thf(2001,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( B @ m2_card_fil ) )
<=> ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_subset_1 ) ) @ r2_hidden ) ) ) ) ) )
& ~ ( B @ ( A @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_card_fil) ).
thf(12732,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_subset_1 ) ) @ r2_hidden ) ) ) ) ) )
& ~ ( B @ ( A @ r2_hidden ) ) )
=> ( A @ ( B @ m2_card_fil ) ) )
& ( ( A @ ( B @ m2_card_fil ) )
=> ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k4_subset_1 ) ) @ r2_hidden ) ) ) ) ) )
& ~ ( B @ ( A @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2001]) ).
thf(1051,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_ens_1 @ v1_fraenkel )
& ~ ( A @ k1_ens_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ens_1) ).
thf(7535,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_ens_1 @ v1_fraenkel )
& ~ ( A @ k1_ens_1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(866,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ k13_funct_3 ) @ k10_relat_1 ) )
= ( B @ ( D @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_funct_3) ).
thf(6529,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ k13_funct_3 ) @ k10_relat_1 ) )
= ( B @ ( D @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(1666,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ k7_setfam_1 ) )
= k1_xboole_0 )
& ( B != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(10725,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ k7_setfam_1 ) )
= k1_xboole_0 )
& ( B != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1666]) ).
thf(650,axiom,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finseq_1) ).
thf(5406,plain,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(602,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
=> ( A @ k6_partfun1 @ ( C @ ( C @ ( B @ ( B @ ( A @ ( A @ k16_funct_3 ) ) ) ) ) @ ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ ( A @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) @ ( B @ k6_partfun1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_functor0) ).
thf(5157,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
=> ( A @ k6_partfun1 @ ( C @ ( C @ ( B @ ( B @ ( A @ ( A @ k16_funct_3 ) ) ) ) ) @ ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ ( A @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) @ ( B @ k6_partfun1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(2313,axiom,
! [A: $i] :
( ( A @ k1_eqrel_1 )
= ( A @ ( A @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_eqrel_1) ).
thf(14308,plain,
! [A: $i] :
( ( A @ k1_eqrel_1 )
= ( A @ ( A @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2313]) ).
thf(1460,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_partfun1) ).
thf(9682,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460]) ).
thf(1323,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finset_1) ).
thf(8999,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).
thf(410,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k7_relat_1 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_relat_1) ).
thf(4199,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k7_relat_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(2110,axiom,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_triang_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_triang_1) ).
thf(13337,plain,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_triang_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2110]) ).
thf(732,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m1_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_cat_2 ) ) ) ) ) )
= ( F @ ( E @ k15_funct_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_cat_2) ).
thf(5783,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m1_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_cat_2 ) ) ) ) ) )
= ( F @ ( E @ k15_funct_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(1440,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( k1_xboole_0 @ k8_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_relat_1) ).
thf(9571,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( k1_xboole_0 @ k8_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440]) ).
thf(213,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ k4_relat_1 )
= ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ k4_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_relat_1) ).
thf(3301,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ k4_relat_1 )
= ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ k4_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(1645,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( k1_numbers @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( k1_numbers @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_metric_1 ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_metric_1) ).
thf(10593,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( k1_numbers @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( k1_numbers @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_metric_1 ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1645]) ).
thf(1257,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
thf(8655,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(2026,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_relset_1) ).
thf(12895,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( D @ r2_hidden ) ) )
& ( ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( C @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2026]) ).
thf(2083,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_finset_1 )
& ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_finset_1) ).
thf(13228,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_finset_1 )
& ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2083]) ).
thf(556,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 )
= ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_relat_1) ).
thf(4962,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 )
= ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(1396,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(9340,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) )
=> ( B
= ( A @ k1_tarski ) ) )
& ( ( B
= ( A @ k1_tarski ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396]) ).
thf(1932,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( E @ ( E @ ( D @ ( C @ ( B @ ( A @ r4_nattra_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r4_nattra_1) ).
thf(12275,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( E @ ( E @ ( D @ ( C @ ( B @ ( A @ r4_nattra_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1932]) ).
thf(2048,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ k3_pua2mss1 @ ( D @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) )
= k1_xboole_0 )
<=> ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relset_2) ).
thf(13017,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C = k1_xboole_0 )
=> ( ( C @ k3_pua2mss1 @ ( D @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) )
= k1_xboole_0 ) )
& ( ( ( C @ k3_pua2mss1 @ ( D @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) )
= k1_xboole_0 )
=> ( C = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2048]) ).
thf(1336,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) )
=> ( C @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_partfun1) ).
thf(9090,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ k1_funct_1 ) )
= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) )
=> ( D = E ) ) ) )
=> ( C @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(741,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ( C @ k2_relat_1 )
= B )
<=> ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( B @ ( E @ m2_relset_1 ) ) )
& ( D @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( B @ ( F @ m2_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( E @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_2) ).
thf(5839,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( B @ ( E @ m2_relset_1 ) ) )
& ( D @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( B @ ( F @ m2_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( E @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) )
=> ( ( C @ k2_relat_1 )
= B ) )
& ( ( ( C @ k2_relat_1 )
= B )
=> ! [D: $i] :
( ( D != k1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( B @ ( E @ m2_relset_1 ) ) )
& ( D @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( B @ ( F @ m2_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( E @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( F @ ( C @ ( D @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(303,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_funct_1 )
= ( A @ k2_funct_1 @ ( B @ k2_funct_1 @ k5_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_1) ).
thf(3720,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_funct_1 )
= ( A @ k2_funct_1 @ ( B @ k2_funct_1 @ k5_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(652,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
<=> ! [B: $i] :
? [C: $i] : ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t159_funct_1) ).
thf(5411,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i] :
? [C: $i] : ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k10_relat_1 ) @ r1_tarski ) )
=> ( A @ v2_funct_1 ) )
& ( ( A @ v2_funct_1 )
=> ! [B: $i] :
? [C: $i] : ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(1817,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_funct_2) ).
thf(11550,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i,G: $i] :
( ( ( B @ ( G @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1817]) ).
thf(2184,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ k2_cantor_1 ) @ ( D @ r1_tarski ) )
& ( B @ ( A @ k2_cantor_1 ) @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k2_cantor_1 ) @ ( D @ ( C @ k3_setfam_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_cantor_1) ).
thf(13767,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ k2_cantor_1 ) @ ( D @ r1_tarski ) )
& ( B @ ( A @ k2_cantor_1 ) @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k2_cantor_1 ) @ ( D @ ( C @ k3_setfam_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2184]) ).
thf(2060,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k4_funct_2 ) ) )
= ( C @ ( B @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_funct_2) ).
thf(13104,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k4_funct_2 ) ) )
= ( C @ ( B @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2060]) ).
thf(814,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_lattice2) ).
thf(6250,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(1312,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( C @ ( B @ k2_zfmisc_1 ) @ ( E @ ( D @ k13_funct_3 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_funct_3) ).
thf(8959,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( C @ ( B @ k2_zfmisc_1 ) @ ( E @ ( D @ k13_funct_3 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).
thf(970,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_realset1 ) ) @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_realset1 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_realset1) ).
thf(7019,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_realset1 ) ) @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ ( A @ k2_realset1 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_realset1 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(1777,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funcop_1) ).
thf(11324,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1777]) ).
thf(219,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k7_funct_6 @ v1_funct_1 )
& ( A @ k7_funct_6 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funct_6) ).
thf(3318,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k7_funct_6 @ v1_funct_1 )
& ( A @ k7_funct_6 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(1326,axiom,
( ( k1_numbers @ ( k35_binop_2 @ v1_setwiseo ) )
& ( k1_numbers @ ( k35_binop_2 @ v2_binop_1 ) )
& ( k1_numbers @ ( k35_binop_2 @ v1_binop_1 ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k35_binop_2 @ v1_funct_2 ) ) )
& ( k35_binop_2 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc17_binop_2) ).
thf(9009,plain,
( ( k1_numbers @ ( k35_binop_2 @ v1_setwiseo ) )
& ( k1_numbers @ ( k35_binop_2 @ v2_binop_1 ) )
& ( k1_numbers @ ( k35_binop_2 @ v1_binop_1 ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k35_binop_2 @ v1_funct_2 ) ) )
& ( k35_binop_2 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).
thf(877,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( E @ ( F @ ( B @ k2_setwiseo ) @ ( D @ ( B @ k5_setwiseo ) ) @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= ( F @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_setwiseo) ).
thf(6571,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( E @ ( F @ ( B @ k2_setwiseo ) @ ( D @ ( B @ k5_setwiseo ) ) @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= ( F @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(1728,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ k2_funct_2 ) ) ) )
= k1_xboole_0 )
=> ( D = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_setwiseo) ).
thf(11069,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ k2_funct_2 ) ) ) )
= k1_xboole_0 )
=> ( D = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1728]) ).
thf(653,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_pboole ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_pboole ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_pboole ) )
=> ! [I: $i] :
( ( G @ ( F @ ( D @ ( B @ ( A @ ( I @ m1_functor0 ) ) ) ) ) )
=> ! [J: $i] :
( ( H @ ( G @ ( D @ ( B @ ( A @ k7_pboole ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ ( J @ m1_functor0 ) ) ) ) ) )
=> ( ! [K: $i] :
~ ( ( ( K @ ( H @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ k7_pboole ) ) ) @ k1_funct_1 ) )
!= k1_xboole_0 )
& ( ( K @ ( F @ k1_funct_1 ) )
!= k1_xboole_0 )
& ( ( K @ ( G @ ( D @ ( B @ ( A @ k7_pboole ) ) ) @ k1_funct_1 ) )
= k1_xboole_0 )
& ( A @ ( K @ r2_hidden ) ) )
=> ( H @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ ( J @ ( I @ k13_pboole ) @ m1_functor0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_functor0) ).
thf(5416,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_pboole ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_pboole ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_pboole ) )
=> ! [I: $i] :
( ( G @ ( F @ ( D @ ( B @ ( A @ ( I @ m1_functor0 ) ) ) ) ) )
=> ! [J: $i] :
( ( H @ ( G @ ( D @ ( B @ ( A @ k7_pboole ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ ( J @ m1_functor0 ) ) ) ) ) )
=> ( ! [K: $i] :
~ ( ( ( K @ ( H @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ k7_pboole ) ) ) @ k1_funct_1 ) )
!= k1_xboole_0 )
& ( ( K @ ( F @ k1_funct_1 ) )
!= k1_xboole_0 )
& ( ( K @ ( G @ ( D @ ( B @ ( A @ k7_pboole ) ) ) @ k1_funct_1 ) )
= k1_xboole_0 )
& ( A @ ( K @ r2_hidden ) ) )
=> ( H @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ ( J @ ( I @ k13_pboole ) @ m1_functor0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(1349,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( C @ k7_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
<=> ( ( C @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
thf(9164,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( ( C @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( B @ ( C @ k7_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ ( C @ k7_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( C @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).
thf(670,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ k5_funcop_1 ) ) @ k5_relat_1 ) )
= ( B @ ( D @ ( A @ ( C @ k5_relat_1 ) @ k5_funcop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_funcop_1) ).
thf(5487,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ k5_funcop_1 ) ) @ k5_relat_1 ) )
= ( B @ ( D @ ( A @ ( C @ k5_relat_1 ) @ k5_funcop_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(968,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v7_monoid_0 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_monoid_0) ).
thf(7005,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) )
=> ( D = E ) ) ) ) )
=> ( A @ ( B @ v7_monoid_0 ) ) )
& ( ( A @ ( B @ v7_monoid_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(742,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k5_finsub_1 @ ( B @ ( A @ k2_setwiseo ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_setwiseo) ).
thf(5862,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k5_finsub_1 @ ( B @ ( A @ k2_setwiseo ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(51,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( D @ v1_finseq_1 )
& ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m2_finseq_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m2_finseq_1 ) )
=> ( ( ( D
= ( G @ ( F @ ( E @ k3_funcop_1 ) ) ) )
& ( ( F @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) ) )
=> ( ( ( D @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) )
& ( ( D @ k3_finseq_1 )
= ( F @ k3_finseq_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_finseq_2) ).
thf(2641,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( D @ v1_finseq_1 )
& ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m2_finseq_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m2_finseq_1 ) )
=> ( ( ( D
= ( G @ ( F @ ( E @ k3_funcop_1 ) ) ) )
& ( ( F @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) ) )
=> ( ( ( D @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) )
& ( ( D @ k3_finseq_1 )
= ( F @ k3_finseq_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(945,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_partfun1) ).
thf(6884,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= ( C @ ( B @ ( A @ k4_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(677,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( F @ ( E @ r1_partfun1 ) )
=> ( ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( F @ ( E @ k3_xboole_0 ) @ m2_relset_1 ) ) )
& ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( F @ ( E @ k3_xboole_0 ) @ v1_funct_2 ) ) )
& ( F @ ( E @ k3_xboole_0 ) @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_yellow20) ).
thf(5519,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( F @ ( E @ r1_partfun1 ) )
=> ( ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( F @ ( E @ k3_xboole_0 ) @ m2_relset_1 ) ) )
& ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ ( F @ ( E @ k3_xboole_0 ) @ v1_funct_2 ) ) )
& ( F @ ( E @ k3_xboole_0 ) @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(1974,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D )
& ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_binop_1) ).
thf(12565,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D )
& ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ ( B @ k1_binop_1 ) ) )
= D )
& ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1974]) ).
thf(1481,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( C @ v1_setwiseo ) )
& ( B @ ( C @ v3_binop_1 ) )
& ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ k5_finsub_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ k5_finsub_1 @ ( G @ m1_subset_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k8_setwiseo ) ) ) )
= ( G @ ( E @ ( B @ ( A @ k8_setwiseo ) ) ) ) )
=> ( ( D @ ( F @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) )
= ( E @ ( G @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_setwiseo) ).
thf(9785,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( C @ v1_setwiseo ) )
& ( B @ ( C @ v3_binop_1 ) )
& ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ k5_finsub_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ k5_finsub_1 @ ( G @ m1_subset_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k8_setwiseo ) ) ) )
= ( G @ ( E @ ( B @ ( A @ k8_setwiseo ) ) ) ) )
=> ( ( D @ ( F @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) )
= ( E @ ( G @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481]) ).
thf(433,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_binop_1) ).
thf(4312,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r4_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r6_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r4_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(1911,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relset_2 ) @ v1_funct_1 )
& ( B @ ( A @ k5_relset_2 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_2) ).
thf(12127,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relset_2 ) @ v1_funct_1 )
& ( B @ ( A @ k5_relset_2 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1911]) ).
thf(1929,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k2_cantor_1 ) ) )
<=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( D
= ( E @ ( A @ k8_setfam_1 ) ) )
& ( E @ v1_finset_1 )
& ( B @ ( E @ r1_tarski ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_cantor_1) ).
thf(12232,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( D
= ( E @ ( A @ k8_setfam_1 ) ) )
& ( E @ v1_finset_1 )
& ( B @ ( E @ r1_tarski ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ k8_setfam_1 ) ) )
& ( E @ v1_finset_1 )
& ( B @ ( E @ r1_tarski ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) )
=> ( C
= ( B @ ( A @ k2_cantor_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k2_cantor_1 ) ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( D
= ( E @ ( A @ k8_setfam_1 ) ) )
& ( E @ v1_finset_1 )
& ( B @ ( E @ r1_tarski ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ k8_setfam_1 ) ) )
& ( E @ v1_finset_1 )
& ( B @ ( E @ r1_tarski ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1929]) ).
thf(1991,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(12673,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1991]) ).
thf(1794,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_2) ).
thf(11410,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_2 ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1794]) ).
thf(1266,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ ( A @ ( B @ k7_relat_1 ) @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_partfun1) ).
thf(8712,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ ( A @ ( B @ k7_relat_1 ) @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(1426,axiom,
( ( k1_numbers @ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ ( k3_metric_1 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ ( k3_metric_1 @ v1_funct_2 ) ) )
& ( k3_metric_1 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_metric_1) ).
thf(9488,plain,
( ( k1_numbers @ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ ( k3_metric_1 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_xboole_0 @ k1_tarski @ ( k1_xboole_0 @ k1_tarski @ k2_zfmisc_1 ) @ ( k3_metric_1 @ v1_funct_2 ) ) )
& ( k3_metric_1 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1426]) ).
thf(1201,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_funct_2) ).
thf(8343,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(781,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( F @ v1_funct_1 )
& ( F @ v1_relat_1 ) )
=> ( ( F @ ( E @ k3_funct_4 ) @ k1_relat_1 @ ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) @ ( F @ ( E @ k3_funct_4 ) @ k1_funct_1 ) )
= ( D @ ( B @ k4_tarski ) @ ( F @ k1_funct_1 ) @ ( C @ ( A @ k4_tarski ) @ ( E @ k1_funct_1 ) @ k4_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_funct_4) ).
thf(6079,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( F @ v1_funct_1 )
& ( F @ v1_relat_1 ) )
=> ( ( F @ ( E @ k3_funct_4 ) @ k1_relat_1 @ ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) @ ( F @ ( E @ k3_funct_4 ) @ k1_funct_1 ) )
= ( D @ ( B @ k4_tarski ) @ ( F @ k1_funct_1 ) @ ( C @ ( A @ k4_tarski ) @ ( E @ k1_funct_1 ) @ k4_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(1824,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
thf(11587,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: $i,D: $i] :
( ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1824]) ).
thf(1607,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
=> ( ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= B )
& ( ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relset_1) ).
thf(10426,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
=> ( ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= B )
& ( ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1607]) ).
thf(1357,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_mcart_1 ) ) )
= ( C @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_mcart_1) ).
thf(9207,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_mcart_1 ) ) )
= ( C @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(2013,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C
= ( B @ ( A @ k2_borsuk_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_borsuk_1) ).
thf(12809,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( D @ r2_hidden ) ) )
=> ( C
= ( B @ ( A @ k2_borsuk_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k2_borsuk_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2013]) ).
thf(526,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_binop_1) ).
thf(4785,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
=> ( B @ ( C @ ( A @ r6_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(1302,axiom,
? [A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_realset1) ).
thf(8878,plain,
? [A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).
thf(1555,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t107_zfmisc_1) ).
thf(10133,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( C @ ( D @ k2_zfmisc_1 ) @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1555]) ).
thf(1231,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ v1_finseq_1 )
& ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ v1_funct_1 )
& ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ v1_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_finseq_2) ).
thf(8513,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ v1_finseq_1 )
& ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ v1_funct_1 )
& ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ v1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(1549,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ g2_vectsp_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ g2_vectsp_1 ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g2_vectsp_1) ).
thf(10099,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ g2_vectsp_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ g2_vectsp_1 ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1549]) ).
thf(1471,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
& ( D @ ( B @ k1_relat_1 @ r1_tarski ) )
& ( C @ ( A @ k1_relat_1 @ r1_tarski ) ) )
=> ( ( ( D @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= B )
& ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_funct_4) ).
thf(9722,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( ( D @ ( C @ r1_xboole_0 ) )
& ( D @ ( B @ k1_relat_1 @ r1_tarski ) )
& ( C @ ( A @ k1_relat_1 @ r1_tarski ) ) )
=> ( ( ( D @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= B )
& ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471]) ).
thf(203,axiom,
( ( ( k1_xboole_0 @ k5_funct_5 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k3_funct_5 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funct_5) ).
thf(3261,plain,
( ( ( k1_xboole_0 @ k5_funct_5 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k3_funct_5 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(1844,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(11751,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r2_hidden ) ) )
& ( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1844]) ).
thf(1981,axiom,
! [A: $i] :
( ( ( ( A @ k2_funct_5 )
= k1_xboole_0 )
| ( ( A @ k1_funct_5 )
= k1_xboole_0 ) )
=> ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_5) ).
thf(12613,plain,
! [A: $i] :
( ( ( ( A @ k2_funct_5 )
= k1_xboole_0 )
| ( ( A @ k1_funct_5 )
= k1_xboole_0 ) )
=> ! [B: $i,C: $i] :
~ ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1981]) ).
thf(698,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k1_funct_4 ) @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funct_4) ).
thf(5611,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k1_funct_4 ) @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(2126,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g2_lattices ) )
= ( D @ ( C @ g2_lattices ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g2_lattices) ).
thf(13423,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g2_lattices ) )
= ( D @ ( C @ g2_lattices ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2126]) ).
thf(1282,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
<=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_partfun1) ).
thf(8783,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A )
=> ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
& ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(1179,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ~ ( ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ~ ( ! [F: $i] :
( ( A @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( C @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) ) ) )
& ( D @ k2_relat_1 @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( ( C @ ( D @ k5_funct_5 @ k1_funct_1 ) )
= E ) ) )
& ( B @ ( C @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_funct_5) ).
thf(8168,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ~ ( ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ~ ( ! [F: $i] :
( ( A @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( C @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) ) ) )
& ( D @ k2_relat_1 @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( ( C @ ( D @ k5_funct_5 @ k1_funct_1 ) )
= E ) ) )
& ( B @ ( C @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(1096,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ ( A @ k2_funct_4 @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_funct_4) ).
thf(7703,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ ( A @ k2_funct_4 @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(830,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k3_mcart_1 ) ) )
= ( F @ ( E @ ( D @ k3_mcart_1 ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_mcart_1) ).
thf(6328,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k3_mcart_1 ) ) )
= ( F @ ( E @ ( D @ k3_mcart_1 ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(1564,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_2_domain_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( C @ p1_s1_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_2_domain_1) ).
thf(10171,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( C @ p1_s1_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_2_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_2_domain_1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( C @ p1_s1_domain_1 )
& ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1564]) ).
thf(930,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_cat_2 ) ) ) )
= ( D @ ( C @ k3_funct_4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_cat_2) ).
thf(6820,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_cat_2 ) ) ) )
= ( D @ ( C @ k3_funct_4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(2357,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(14501,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2357]) ).
thf(872,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_0_ens_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( B @ k2_ens_1 @ ( E @ ( D @ ( C @ ( B @ ( B @ k1_domain_1 ) ) ) @ ( B @ k1_ens_1 @ ( B @ ( B @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ ( B @ k1_domain_1 ) ) ) @ ( B @ k1_ens_1 @ ( B @ ( B @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) ) )
& ( B @ k1_ens_1 @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_0_ens_1) ).
thf(6550,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( B @ k2_ens_1 @ ( E @ ( D @ ( C @ ( B @ ( B @ k1_domain_1 ) ) ) @ ( B @ k1_ens_1 @ ( B @ ( B @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ ( B @ k1_domain_1 ) ) ) @ ( B @ k1_ens_1 @ ( B @ ( B @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) ) )
& ( B @ k1_ens_1 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_0_ens_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_0_ens_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ k2_ens_1 @ ( E @ ( D @ ( C @ ( B @ ( B @ k1_domain_1 ) ) ) @ ( B @ k1_ens_1 @ ( B @ ( B @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) @ r2_hidden ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ ( B @ k1_domain_1 ) ) ) @ ( B @ k1_ens_1 @ ( B @ ( B @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) ) )
& ( B @ k1_ens_1 @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(2245,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_funct_1) ).
thf(14032,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2245]) ).
thf(1321,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_partfun1) ).
thf(8994,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321]) ).
thf(37,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(2596,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k4_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1199,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ k6_partfun1 @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k6_partfun1 @ v1_partfun1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_partfun1) ).
thf(8329,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ k6_partfun1 @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k6_partfun1 @ v1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(1712,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) ) )
=> ( A
= ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_domain_1) ).
thf(10975,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( ! [E: $i] :
( ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) )
=> ( A @ ( E @ r2_hidden ) ) )
& ( ( A @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) )
=> ( A
= ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1712]) ).
thf(1228,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( A @ k1_enumset1 ) ) @ ( D @ r1_tarski ) )
<=> ~ ( ( D
!= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) )
& ( D
!= ( C @ ( A @ k2_tarski ) ) )
& ( D
!= ( C @ ( B @ k2_tarski ) ) )
& ( D
!= ( B @ ( A @ k2_tarski ) ) )
& ( D
!= ( C @ k1_tarski ) )
& ( D
!= ( B @ k1_tarski ) )
& ( D
!= ( A @ k1_tarski ) )
& ( D != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_waybel18) ).
thf(8476,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( ( D
!= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) )
& ( D
!= ( C @ ( A @ k2_tarski ) ) )
& ( D
!= ( C @ ( B @ k2_tarski ) ) )
& ( D
!= ( B @ ( A @ k2_tarski ) ) )
& ( D
!= ( C @ k1_tarski ) )
& ( D
!= ( B @ k1_tarski ) )
& ( D
!= ( A @ k1_tarski ) )
& ( D != k1_xboole_0 ) )
=> ( C @ ( B @ ( A @ k1_enumset1 ) ) @ ( D @ r1_tarski ) ) )
& ( ( C @ ( B @ ( A @ k1_enumset1 ) ) @ ( D @ r1_tarski ) )
=> ~ ( ( D
!= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) )
& ( D
!= ( C @ ( A @ k2_tarski ) ) )
& ( D
!= ( C @ ( B @ k2_tarski ) ) )
& ( D
!= ( B @ ( A @ k2_tarski ) ) )
& ( D
!= ( C @ k1_tarski ) )
& ( D
!= ( B @ k1_tarski ) )
& ( D
!= ( A @ k1_tarski ) )
& ( D != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(1013,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t179_relat_1) ).
thf(7353,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(1827,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m1_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_cat_2 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_cat_2 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_cat_2 ) ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_cat_2) ).
thf(11619,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m1_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_cat_2 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_cat_2 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_cat_2 ) ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1827]) ).
thf(772,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_tarski ) @ k1_tarski @ k2_funct_5 )
= ( B @ k1_tarski ) )
& ( ( B @ ( A @ k4_tarski ) @ k1_tarski @ k1_funct_5 )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funct_5) ).
thf(6032,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_tarski ) @ k1_tarski @ k2_funct_5 )
= ( B @ k1_tarski ) )
& ( ( B @ ( A @ k4_tarski ) @ k1_tarski @ k1_funct_5 )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) ) )
<=> ! [G: $i] :
( ( F @ ( G @ r2_hidden ) )
<=> ~ ( ( G != E )
& ( G != D )
& ( G != C )
& ( G != B )
& ( G != A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_enumset1) ).
thf(4375,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i] :
( ( ~ ( ( G != E )
& ( G != D )
& ( G != C )
& ( G != B )
& ( G != A ) )
=> ( F @ ( G @ r2_hidden ) ) )
& ( ( F @ ( G @ r2_hidden ) )
=> ~ ( ( G != E )
& ( G != D )
& ( G != C )
& ( G != B )
& ( G != A ) ) ) )
=> ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) ) ) )
& ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) ) )
=> ! [G: $i] :
( ( ~ ( ( G != E )
& ( G != D )
& ( G != C )
& ( G != B )
& ( G != A ) )
=> ( F @ ( G @ r2_hidden ) ) )
& ( ( F @ ( G @ r2_hidden ) )
=> ~ ( ( G != E )
& ( G != D )
& ( G != C )
& ( G != B )
& ( G != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(1989,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ k9_funcop_1 ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_funcop_1) ).
thf(12664,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ k9_funcop_1 ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1989]) ).
thf(1721,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( C @ ( H @ m1_subset_1 ) )
& ( B @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( D @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_multop_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_multop_1) ).
thf(11037,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( C @ ( H @ m1_subset_1 ) )
& ( B @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( D @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_multop_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1721]) ).
thf(840,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_funct_2 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_5) ).
thf(6371,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_funct_2 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(1305,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_realset1) ).
thf(8888,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(564,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( A @ k2_ens_1 @ ( C @ ( B @ ( A @ k7_ens_1 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_ens_1) ).
thf(4989,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( A @ k2_ens_1 @ ( C @ ( B @ ( A @ k7_ens_1 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(2147,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ k3_pre_circ ) ) )
= ( C @ ( B @ k7_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_pre_circ) ).
thf(13572,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ k3_pre_circ ) ) )
= ( C @ ( B @ k7_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2147]) ).
thf(2065,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(13131,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2065]) ).
thf(1134,axiom,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k1_relat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(7881,plain,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k1_relat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(644,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B
= ( C @ ( A @ k8_relat_1 ) ) )
<=> ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
& ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
<=> ( ( A @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).
thf(5349,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
& ! [D: $i] :
( ( ( ( A @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( A @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) )
=> ( B
= ( C @ ( A @ k8_relat_1 ) ) ) )
& ( ( B
= ( C @ ( A @ k8_relat_1 ) ) )
=> ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
& ! [D: $i] :
( ( ( ( A @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( A @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(2225,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t156_relat_1) ).
thf(13949,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2225]) ).
thf(752,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( C @ ( C @ ( C @ ( A @ ( A @ k12_mcart_1 ) ) ) @ ( G @ m2_relset_1 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( G
= ( C @ ( E @ k1_realset1 ) ) )
=> ! [H: $i] :
( ( ( D @ ( D @ ( D @ ( B @ ( B @ k12_mcart_1 ) ) ) @ ( H @ m2_relset_1 ) ) )
& ( H @ v1_funct_1 ) )
=> ( ( H
= ( D @ ( F @ k1_realset1 ) ) )
=> ( ( H @ ( G @ ( D @ ( C @ ( B @ ( A @ k2_nattra_1 ) ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( F @ ( E @ ( B @ ( A @ k10_cat_2 ) ) ) @ k1_realset1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_nattra_1) ).
thf(5956,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( C @ ( C @ ( C @ ( A @ ( A @ k12_mcart_1 ) ) ) @ ( G @ m2_relset_1 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( G
= ( C @ ( E @ k1_realset1 ) ) )
=> ! [H: $i] :
( ( ( D @ ( D @ ( D @ ( B @ ( B @ k12_mcart_1 ) ) ) @ ( H @ m2_relset_1 ) ) )
& ( H @ v1_funct_1 ) )
=> ( ( H
= ( D @ ( F @ k1_realset1 ) ) )
=> ( ( H @ ( G @ ( D @ ( C @ ( B @ ( A @ k2_nattra_1 ) ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( F @ ( E @ ( B @ ( A @ k10_cat_2 ) ) ) @ k1_realset1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(1865,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( D = C ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finset_1) ).
thf(11865,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( D = C ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1865]) ).
thf(2289,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relset_2) ).
thf(14222,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2289]) ).
thf(1122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relset_1) ).
thf(7834,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(1691,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( C @ k3_pua2mss1 @ ( E @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) )
= k1_xboole_0 )
=> ( ( E @ ( D @ ( C @ ( A @ k4_subset_1 ) ) @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_relset_2) ).
thf(10843,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( C @ k3_pua2mss1 @ ( E @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) )
= k1_xboole_0 )
=> ( ( E @ ( D @ ( C @ ( A @ k4_subset_1 ) ) @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1691]) ).
thf(1450,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_relat_1) ).
thf(9618,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450]) ).
thf(2349,axiom,
( ! [A: $i] :
( ( f1_s1_filter_1 @ ( A @ m1_subset_1 ) )
=> ( A @ ( f2_s1_filter_1 @ ( f1_s1_filter_1 @ k2_filter_1 ) ) @ p1_s1_filter_1 ) )
=> ! [A: $i] :
( ( f2_s1_filter_1 @ ( f1_s1_filter_1 @ k8_eqrel_1 ) @ ( f1_s1_filter_1 @ k1_zfmisc_1 @ ( A @ m2_subset_1 ) ) )
=> ( A @ p1_s1_filter_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_filter_1) ).
thf(14465,plain,
( ! [A: $i] :
( ( f1_s1_filter_1 @ ( A @ m1_subset_1 ) )
=> ( A @ ( f2_s1_filter_1 @ ( f1_s1_filter_1 @ k2_filter_1 ) ) @ p1_s1_filter_1 ) )
=> ! [A: $i] :
( ( f2_s1_filter_1 @ ( f1_s1_filter_1 @ k8_eqrel_1 ) @ ( f1_s1_filter_1 @ k1_zfmisc_1 @ ( A @ m2_subset_1 ) ) )
=> ( A @ p1_s1_filter_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2349]) ).
thf(2041,axiom,
( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k7_metric_1 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k7_metric_1 @ v1_funct_2 ) ) )
& ( k7_metric_1 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_metric_1) ).
thf(12970,plain,
( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k7_metric_1 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k7_metric_1 @ v1_funct_2 ) ) )
& ( k7_metric_1 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2041]) ).
thf(1525,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_binop_1) ).
thf(9981,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ v1_binop_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
=> ( B @ ( C @ ( A @ r6_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r6_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525]) ).
thf(1343,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ r2_hidden ) )
<=> ( ( F @ ( C @ r2_hidden ) )
& ( E @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_mcart_1) ).
thf(9126,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( F @ ( C @ r2_hidden ) )
& ( E @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
=> ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ r2_hidden ) ) )
& ( ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ r2_hidden ) )
=> ( ( F @ ( C @ r2_hidden ) )
& ( E @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(131,axiom,
! [A: $i] :
( ( k5_numbers @ ( A @ m1_subset_1 ) )
=> ( ( A @ k3_urysohn1 @ v2_membered )
& ( A @ k3_urysohn1 @ v1_membered )
& ~ ( A @ k3_urysohn1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_urysohn1) ).
thf(2937,plain,
! [A: $i] :
( ( k5_numbers @ ( A @ m1_subset_1 ) )
=> ( ( A @ k3_urysohn1 @ v2_membered )
& ( A @ k3_urysohn1 @ v1_membered )
& ~ ( A @ k3_urysohn1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(1082,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k9_funct_3 ) @ ( A @ k1_relat_1 @ ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) )
= ( A @ k1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_funct_3) ).
thf(7640,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k9_funct_3 ) @ ( A @ k1_relat_1 @ ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) )
= ( A @ k1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(465,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( B @ ( A @ k8_relat_1 ) @ k5_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_relat_1) ).
thf(4493,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( B @ ( A @ k8_relat_1 ) @ k5_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(726,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v2_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_binop_1) ).
thf(5754,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
=> ( A @ ( B @ v2_binop_1 ) ) )
& ( ( A @ ( B @ v2_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(1819,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k5_finsub_1 @ ( B @ ( A @ k18_group_2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k18_group_2) ).
thf(11565,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k5_finsub_1 @ ( B @ ( A @ k18_group_2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1819]) ).
thf(1142,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_mcart_1 ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_mcart_1) ).
thf(7984,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_mcart_1 ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(589,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k3_setwiseo ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_setwiseo) ).
thf(5102,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k3_setwiseo ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(1267,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
~ ( ( ( A @ ( C @ ( B @ k2_funcop_1 ) @ k5_relat_1 ) @ k1_relat_1 )
= k1_xboole_0 )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_funcop_1) ).
thf(8714,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
~ ( ( ( A @ ( C @ ( B @ k2_funcop_1 ) @ k5_relat_1 ) @ k1_relat_1 )
= k1_xboole_0 )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(1872,axiom,
! [A: $i] :
( ( A @ k6_relat_1 @ v1_funct_1 )
& ( A @ k6_relat_1 @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(11908,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ v1_funct_1 )
& ( A @ k6_relat_1 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1872]) ).
thf(199,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ k3_funct_5 @ m2_relset_1 ) ) )
& ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ k3_funct_5 @ v1_funct_2 ) ) )
& ( D @ k3_funct_5 @ v1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_cat_2) ).
thf(3250,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ k3_funct_5 @ m2_relset_1 ) ) )
& ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ k3_funct_5 @ v1_funct_2 ) ) )
& ( D @ k3_funct_5 @ v1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(863,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ k3_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relat_1) ).
thf(6509,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ k3_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(1138,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_funcop_1 ) )
= ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funcop_1) ).
thf(7906,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_funcop_1 ) )
= ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_relset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(7565,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_relset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(371,axiom,
! [A: $i,B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( B @ ( A @ k6_partfun1 @ k9_funct_7 ) )
= ( A @ k6_partfun1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_funct_7) ).
thf(4021,plain,
! [A: $i,B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( B @ ( A @ k6_partfun1 @ k9_funct_7 ) )
= ( A @ k6_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(1898,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_4_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_domain_1) ).
thf(12058,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_4_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1898]) ).
thf(2302,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_cantor_1 ) )
= ( B @ ( A @ k2_cantor_1 ) @ ( A @ k2_cantor_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_cantor_1) ).
thf(14280,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k2_cantor_1 ) )
= ( B @ ( A @ k2_cantor_1 ) @ ( A @ k2_cantor_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2302]) ).
thf(1673,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
~ ( ( B
= ( D @ ( C @ k4_tarski ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_mcart_1) ).
thf(10756,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i] :
~ ( ( B
= ( D @ ( C @ k4_tarski ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1673]) ).
thf(2353,axiom,
f2_s1_group_5 @ k1_zfmisc_1 @ ( a_0_0_group_5 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_group_5) ).
thf(14477,plain,
f2_s1_group_5 @ k1_zfmisc_1 @ ( a_0_0_group_5 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2353]) ).
thf(352,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( A @ k1_setfam_1 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_setfam_1) ).
thf(3926,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( A @ k1_setfam_1 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(1247,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) )
<=> ! [E: $i] :
( ( D @ ( E @ r2_hidden ) )
<=> ~ ( ( E != C )
& ( E != B )
& ( E != A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_enumset1) ).
thf(8577,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( ~ ( ( E != C )
& ( E != B )
& ( E != A ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( ( D @ ( E @ r2_hidden ) )
=> ~ ( ( E != C )
& ( E != B )
& ( E != A ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) )
=> ! [E: $i] :
( ( ~ ( ( E != C )
& ( E != B )
& ( E != A ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( ( D @ ( E @ r2_hidden ) )
=> ~ ( ( E != C )
& ( E != B )
& ( E != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(209,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ k2_funct_1 @ ( B @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k1_funct_1 ) @ ( B @ k2_funct_1 @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funct_1) ).
thf(3282,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ k2_funct_1 @ ( B @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k1_funct_1 ) @ ( B @ k2_funct_1 @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(2067,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_relat_1) ).
thf(13158,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k9_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2067]) ).
thf(1664,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_finset_1 )
& ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc16_finset_1) ).
thf(10721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_finset_1 )
& ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1664]) ).
thf(357,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A = k1_xboole_0 )
<=> ( ( A @ k4_finseq_1 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finseq_1) ).
thf(3958,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( ( A @ k4_finseq_1 )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( ( A @ k4_finseq_1 )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_funct_2) ).
thf(4295,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ~ ( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) ) ) )
& ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(1581,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k5_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_subset_1) ).
thf(10263,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k5_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1581]) ).
thf(1340,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( A @ k12_mcart_1 ) ) ) @ ( C @ k6_partfun1 @ ( D @ ( C @ ( B @ ( C @ ( A @ k16_funct_3 ) ) ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) )
= ( F @ ( E @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ k12_mcart_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_borsuk_1) ).
thf(9113,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( A @ k12_mcart_1 ) ) ) @ ( C @ k6_partfun1 @ ( D @ ( C @ ( B @ ( C @ ( A @ k16_funct_3 ) ) ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) )
= ( F @ ( E @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( C @ ( B @ k12_mcart_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).
thf(737,axiom,
! [A: $i] :
( ( A @ k3_pua2mss1 )
= ( A @ k6_partfun1 @ ( A @ k8_eqrel_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_pua2mss1) ).
thf(5826,plain,
! [A: $i] :
( ( A @ k3_pua2mss1 )
= ( A @ k6_partfun1 @ ( A @ k8_eqrel_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(1768,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_5_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_domain_1) ).
thf(11244,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_5_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1768]) ).
thf(426,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k5_relat_1 ) )
= A )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( B
= ( B @ k1_relat_1 @ k6_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_1) ).
thf(4280,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k5_relat_1 ) )
= A )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( B
= ( B @ k1_relat_1 @ k6_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k5_funct_5 )
= ( D @ k5_funct_5 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funct_5) ).
thf(2873,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k5_funct_5 )
= ( D @ k5_funct_5 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(636,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( C @ v3_binop_1 ) )
& ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) ) )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( D @ ( D @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( D @ ( D @ ( D @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( E @ v3_binop_1 ) )
& ( D @ ( E @ v2_binop_1 ) )
& ( D @ ( E @ v1_binop_1 ) ) )
=> ! [F: $i] :
( ( ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( D @ ( B @ ( G @ m2_relset_1 ) ) )
& ( D @ ( B @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( B @ ( I @ m1_subset_1 ) )
=> ( ( I @ ( H @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) )
= ( I @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) @ ( H @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( D @ ( D @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ! [H: $i] :
( ( A @ k5_finsub_1 @ ( H @ m1_subset_1 ) )
=> ( ( H != k1_xboole_0 )
=> ( ( F @ ( H @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) )
= ( G @ ( F @ ( D @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( H @ ( E @ ( D @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_setwiseo) ).
thf(5302,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( C @ v3_binop_1 ) )
& ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) ) )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( D @ ( D @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( D @ ( D @ ( D @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( E @ v3_binop_1 ) )
& ( D @ ( E @ v2_binop_1 ) )
& ( D @ ( E @ v1_binop_1 ) ) )
=> ! [F: $i] :
( ( ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( D @ ( B @ ( G @ m2_relset_1 ) ) )
& ( D @ ( B @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( B @ ( I @ m1_subset_1 ) )
=> ( ( I @ ( H @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) )
= ( I @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) @ ( H @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( D @ ( D @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ! [H: $i] :
( ( A @ k5_finsub_1 @ ( H @ m1_subset_1 ) )
=> ( ( H != k1_xboole_0 )
=> ( ( F @ ( H @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) @ ( G @ ( D @ ( B @ k8_funct_2 ) ) ) )
= ( G @ ( F @ ( D @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( H @ ( E @ ( D @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(938,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ k6_enumset1 ) ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_enumset1) ).
thf(6852,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ k6_enumset1 ) ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(1057,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ ( C @ v1_binop_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= ( D @ ( E @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_funcop_1) ).
thf(7555,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ ( C @ v1_binop_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= ( D @ ( E @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(2097,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
thf(13282,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2097]) ).
thf(1063,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_zfmisc_1) ).
thf(7576,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(2030,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( B @ r3_binop_1 ) ) )
& ( E @ ( C @ ( A @ r3_binop_1 ) ) ) )
<=> ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r3_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_filter_1) ).
thf(12910,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r3_binop_1 ) ) )
=> ( ( F @ ( D @ ( B @ r3_binop_1 ) ) )
& ( E @ ( C @ ( A @ r3_binop_1 ) ) ) ) )
& ( ( ( F @ ( D @ ( B @ r3_binop_1 ) ) )
& ( E @ ( C @ ( A @ r3_binop_1 ) ) ) )
=> ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r3_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2030]) ).
thf(380,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(4053,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ r1_tarski ) )
=> ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t165_funct_2) ).
thf(4585,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ r1_tarski ) )
=> ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(2162,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) )
<=> ( C @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_relset_2) ).
thf(13639,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( C @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( B @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) ) )
& ( ( B @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ r2_hidden ) )
=> ( C @ ( A @ ( B @ k4_tarski ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2162]) ).
thf(990,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ( ( C @ k2_funct_4 @ k1_relat_1 )
= ( A @ ( B @ k2_zfmisc_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_funct_4) ).
thf(7185,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ( ( C @ k2_funct_4 @ k1_relat_1 )
= ( A @ ( B @ k2_zfmisc_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(1458,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) )
=> ( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( A @ k1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_relat_1) ).
thf(9671,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) )
=> ( ( ( C @ k2_relat_1 )
= ( B @ k1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( A @ k1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458]) ).
thf(774,axiom,
! [A: $i] :
( ( A @ k9_setwiseo @ ( A @ k5_finsub_1 @ k3_binop_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_setwiseo) ).
thf(6043,plain,
! [A: $i] :
( ( A @ k9_setwiseo @ ( A @ k5_finsub_1 @ k3_binop_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(1028,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_enumset1 ) ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_subset_1) ).
thf(7449,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k5_enumset1 ) ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(217,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k1_relat_1 @ r2_hidden ) ) )
=> ( B @ ( A @ k2_relat_1 @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_zfrefle1) ).
thf(3314,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( B @ ( A @ k2_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k1_relat_1 @ r2_hidden ) ) )
=> ( B @ ( A @ k2_relat_1 @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(566,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( A @ k1_setwiseo @ ( B @ ( A @ k10_setwiseo ) ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_setwiseo) ).
thf(4994,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( A @ k1_setwiseo @ ( B @ ( A @ k10_setwiseo ) ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ k1_tarski @ ( C @ ( B @ k4_xboole_0 ) @ k9_relat_1 ) )
= ( A @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ k1_tarski @ ( B @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_2) ).
thf(3499,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ k1_tarski @ ( C @ ( B @ k4_xboole_0 ) @ k9_relat_1 ) )
= ( A @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ k1_tarski @ ( B @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(608,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k8_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k8_relat_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(5177,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k8_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k8_relat_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(3349,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ~ ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(3578,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ~ ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(2191,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ r2_wellord1 ) )
=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r2_hidden ) )
=> ( B @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( C @ ( D @ r2_hidden ) ) )
& ( C != k1_xboole_0 )
& ( A @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_wellord1) ).
thf(13799,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ r2_wellord1 ) )
=> ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r2_hidden ) )
=> ( B @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( C @ ( D @ r2_hidden ) ) )
& ( C != k1_xboole_0 )
& ( A @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2191]) ).
thf(1552,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( k9_zf_lang @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k9_zf_lang @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ r1_zfrefle1 ) )
& ( B @ ( A @ r1_zfrefle1 ) ) )
=> ( C @ ( B @ ( k9_zf_lang @ k4_subset_1 ) ) @ ( A @ r1_zfrefle1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_zfrefle1) ).
thf(10116,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( k9_zf_lang @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k9_zf_lang @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ r1_zfrefle1 ) )
& ( B @ ( A @ r1_zfrefle1 ) ) )
=> ( C @ ( B @ ( k9_zf_lang @ k4_subset_1 ) ) @ ( A @ r1_zfrefle1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1552]) ).
thf(664,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ v1_finset_1 )
<=> ( A @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finset_1) ).
thf(5460,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ v1_finset_1 )
=> ( A @ k1_relat_1 @ v1_finset_1 ) )
& ( ( A @ k1_relat_1 @ v1_finset_1 )
=> ( A @ v1_finset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(2187,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_subset_1) ).
thf(13789,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2187]) ).
thf(2363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ k1_cat_5 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_cat_5) ).
thf(14556,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ k1_cat_5 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2363]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ k5_relset_2 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( D @ ( B @ k5_relset_2 ) @ k1_funct_1 ) )
= ( A @ ( D @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_relset_2) ).
thf(4553,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ k5_relset_2 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( D @ ( B @ k5_relset_2 ) @ k1_funct_1 ) )
= ( A @ ( D @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(1076,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( A @ r2_hidden ) )
& ( C @ ( B @ ( A @ k2_tarski ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_zfmisc_1) ).
thf(7625,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( A @ r2_hidden ) )
& ( C @ ( B @ ( A @ k2_tarski ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(1674,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( B = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_subset_1) ).
thf(10765,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( B = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1674]) ).
thf(340,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v1_setwiseo ) )
<=> ? [C: $i] :
( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_setwiseo) ).
thf(3894,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ? [C: $i] :
( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) )
=> ( A @ ( B @ v1_setwiseo ) ) )
& ( ( A @ ( B @ v1_setwiseo ) )
=> ? [C: $i] :
( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(1453,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C
= ( B @ ( A @ k15_funct_3 ) ) )
<=> ( ! [D: $i,E: $i] :
( ( ( B @ k1_relat_1 @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( E @ ( D @ k4_tarski ) @ ( C @ k1_funct_1 ) )
= ( E @ ( B @ k1_funct_1 ) @ ( D @ ( A @ k1_funct_1 ) @ k4_tarski ) ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_3) ).
thf(9626,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ! [D: $i,E: $i] :
( ( ( B @ k1_relat_1 @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( E @ ( D @ k4_tarski ) @ ( C @ k1_funct_1 ) )
= ( E @ ( B @ k1_funct_1 ) @ ( D @ ( A @ k1_funct_1 ) @ k4_tarski ) ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) ) ) )
=> ( C
= ( B @ ( A @ k15_funct_3 ) ) ) )
& ( ( C
= ( B @ ( A @ k15_funct_3 ) ) )
=> ( ! [D: $i,E: $i] :
( ( ( B @ k1_relat_1 @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( ( E @ ( D @ k4_tarski ) @ ( C @ k1_funct_1 ) )
= ( E @ ( B @ k1_funct_1 ) @ ( D @ ( A @ k1_funct_1 ) @ k4_tarski ) ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453]) ).
thf(2139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_2) ).
thf(13530,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2139]) ).
thf(436,axiom,
! [A: $i] :
( ~ ( ( A @ v1_realset1 )
& ? [B: $i,C: $i] :
( ( B != C )
& ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) ) )
& ~ ( ! [B: $i,C: $i] :
~ ( ( B != C )
& ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
& ~ ( A @ v1_realset1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_realset1) ).
thf(4327,plain,
! [A: $i] :
( ~ ( ( A @ v1_realset1 )
& ? [B: $i,C: $i] :
( ( B != C )
& ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) ) )
& ~ ( ! [B: $i,C: $i] :
~ ( ( B != C )
& ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
& ~ ( A @ v1_realset1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(1890,axiom,
f2_s18_fraenkel @ ( a_0_33_fraenkel @ r1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s18_fraenkel) ).
thf(12025,plain,
f2_s18_fraenkel @ ( a_0_33_fraenkel @ r1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1890]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_pboole ) )
=> ! [F: $i] :
( ( E @ ( D @ ( B @ ( F @ m3_pboole ) ) ) )
=> ( E @ ( C @ ( B @ ( A @ k7_pboole ) ) ) @ ( D @ ( C @ ( B @ ( A @ k7_pboole ) ) ) @ ( A @ ( F @ ( C @ ( B @ ( A @ k7_pboole ) ) ) @ m3_pboole ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_altcat_2) ).
thf(2609,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_pboole ) )
=> ! [F: $i] :
( ( E @ ( D @ ( B @ ( F @ m3_pboole ) ) ) )
=> ( E @ ( C @ ( B @ ( A @ k7_pboole ) ) ) @ ( D @ ( C @ ( B @ ( A @ k7_pboole ) ) ) @ ( A @ ( F @ ( C @ ( B @ ( A @ k7_pboole ) ) ) @ m3_pboole ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1054,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( D @ k1_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_3) ).
thf(7545,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( D @ k1_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(2115,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ a_2_0_cantor_1 ) ) )
=> ( ( C @ ( A @ k8_setfam_1 ) )
= ( B @ ( A @ k1_zfmisc_1 @ k5_setfam_1 ) @ ( A @ k8_setfam_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_cantor_1) ).
thf(13359,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ a_2_0_cantor_1 ) ) )
=> ( ( C @ ( A @ k8_setfam_1 ) )
= ( B @ ( A @ k1_zfmisc_1 @ k5_setfam_1 ) @ ( A @ k8_setfam_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2115]) ).
thf(1383,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( D @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t133_relat_1) ).
thf(9301,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( D @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383]) ).
thf(1682,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funcop_1) ).
thf(10794,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1682]) ).
thf(934,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( A
= ( C @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( ( ( A @ k2_relat_1 )
= C )
& ( ( A @ k1_relat_1 )
= B ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funcop_1) ).
thf(6833,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( A
= ( C @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( ( ( A @ k2_relat_1 )
= C )
& ( ( A @ k1_relat_1 )
= B ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(591,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t135_partfun1) ).
thf(5113,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(1530,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ~ ( C @ ( B @ ( A @ k5_relset_1 ) ) @ ( E @ r2_hidden ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_relset_1) ).
thf(10006,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ~ ( C @ ( B @ ( A @ k5_relset_1 ) ) @ ( E @ r2_hidden ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1530]) ).
thf(613,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_1) ).
thf(5201,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( A @ ( B @ k9_relat_1 ) @ ( B @ k10_relat_1 ) @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(2020,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( A @ ( k1_numbers @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( A @ ( A @ ( k1_numbers @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_funcsdom ) ) ) ) ) )
= ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ g1_funcsdom ) ) ) ) ) ) )
=> ( ( F = L )
& ( E = K )
& ( D = J )
& ( C = I )
& ( B = H )
& ( A = G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_funcsdom) ).
thf(12849,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( A @ ( k1_numbers @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( A @ ( A @ ( k1_numbers @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_funcsdom ) ) ) ) ) )
= ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ g1_funcsdom ) ) ) ) ) ) )
=> ( ( F = L )
& ( E = K )
& ( D = J )
& ( C = I )
& ( B = H )
& ( A = G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2020]) ).
thf(845,axiom,
! [A: $i] :
( ( A @ v1_setfam_1 )
<=> ~ ( A @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_setfam_1) ).
thf(6402,plain,
! [A: $i] :
( ( ~ ( A @ ( k1_xboole_0 @ r2_hidden ) )
=> ( A @ v1_setfam_1 ) )
& ( ( A @ v1_setfam_1 )
=> ~ ( A @ ( k1_xboole_0 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(1904,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_finseq_1) ).
thf(12095,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1904]) ).
thf(1125,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( D @ k1_funct_1 ) )
= ( F @ ( E @ k1_funct_1 ) ) ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( E @ k1_funct_4 ) )
= E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_lattice2) ).
thf(7853,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( ( F @ ( D @ k1_funct_1 ) )
= ( F @ ( E @ k1_funct_1 ) ) ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( E @ k1_funct_4 ) )
= E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(1650,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ k5_finsub_1 @ ( D @ ( C @ ( B @ ( A @ k8_setwiseo ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_setwiseo) ).
thf(10615,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ k5_finsub_1 @ ( D @ ( C @ ( B @ ( A @ k8_setwiseo ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1650]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_pua2mss1 ) )
=> ( ( B @ v2_funct_1 )
& ( B @ v2_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_pua2mss1) ).
thf(2741,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m2_pua2mss1 ) )
=> ( ( B @ v2_funct_1 )
& ( B @ v2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(1828,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k3_funct_2 ) ) ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funct_2) ).
thf(11624,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ ( A @ ( k1_xboole_0 @ k3_funct_2 ) ) ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1828]) ).
thf(1333,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B
= ( C @ k1_tarski ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_mssubfam) ).
thf(9080,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B
= ( C @ k1_tarski ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(1448,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(9613,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448]) ).
thf(1502,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( C @ k2_relat_1 )
= ( A @ ( C @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_2) ).
thf(9885,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( C @ k2_relat_1 )
= ( A @ ( C @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1502]) ).
thf(2124,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k3_zfmisc_1 ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_mcart_1) ).
thf(13411,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k3_zfmisc_1 ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2124]) ).
thf(1633,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_partfun1) ).
thf(10543,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1633]) ).
thf(1501,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
<=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_zfmisc_1) ).
thf(9868,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) )
=> ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) ) )
& ( ( C @ ( B @ k2_tarski ) @ ( A @ r1_tarski ) )
=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1501]) ).
thf(513,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( ( B @ ( A @ k3_pralg_3 ) @ k2_relat_1 )
= ( B @ ( A @ k1_funct_1 ) ) )
| ( ( A @ k4_card_3 )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_yellow17) ).
thf(4732,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( ( B @ ( A @ k3_pralg_3 ) @ k2_relat_1 )
= ( B @ ( A @ k1_funct_1 ) ) )
| ( ( A @ k4_card_3 )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(1738,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v3_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ k1_binop_1 ) ) )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_binop_1) ).
thf(11101,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ k1_binop_1 ) ) )
= C ) )
=> ( A @ ( B @ v3_binop_1 ) ) )
& ( ( A @ ( B @ v3_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( C @ ( B @ k1_binop_1 ) ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1738]) ).
thf(2044,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_partfun1) ).
thf(12991,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2044]) ).
thf(1795,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_pboole ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ k1_binop_1 ) ) )
= ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ r6_pboole ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_altcat_1) ).
thf(11420,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_pboole ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ k1_binop_1 ) ) )
= ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ r6_pboole ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1795]) ).
thf(761,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_funct_4) ).
thf(5993,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(501,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v1_setfam_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_setfam_1) ).
thf(4680,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_tarski ) @ v1_setfam_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(2093,axiom,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(13269,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2093]) ).
thf(642,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
<=> ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(5330,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r1_xboole_0 ) ) )
& ( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(1232,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k3_funcop_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k3_funcop_1 ) ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funcop_1) ).
thf(8518,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k3_funcop_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k3_funcop_1 ) ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(276,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k3_funct_3 @ v1_funct_1 )
& ( A @ k3_funct_3 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_funct_3) ).
thf(3595,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k3_funct_3 @ v1_funct_1 )
& ( A @ k3_funct_3 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_zfmisc_1) ).
thf(4316,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(785,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i,F: $i] :
( ( ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) )
=> ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) ) ) )
& ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_2) ).
thf(6090,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i,F: $i] :
( ( ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) )
=> ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) ) )
& ( ( ( ( E @ ( D @ k1_funct_1 ) )
= F )
& ( B @ ( E @ r2_hidden ) ) )
=> ( ( ( F @ ( C @ k1_funct_1 ) )
= E )
& ( A @ ( F @ r2_hidden ) ) ) ) )
& ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(2653,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(2243,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finsub_1) ).
thf(14028,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2243]) ).
thf(1845,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_cantor_1 ) @ ( A @ k1_cantor_1 ) @ ( A @ g1_pre_topc ) @ v2_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_waybel18) ).
thf(11762,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_cantor_1 ) @ ( A @ k1_cantor_1 ) @ ( A @ g1_pre_topc ) @ v2_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1845]) ).
thf(1036,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k4_funcop_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k4_funcop_1 ) ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funcop_1) ).
thf(7481,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k4_funcop_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k4_funcop_1 ) ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(1514,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( k1_xboole_0 @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t176_partfun1) ).
thf(9936,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( k1_xboole_0 @ k5_partfun1 ) ) )
= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1514]) ).
thf(1068,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(7593,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ k3_xboole_0 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t177_relat_1) ).
thf(3916,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_3) ).
thf(3205,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(1171,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
<=> ( ( A @ k1_tarski @ ( B @ k10_relat_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_funct_1) ).
thf(8138,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( A @ k1_tarski @ ( B @ k10_relat_1 ) )
!= k1_xboole_0 )
=> ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k10_relat_1 ) )
!= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(1941,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k7_setfam_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_card_fil) ).
thf(12372,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k7_setfam_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1941]) ).
thf(1882,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( ( B = k1_xboole_0 )
& ( ( B @ ( A @ k7_setfam_1 ) )
!= k1_xboole_0 ) )
& ~ ( ( ( B @ ( A @ k7_setfam_1 ) )
= k1_xboole_0 )
& ( B != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_tops_2) ).
thf(11961,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( ( B = k1_xboole_0 )
& ( ( B @ ( A @ k7_setfam_1 ) )
!= k1_xboole_0 ) )
& ~ ( ( ( B @ ( A @ k7_setfam_1 ) )
= k1_xboole_0 )
& ( B != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1882]) ).
thf(1767,axiom,
! [A: $i] :
( ( ( f2_s1_binop_2 @ ( f1_s1_binop_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s1_binop_2 @ ( f1_s1_binop_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ! [B: $i] :
( ( ( f2_s1_binop_2 @ ( f1_s1_binop_2 @ ( B @ m2_relset_1 ) ) )
& ( f2_s1_binop_2 @ ( f1_s1_binop_2 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( f1_s1_binop_2 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( f2_s1_binop_2 @ ( f1_s1_binop_2 @ k8_funct_2 ) ) ) )
= ( C @ f3_s1_binop_2 ) ) )
& ! [C: $i] :
( ( f1_s1_binop_2 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( f2_s1_binop_2 @ ( f1_s1_binop_2 @ k8_funct_2 ) ) ) )
= ( C @ f3_s1_binop_2 ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_binop_2) ).
thf(11234,plain,
! [A: $i] :
( ( ( f2_s1_binop_2 @ ( f1_s1_binop_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s1_binop_2 @ ( f1_s1_binop_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ! [B: $i] :
( ( ( f2_s1_binop_2 @ ( f1_s1_binop_2 @ ( B @ m2_relset_1 ) ) )
& ( f2_s1_binop_2 @ ( f1_s1_binop_2 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( f1_s1_binop_2 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( f2_s1_binop_2 @ ( f1_s1_binop_2 @ k8_funct_2 ) ) ) )
= ( C @ f3_s1_binop_2 ) ) )
& ! [C: $i] :
( ( f1_s1_binop_2 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ ( f2_s1_binop_2 @ ( f1_s1_binop_2 @ k8_funct_2 ) ) ) )
= ( C @ f3_s1_binop_2 ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1767]) ).
thf(1189,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ k1_enumset1 ) ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_enumset1) ).
thf(8238,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ k1_enumset1 ) ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(1197,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B
= ( A @ k3_funct_5 ) )
<=> ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ~ ( ! [E: $i] :
( ( D @ k1_relat_1 @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k4_tarski ) @ ( A @ k1_funct_1 ) ) ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_relat_1 @ k2_funct_5 @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ k2_funct_5 ) )
& ( ( C @ ( B @ k1_funct_1 ) )
= D ) ) )
& ( A @ k1_relat_1 @ k1_funct_5 @ ( C @ r2_hidden ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k1_relat_1 @ k1_funct_5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_funct_5) ).
thf(8297,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ~ ( ! [E: $i] :
( ( D @ k1_relat_1 @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k4_tarski ) @ ( A @ k1_funct_1 ) ) ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_relat_1 @ k2_funct_5 @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ k2_funct_5 ) )
& ( ( C @ ( B @ k1_funct_1 ) )
= D ) ) )
& ( A @ k1_relat_1 @ k1_funct_5 @ ( C @ r2_hidden ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k1_relat_1 @ k1_funct_5 ) ) )
=> ( B
= ( A @ k3_funct_5 ) ) )
& ( ( B
= ( A @ k3_funct_5 ) )
=> ( ! [C: $i] :
~ ( ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ~ ( ! [E: $i] :
( ( D @ k1_relat_1 @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( C @ k4_tarski ) @ ( A @ k1_funct_1 ) ) ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_relat_1 @ k2_funct_5 @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ k2_funct_5 ) )
& ( ( C @ ( B @ k1_funct_1 ) )
= D ) ) )
& ( A @ k1_relat_1 @ k1_funct_5 @ ( C @ r2_hidden ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k1_relat_1 @ k1_funct_5 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(305,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( A @ k2_funct_1 @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
thf(3731,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( A @ k2_funct_1 @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(531,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( B @ v1_setfam_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_eqrel_1) ).
thf(4808,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( B @ v1_setfam_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(1203,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r3_binop_1 ) ) )
<=> ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
& ( C @ ( B @ ( A @ r1_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_binop_1) ).
thf(8354,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
& ( C @ ( B @ ( A @ r1_binop_1 ) ) ) )
=> ( C @ ( B @ ( A @ r3_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r3_binop_1 ) ) )
=> ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
& ( C @ ( B @ ( A @ r1_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(610,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k8_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_relat_1) ).
thf(5189,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k8_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(701,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 )
=> ( ( D @ v2_funct_1 )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_funct_2) ).
thf(5626,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 )
=> ( ( D @ v2_funct_1 )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_xboole_1) ).
thf(3699,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(1840,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_domain_1 ) ) ) )
= ( D @ ( C @ ( B @ k1_enumset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_domain_1) ).
thf(11736,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_domain_1 ) ) ) )
= ( D @ ( C @ ( B @ k1_enumset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1840]) ).
thf(2021,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_2_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_2_domain_1) ).
thf(12863,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_2_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_2_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2021]) ).
thf(282,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B
= ( A @ k4_relat_1 ) )
<=> ! [C: $i,D: $i] :
( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
thf(3615,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( B
= ( A @ k4_relat_1 ) ) )
& ( ( B
= ( A @ k4_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(2224,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_finset_1) ).
thf(13946,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2224]) ).
thf(1693,axiom,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_triang_1 ) ) )
<=> ( B @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m1_triang_1) ).
thf(10848,plain,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ ( C @ m1_triang_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_triang_1 ) ) )
=> ( B @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1693]) ).
thf(345,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( A @ k2_funct_1 )
= ( A @ k4_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
thf(3909,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( A @ k2_funct_1 )
= ( A @ k4_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(1427,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) )
=> ( C @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_zfmisc_1) ).
thf(9493,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k3_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) )
=> ( C @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427]) ).
thf(903,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
<=> ? [F: $i,G: $i,H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ r2_hidden ) )
& ( C @ ( G @ r2_hidden ) )
& ( B @ ( F @ r2_hidden ) ) ) )
=> ( A
= ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_mcart_1) ).
thf(6677,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( ? [F: $i,G: $i,H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ r2_hidden ) )
& ( C @ ( G @ r2_hidden ) )
& ( B @ ( F @ r2_hidden ) ) )
=> ( A @ ( E @ r2_hidden ) ) )
& ( ( A @ ( E @ r2_hidden ) )
=> ? [F: $i,G: $i,H: $i] :
( ( E
= ( H @ ( G @ ( F @ k3_mcart_1 ) ) ) )
& ( D @ ( H @ r2_hidden ) )
& ( C @ ( G @ r2_hidden ) )
& ( B @ ( F @ r2_hidden ) ) ) ) )
=> ( A
= ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(981,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
=> ( ( C @ v1_fraenkel )
& ~ ( C @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
thf(7142,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
=> ( ( C @ v1_fraenkel )
& ~ ( C @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(330,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ v2_relat_1 )
<=> ~ ( A @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_1) ).
thf(3831,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ~ ( A @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) )
=> ( A @ v2_relat_1 ) )
& ( ( A @ v2_relat_1 )
=> ~ ( A @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m2_finseq_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( C
= ( E @ ( D @ ( B @ ( A @ ( A @ ( k5_numbers @ k1_partfun1 ) ) ) ) ) ) )
=> ( ( C @ k3_finseq_1 )
= ( D @ k3_finseq_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_finseq_2) ).
thf(2840,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m2_finseq_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( C
= ( E @ ( D @ ( B @ ( A @ ( A @ ( k5_numbers @ k1_partfun1 ) ) ) ) ) ) )
=> ( ( C @ k3_finseq_1 )
= ( D @ k3_finseq_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(618,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k1_zfmisc_1 )
= ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_zfmisc_1) ).
thf(5221,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ k1_zfmisc_1 )
= ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(1239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_partfun1) ).
thf(8545,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(1999,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_relset_1) ).
thf(12728,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1999]) ).
thf(1671,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(10748,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1671]) ).
thf(2222,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_subset_1) ).
thf(13939,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ k5_subset_1 ) ) @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2222]) ).
thf(601,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C
= ( B @ ( A @ k5_relset_2 ) ) )
<=> ( ! [D: $i] :
( ( A @ ( D @ r1_tarski ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k9_relat_1 ) ) ) )
& ( ( C @ k1_relat_1 )
= ( A @ k1_zfmisc_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relset_2) ).
thf(5145,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ! [D: $i] :
( ( A @ ( D @ r1_tarski ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k9_relat_1 ) ) ) )
& ( ( C @ k1_relat_1 )
= ( A @ k1_zfmisc_1 ) ) )
=> ( C
= ( B @ ( A @ k5_relset_2 ) ) ) )
& ( ( C
= ( B @ ( A @ k5_relset_2 ) ) )
=> ( ! [D: $i] :
( ( A @ ( D @ r1_tarski ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k9_relat_1 ) ) ) )
& ( ( C @ k1_relat_1 )
= ( A @ k1_zfmisc_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(2317,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k1_relset_2 ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k1_relset_2) ).
thf(14327,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k1_relset_2 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2317]) ).
thf(588,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( B @ ( A @ k8_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_funct_1) ).
thf(5098,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( B @ ( A @ k8_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(926,axiom,
( ( k1_numbers @ ( k33_binop_2 @ v2_binop_1 ) )
& ( k1_numbers @ ( k33_binop_2 @ v1_binop_1 ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k33_binop_2 @ v1_funct_2 ) ) )
& ( k33_binop_2 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_binop_2) ).
thf(6801,plain,
( ( k1_numbers @ ( k33_binop_2 @ v2_binop_1 ) )
& ( k1_numbers @ ( k33_binop_2 @ v1_binop_1 ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k33_binop_2 @ v1_funct_2 ) ) )
& ( k33_binop_2 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(2112,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ k1_funct_5 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_yellow_3) ).
thf(13347,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ k1_funct_5 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2112]) ).
thf(959,axiom,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(6940,plain,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(63,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v2_relat_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k4_card_3 @ ( A @ k4_card_3 @ r1_tarski ) )
=> ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ ( C @ ( A @ k1_funct_1 ) @ r1_tarski ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_pua2mss1) ).
thf(2685,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v2_relat_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k4_card_3 @ ( A @ k4_card_3 @ r1_tarski ) )
=> ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ ( C @ ( A @ k1_funct_1 ) @ r1_tarski ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(569,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m2_card_fil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_card_fil) ).
thf(5006,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m2_card_fil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(1327,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_realset1) ).
thf(9016,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).
thf(699,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k10_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t172_relat_1) ).
thf(5615,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k10_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(1193,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) )
= ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_relat_1) ).
thf(8282,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) )
= ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ~ ( C @ v2_funct_1 )
& ? [D: $i] :
( ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
& ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
& ( B != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_2) ).
thf(4048,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ~ ( C @ v2_funct_1 )
& ? [D: $i] :
( ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
& ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
& ( B != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(1765,axiom,
! [A: $i] :
( ( ( k1_numbers @ ( k1_numbers @ ( A @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( A = k32_binop_2 )
<=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ k8_funct_2 ) ) ) )
= ( B @ k8_binop_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_binop_2) ).
thf(11221,plain,
! [A: $i] :
( ( ( k1_numbers @ ( k1_numbers @ ( A @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ k8_funct_2 ) ) ) )
= ( B @ k8_binop_2 ) ) )
=> ( A = k32_binop_2 ) )
& ( ( A = k32_binop_2 )
=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ k8_funct_2 ) ) ) )
= ( B @ k8_binop_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1765]) ).
thf(454,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_setfam_1 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_setfam_1) ).
thf(4429,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_setfam_1 ) @ k3_tarski )
= ( B @ k3_tarski @ ( A @ k3_tarski @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(1416,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( B @ ( A @ ( D @ v1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t169_partfun1) ).
thf(9444,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( B @ ( A @ ( D @ v1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416]) ).
thf(1582,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
<=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_realset1) ).
thf(10266,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m1_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1582]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t155_funct_1) ).
thf(2692,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(2335,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ k1_funct_5 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_yellow_3) ).
thf(14398,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ k1_funct_5 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2335]) ).
thf(1368,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_funct_2 ) )
= ( B @ ( A @ k2_funcop_1 ) @ k4_card_3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_card_3) ).
thf(9244,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_funct_2 ) )
= ( B @ ( A @ k2_funcop_1 ) @ k4_card_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368]) ).
thf(1252,axiom,
! [A: $i] :
( ( A @ k1_eqrel_1 @ ( A @ ( A @ k5_relset_1 ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_toler_1) ).
thf(8619,plain,
! [A: $i] :
( ( A @ k1_eqrel_1 @ ( A @ ( A @ k5_relset_1 ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(2270,axiom,
k1_numbers @ k1_zfmisc_1 @ ( k1_urysohn1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_urysohn1) ).
thf(14147,plain,
k1_numbers @ k1_zfmisc_1 @ ( k1_urysohn1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2270]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_partfun1) ).
thf(3518,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(1798,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k4_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_subset_1) ).
thf(11435,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ( D @ ( E @ r2_hidden ) )
| ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k4_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1798]) ).
thf(235,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_funct_1 @ v1_funct_1 )
& ( A @ k2_funct_1 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(3386,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_funct_1 @ v1_funct_1 )
& ( A @ k2_funct_1 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(2037,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t157_relat_1) ).
thf(12950,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2037]) ).
thf(283,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( A @ ( A @ k2_finseq_1 @ r2_wellord2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_finseq_1) ).
thf(3632,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( A @ ( A @ k2_finseq_1 @ r2_wellord2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_zfmisc_1) ).
thf(3119,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k2_zfmisc_1 ) )
= ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) )
& ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(311,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( A @ ( B @ k1_fraenkel ) @ ( A @ ( B @ ( D @ m2_fraenkel ) ) ) )
=> ( ( C @ ( D @ k7_relat_1 ) )
= ( C @ ( B @ k3_xboole_0 ) @ ( D @ k7_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_fraenkel) ).
thf(3746,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( A @ ( B @ k1_fraenkel ) @ ( A @ ( B @ ( D @ m2_fraenkel ) ) ) )
=> ( ( C @ ( D @ k7_relat_1 ) )
= ( C @ ( B @ k3_xboole_0 ) @ ( D @ k7_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(836,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( A @ a_2_0_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_domain_1) ).
thf(6360,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( A @ a_2_0_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(548,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k7_relat_1 ) @ ( A @ ( B @ k7_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t105_relat_1) ).
thf(4883,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( A @ ( C @ k7_relat_1 ) @ ( A @ ( B @ k7_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(786,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( ( D @ k1_tarski @ ( C @ ( A @ ( B @ k2_funct_2 ) ) ) )
= ( D @ ( C @ ( A @ ( B @ k8_funct_2 ) ) ) @ k1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_setwiseo) ).
thf(6111,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( ( D @ k1_tarski @ ( C @ ( A @ ( B @ k2_funct_2 ) ) ) )
= ( D @ ( C @ ( A @ ( B @ k8_funct_2 ) ) ) @ k1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_2 ) @ ( A @ k1_funct_2 ) @ ( D @ r2_hidden ) )
=> ( ( ( D @ k10_funct_6 @ k10_funct_6 )
= D )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_funct_6) ).
thf(3078,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_2 ) @ ( A @ k1_funct_2 ) @ ( D @ r2_hidden ) )
=> ( ( ( D @ k10_funct_6 @ k10_funct_6 )
= D )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1174,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t168_partfun1) ).
thf(8149,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(962,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k6_relat_1 @ k1_funct_1 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
thf(6958,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k6_relat_1 @ k1_funct_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(1756,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( k1_xboole_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_partfun1) ).
thf(11189,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( k1_xboole_0 @ ( B @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1756]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ r2_hidden ) )
& ( D @ v2_funct_1 ) )
=> ( ( ( C @ ( D @ k1_funct_1 ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_funct_2) ).
thf(3650,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ r2_hidden ) )
& ( D @ v2_funct_1 ) )
=> ( ( ( C @ ( D @ k1_funct_1 ) @ ( D @ k2_funct_1 @ k1_funct_1 ) )
= C )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(1507,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( C @ k4_card_3 @ ( B @ r2_hidden ) )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) ) )
& ( A @ k3_tarski @ ( B @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_pua2mss1) ).
thf(9904,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ~ ( ( C @ k4_card_3 @ ( B @ r2_hidden ) )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) ) )
& ( A @ k3_tarski @ ( B @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1507]) ).
thf(792,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_partfun1) ).
thf(6128,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1131,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_partfun1) ).
thf(7874,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(710,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_4) ).
thf(5687,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_xboole_1) ).
thf(3176,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( D @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(1867,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_relat_1) ).
thf(11877,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1867]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) @ ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t155_relat_1) ).
thf(3018,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) @ ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1284,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ ( D @ v1_yellow18 ) ) ) )
<=> ( D @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_v1_yellow18) ).
thf(8792,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( ( D @ v2_funct_1 )
=> ( C @ ( B @ ( A @ ( D @ v1_yellow18 ) ) ) ) )
& ( ( C @ ( B @ ( A @ ( D @ v1_yellow18 ) ) ) )
=> ( D @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(95,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k3_funct_3 @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_funct_3) ).
thf(2798,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k3_funct_3 @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(2369,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A @ ( I @ m1_subset_1 ) )
& ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_domain_1) ).
thf(14580,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( A @ ( I @ m1_subset_1 ) )
& ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_domain_1 ) ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2369]) ).
thf(2273,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_subset_1) ).
thf(14153,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2273]) ).
thf(1447,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k2_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
thf(9609,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ k2_relat_1 @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447]) ).
thf(407,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( B @ v2_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_funct_1) ).
thf(4191,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( B @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(1337,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
<=> ( A @ ( B @ k2_relat_1 @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t173_relat_1) ).
thf(9100,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k2_relat_1 @ r1_xboole_0 ) )
=> ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
=> ( A @ ( B @ k2_relat_1 @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(1737,axiom,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_setfam_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] :
( ~ ( C @ v1_xboole_0 )
& ( B @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_triang_1) ).
thf(11097,plain,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_setfam_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] :
( ~ ( C @ v1_xboole_0 )
& ( B @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1737]) ).
thf(1188,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
& ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_zfmisc_1) ).
thf(8230,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( ( B @ k1_tarski @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
& ( ( A @ ( B @ k1_tarski @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(2218,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ a_4_2_domain_1 ) ) ) @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_domain_1) ).
thf(13928,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ a_4_2_domain_1 ) ) ) @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2218]) ).
thf(494,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
thf(4653,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(1137,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_binop_1) ).
thf(7898,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( A @ ( B @ v1_binop_1 ) ) )
& ( ( A @ ( B @ v1_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(319,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_funct_1 )
& ( B @ v2_relat_1 )
& ( B @ v1_relat_1 )
& ( A @ ( B @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_pboole) ).
thf(3775,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_funct_1 )
& ( B @ v2_relat_1 )
& ( B @ v1_relat_1 )
& ( A @ ( B @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(1707,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_subset_1 @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_subset_1) ).
thf(10946,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ k2_subset_1 @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1707]) ).
thf(1863,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_cantor_1 ) @ ( A @ k1_cantor_1 ) @ ( A @ g1_pre_topc ) @ v2_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_cantor_1) ).
thf(11860,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_cantor_1 ) @ ( A @ k1_cantor_1 ) @ ( A @ g1_pre_topc ) @ v2_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1863]) ).
thf(2209,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_setfam_1) ).
thf(13883,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2209]) ).
thf(1454,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( ( D @ ( B @ k5_relat_1 ) )
= ( A @ k6_relat_1 ) )
& ( ( B @ ( C @ k5_relat_1 ) )
= ( D @ k1_relat_1 @ k6_relat_1 ) )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_relat_1) ).
thf(9640,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( ( D @ ( B @ k5_relat_1 ) )
= ( A @ k6_relat_1 ) )
& ( ( B @ ( C @ k5_relat_1 ) )
= ( D @ k1_relat_1 @ k6_relat_1 ) )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454]) ).
thf(965,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k3_setfam_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k3_xboole_0 ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_setfam_1) ).
thf(6967,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k3_xboole_0 ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k3_xboole_0 ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k3_setfam_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_setfam_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k3_xboole_0 ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k3_xboole_0 ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(1688,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( A @ k2_ens_1 @ ( B @ ( D @ ( C @ k4_tarski ) @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ens_1) ).
thf(10830,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( A @ k2_ens_1 @ ( B @ ( D @ ( C @ k4_tarski ) @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( C @ ( B @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1688]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( A @ ( E @ k1_relat_1 @ ( D @ k2_relat_1 @ k3_xboole_0 ) @ r1_tarski ) )
=> ( ( B @ ( A @ ( E @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( A @ ( C @ k1_partfun1 ) ) ) ) ) )
= ( B @ ( C @ ( E @ ( D @ k5_relat_1 ) @ k3_partfun1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_partfun1) ).
thf(4582,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( A @ ( E @ k1_relat_1 @ ( D @ k2_relat_1 @ k3_xboole_0 ) @ r1_tarski ) )
=> ( ( B @ ( A @ ( E @ k3_partfun1 ) ) @ ( A @ ( C @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( A @ ( C @ k1_partfun1 ) ) ) ) ) )
= ( B @ ( C @ ( E @ ( D @ k5_relat_1 ) @ k3_partfun1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(1298,axiom,
! [A: $i,B: $i] :
( ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_funct_5 @ r1_tarski ) )
& ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k1_funct_5 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_funct_5) ).
thf(8864,plain,
! [A: $i,B: $i] :
( ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_funct_5 @ r1_tarski ) )
& ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k1_funct_5 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).
thf(1243,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) )
& ( B != k1_xboole_0 ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_lattice4) ).
thf(8555,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) )
& ( B != k1_xboole_0 ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(1078,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_funct_1) ).
thf(7631,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(2040,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_relat_1) ).
thf(12967,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2040]) ).
thf(562,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ k6_partfun1 @ ( E @ ( C @ ( B @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( D @ ( E @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funcop_1) ).
thf(4983,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ k6_partfun1 @ ( E @ ( C @ ( B @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( D @ ( E @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(609,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( A @ k4_finseq_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) )
& ( ( A @ k4_finseq_1 )
= ( B @ k4_finseq_1 ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finseq_1) ).
thf(5181,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( A @ k4_finseq_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) )
& ( ( A @ k4_finseq_1 )
= ( B @ k4_finseq_1 ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(936,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( D @ ( E @ r2_hidden ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ( E
= ( G @ ( F @ ( B @ ( A @ k12_mcart_1 ) ) ) ) )
& ( B @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) ) )
& ( A @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) ) )
& ( C @ ( E @ r1_tarski ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k10_funct_3 ) @ k1_funct_3 @ k9_relat_1 ) @ k1_setfam_1 @ ( D @ ( B @ ( A @ k9_funct_3 ) @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_borsuk_1) ).
thf(6844,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( D @ ( E @ r2_hidden ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ( E
= ( G @ ( F @ ( B @ ( A @ k12_mcart_1 ) ) ) ) )
& ( B @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) ) )
& ( A @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) ) )
& ( C @ ( E @ r1_tarski ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k10_funct_3 ) @ k1_funct_3 @ k9_relat_1 ) @ k1_setfam_1 @ ( D @ ( B @ ( A @ k9_funct_3 ) @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(1100,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( C @ k3_tarski @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_borsuk_1) ).
thf(7717,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( C @ k3_tarski @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ r1_xboole_0 ) )
=> ( ~ ( H @ ( D @ r1_xboole_0 ) )
& ~ ( G @ ( C @ r1_xboole_0 ) )
& ~ ( F @ ( B @ r1_xboole_0 ) )
& ~ ( E @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_mcart_1) ).
thf(4772,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ~ ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ r1_xboole_0 ) )
=> ( ~ ( H @ ( D @ r1_xboole_0 ) )
& ~ ( G @ ( C @ r1_xboole_0 ) )
& ~ ( F @ ( B @ r1_xboole_0 ) )
& ~ ( E @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(2315,axiom,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_subset_1) ).
thf(14313,plain,
! [A: $i] : ( A @ ( A @ k8_subset_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2315]) ).
thf(189,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ v1_setfam_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_funct_1) ).
thf(3210,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k2_relat_1 @ v1_setfam_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(2014,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k15_domain_1 ) ) ) )
= ( D @ k18_mcart_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k15_domain_1) ).
thf(12818,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k15_domain_1 ) ) ) )
= ( D @ k18_mcart_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2014]) ).
thf(2288,axiom,
! [A: $i] :
( ( a_0_0_domain_1 @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ( B @ p1_s7_domain_1 )
& ( A = B )
& ( f1_s7_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_0_domain_1) ).
thf(14212,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ p1_s7_domain_1 )
& ( A = B )
& ( f1_s7_domain_1 @ ( B @ m1_subset_1 ) ) )
=> ( a_0_0_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( a_0_0_domain_1 @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ( B @ p1_s7_domain_1 )
& ( A = B )
& ( f1_s7_domain_1 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2288]) ).
thf(837,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ ( C @ k5_funcop_1 ) ) @ ( B @ k5_relat_1 ) )
= ( A @ ( B @ k5_relat_1 ) @ ( D @ ( C @ k5_funcop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funcop_1) ).
thf(6363,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ ( C @ k5_funcop_1 ) ) @ ( B @ k5_relat_1 ) )
= ( A @ ( B @ k5_relat_1 ) @ ( D @ ( C @ k5_funcop_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(1145,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( A @ ( F @ m2_subset_1 ) ) )
=> ( ( ( F = E )
& ( D
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( ( ( C @ ( E @ ( A @ r3_binop_1 ) ) )
=> ( D @ ( F @ ( B @ r3_binop_1 ) ) ) )
& ( ( C @ ( E @ ( A @ r2_binop_1 ) ) )
=> ( D @ ( F @ ( B @ r2_binop_1 ) ) ) )
& ( ( C @ ( E @ ( A @ r1_binop_1 ) ) )
=> ( D @ ( F @ ( B @ r1_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_filter_2) ).
thf(8008,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( A @ ( F @ m2_subset_1 ) ) )
=> ( ( ( F = E )
& ( D
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( ( ( C @ ( E @ ( A @ r3_binop_1 ) ) )
=> ( D @ ( F @ ( B @ r3_binop_1 ) ) ) )
& ( ( C @ ( E @ ( A @ r2_binop_1 ) ) )
=> ( D @ ( F @ ( B @ r2_binop_1 ) ) ) )
& ( ( C @ ( E @ ( A @ r1_binop_1 ) ) )
=> ( D @ ( F @ ( B @ r1_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(1409,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(9419,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409]) ).
thf(2025,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ( ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_multop_1 ) ) ) ) ) ) ) )
= ( I @ ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_multop_1 ) ) ) ) ) ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_multop_1) ).
thf(12885,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ( ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_multop_1 ) ) ) ) ) ) ) )
= ( I @ ( H @ ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_multop_1 ) ) ) ) ) ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2025]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( A @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_setfam_1) ).
thf(2455,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( A @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(665,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(5464,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(625,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( A @ k2_funct_4 @ k2_funct_4 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_4) ).
thf(5253,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( A @ k2_funct_4 @ k2_funct_4 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(733,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k3_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(5786,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k3_tarski ) ) )
& ( ( B
= ( A @ k3_tarski ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(681,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( D @ ( A @ ( B @ k4_funcop_1 ) ) @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ ( A @ ( B @ k4_funcop_1 ) ) @ k1_funct_1 ) )
= ( D @ ( C @ ( A @ k1_funct_1 ) @ ( B @ k1_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funcop_1) ).
thf(5547,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( D @ ( A @ ( B @ k4_funcop_1 ) ) @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ ( A @ ( B @ k4_funcop_1 ) ) @ k1_funct_1 ) )
= ( D @ ( C @ ( A @ k1_funct_1 ) @ ( B @ k1_binop_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(797,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t180_relat_1) ).
thf(6164,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_setfam_1) ).
thf(2613,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k1_setfam_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1315,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( E @ ( F @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= ( E @ ( F @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_funcop_1) ).
thf(8968,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( E @ ( F @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= ( E @ ( F @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(1658,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
=> ! [C: $i] :
( ( B @ ( A @ k2_cantor_1 ) @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( C
= ( D @ ( A @ k8_setfam_1 ) ) )
& ( B @ ( D @ r1_tarski ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( D @ v1_finset_1 )
& ~ ( D @ v1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_yellow_9) ).
thf(10688,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ k8_setfam_1 ) ) )
& ( B @ ( D @ r1_tarski ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( D @ v1_finset_1 )
& ~ ( D @ v1_xboole_0 ) )
=> ( B @ ( A @ k2_cantor_1 ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k2_cantor_1 ) @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ k8_setfam_1 ) ) )
& ( B @ ( D @ r1_tarski ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( D @ v1_finset_1 )
& ~ ( D @ v1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1658]) ).
thf(1116,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( k1_xboole_0 @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t141_partfun1) ).
thf(7806,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( k1_xboole_0 @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(1213,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k7_relat_1 ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
<=> ( ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
thf(8390,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k7_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k7_relat_1 ) ) )
=> ! [D: $i,E: $i] :
( ( ( ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(304,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(3723,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_xboole_1) ).
thf(3643,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( A @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ k18_pralg_1 ) ) )
= ( C @ k2_funct_4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k18_pralg_1) ).
thf(4444,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ ( A @ k18_pralg_1 ) ) )
= ( C @ k2_funct_4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(57,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A
= ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ k3_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_partfun1) ).
thf(2666,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A
= ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ ( A @ k3_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(892,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_lattice2) ).
thf(6625,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(870,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ r1_tarski ) )
<=> ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(6541,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_tarski ) ) )
& ( ( B @ ( A @ k1_tarski @ r1_tarski ) )
=> ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(271,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( ( B @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( B @ k5_relat_1 ) )
= A ) )
=> ( ( A @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( B @ ( A @ k5_relat_1 ) )
= A ) )
=> ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_sysrel) ).
thf(3555,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( ( B @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( B @ k5_relat_1 ) )
= A ) )
=> ( ( A @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( B @ ( A @ k5_relat_1 ) )
= A ) )
=> ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(1401,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_domain_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_domain_1) ).
thf(9392,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_domain_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1401]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( D @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ r2_wellord2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_card_1) ).
thf(2649,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( D @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( C @ k1_tarski @ ( A @ k4_xboole_0 ) @ r2_wellord2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_setwiseo ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k5_setwiseo) ).
thf(2781,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_setwiseo ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(779,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ k10_funct_3 ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ ( C @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_funct_2 ) ) ) ) )
= E )
& ( ( C @ ( B @ k9_funct_3 ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ ( B @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_funct_2 ) ) ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funct_3) ).
thf(6065,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ k10_funct_3 ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ ( C @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_funct_2 ) ) ) ) )
= E )
& ( ( C @ ( B @ k9_funct_3 ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ ( B @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_funct_2 ) ) ) ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(909,axiom,
! [A: $i,B: $i] :
( ( A @ k6_relat_1 @ ( B @ k6_relat_1 @ k5_relat_1 ) )
= ( B @ ( A @ k3_xboole_0 ) @ k6_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funct_1) ).
thf(6724,plain,
! [A: $i,B: $i] :
( ( A @ k6_relat_1 @ ( B @ k6_relat_1 @ k5_relat_1 ) )
= ( B @ ( A @ k3_xboole_0 ) @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(2271,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( A @ k3_subset_1 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(14148,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( A @ k3_subset_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2271]) ).
thf(1198,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ ( B @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_relat_1) ).
thf(8326,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ ( B @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ k3_partfun1 ) ) @ ( C @ ( A @ ( E @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_partfun1) ).
thf(3354,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ ( E @ k3_partfun1 ) ) @ ( C @ ( A @ ( E @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(702,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ~ ( ( C @ v2_funct_1 )
<=> ! [D: $i,E: $i] :
( ( ( A @ ( D @ ( E @ m2_relset_1 ) ) )
& ( A @ ( D @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( A @ ( D @ ( F @ m2_relset_1 ) ) )
& ( A @ ( D @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( C @ ( E @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) )
= ( C @ ( F @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_2) ).
thf(5639,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ~ ( ( ! [D: $i,E: $i] :
( ( ( A @ ( D @ ( E @ m2_relset_1 ) ) )
& ( A @ ( D @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( A @ ( D @ ( F @ m2_relset_1 ) ) )
& ( A @ ( D @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( C @ ( E @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) )
= ( C @ ( F @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) )
=> ( C @ v2_funct_1 ) )
& ( ( C @ v2_funct_1 )
=> ! [D: $i,E: $i] :
( ( ( A @ ( D @ ( E @ m2_relset_1 ) ) )
& ( A @ ( D @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( A @ ( D @ ( F @ m2_relset_1 ) ) )
& ( A @ ( D @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( C @ ( E @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) )
= ( C @ ( F @ ( B @ ( A @ ( A @ ( D @ k1_partfun1 ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(944,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k7_funct_6 @ k1_funct_1 ) )
= ( B @ ( C @ k5_relat_1 ) ) ) ) )
& ( ( B @ ( A @ k2_funcop_1 ) @ k7_funct_6 @ k2_relat_1 )
= ( B @ k2_relat_1 @ ( A @ k1_funct_2 ) ) )
& ( ( B @ ( A @ k2_funcop_1 ) @ k7_funct_6 @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_funct_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_6) ).
thf(6876,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k7_funct_6 @ k1_funct_1 ) )
= ( B @ ( C @ k5_relat_1 ) ) ) ) )
& ( ( B @ ( A @ k2_funcop_1 ) @ k7_funct_6 @ k2_relat_1 )
= ( B @ k2_relat_1 @ ( A @ k1_funct_2 ) ) )
& ( ( B @ ( A @ k2_funcop_1 ) @ k7_funct_6 @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_funct_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( A @ k1_setfam_1 @ ( B @ k1_setfam_1 @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_setfam_1) ).
thf(2465,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( A @ k1_setfam_1 @ ( B @ k1_setfam_1 @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( C @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_xboole_1) ).
thf(3540,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) )
= ( B @ ( C @ ( A @ k4_xboole_0 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(529,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ( k1_numbers @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_membered) ).
thf(4804,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ( k1_numbers @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(2231,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ v1_relat_1 )
=> ( ( D @ ( C @ k6_relat_1 @ k5_relat_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( D @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).
thf(13979,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( ( D @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( D @ ( C @ k6_relat_1 @ k5_relat_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ ( C @ k6_relat_1 @ k5_relat_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2231]) ).
thf(1701,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
<=> ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
thf(10919,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1701]) ).
thf(834,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_card_fil ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( B @ ( D @ r1_xboole_0 ) )
& ( C @ ( D @ r2_hidden ) ) ) )
=> ( ( B @ ( C @ ( A @ k3_card_fil ) ) @ ( C @ r1_tarski ) )
& ( A @ ( B @ ( C @ ( A @ k3_card_fil ) ) @ m1_card_fil ) )
& ( B @ ( C @ ( A @ k3_card_fil ) ) @ ( B @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_card_fil) ).
thf(6349,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_card_fil ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( B @ ( D @ r1_xboole_0 ) )
& ( C @ ( D @ r2_hidden ) ) ) )
=> ( ( B @ ( C @ ( A @ k3_card_fil ) ) @ ( C @ r1_tarski ) )
& ( A @ ( B @ ( C @ ( A @ k3_card_fil ) ) @ m1_card_fil ) )
& ( B @ ( C @ ( A @ k3_card_fil ) ) @ ( B @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
<=> ( ( C @ k2_relat_1 )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_funct_2) ).
thf(3703,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
=> ( B @ ( A @ ( C @ v2_funct_2 ) ) ) )
& ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
=> ( ( C @ k2_relat_1 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(1826,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
<=> ( ( B @ ( C @ k2_funct_5 @ r1_tarski ) )
& ( ( C @ k1_funct_5 )
= A )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_yellow18) ).
thf(11608,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( C @ k2_funct_5 @ r1_tarski ) )
& ( ( C @ k1_funct_5 )
= A )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) ) )
& ( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ k2_funct_5 @ r1_tarski ) )
& ( ( C @ k1_funct_5 )
= A )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1826]) ).
thf(1223,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_binop_1) ).
thf(8458,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) )
=> ( C @ ( B @ ( A @ r1_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( B @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(1074,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
<=> ( ( C @ ( A @ ( B @ k4_relset_1 ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_relset_1) ).
thf(7609,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( ( ( C @ ( A @ ( B @ k4_relset_1 ) ) )
= B )
=> ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( C @ ( A @ ( B @ k4_relset_1 ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(2078,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k7_relset_2 ) ) ) )
= ( C @ k3_pua2mss1 @ ( D @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) @ ( B @ k8_setfam_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relset_2) ).
thf(13205,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k7_relset_2 ) ) ) )
= ( C @ k3_pua2mss1 @ ( D @ ( A @ ( B @ k6_relset_2 ) ) @ ( B @ ( A @ k1_zfmisc_1 @ k4_relset_2 ) ) ) @ ( B @ k8_setfam_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2078]) ).
thf(1186,axiom,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finseq_1) ).
thf(8219,plain,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(1983,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k2_cantor_1 ) @ ( B @ ( A @ k2_cantor_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_cantor_1) ).
thf(12632,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k2_cantor_1 ) @ ( B @ ( A @ k2_cantor_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1983]) ).
thf(1085,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_enumset1 ) ) )
= ( A @ ( C @ ( B @ k1_enumset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_enumset1) ).
thf(7651,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_enumset1 ) ) )
= ( A @ ( C @ ( B @ k1_enumset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(34,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) ) )
=> ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) ) )
<=> ? [G: $i] :
( ! [H: $i] :
( ( A @ k5_finsub_1 @ ( H @ m1_subset_1 ) )
=> ( ( D @ ( H @ r1_tarski ) )
=> ( ! [I: $i] :
( ( A @ ( I @ m1_subset_1 ) )
=> ( ( H @ ( D @ ( A @ k6_setwiseo ) ) @ ( I @ r2_hidden ) )
=> ( ( I @ ( A @ k2_setwiseo ) @ ( H @ ( A @ k5_setwiseo ) ) @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( I @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( H @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) ) ) ) )
| ( H = k1_xboole_0 ) ) ) )
& ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( A @ k2_setwiseo ) @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( H @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) ) ) )
& ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ( ( C @ ( H @ ( B @ r3_binop_1 ) ) )
=> ( ( k1_xboole_0 @ ( G @ k1_funct_1 ) )
= H ) ) )
& ( F
= ( D @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) ) )
& ( B @ ( A @ k5_finsub_1 @ ( G @ m2_relset_1 ) ) )
& ( B @ ( A @ k5_finsub_1 @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) ) ) )
| ( ~ ( B @ ( C @ v1_setwiseo ) )
& ( D = k1_xboole_0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_setwiseo) ).
thf(2519,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) ) )
=> ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( ? [G: $i] :
( ! [H: $i] :
( ( A @ k5_finsub_1 @ ( H @ m1_subset_1 ) )
=> ( ( D @ ( H @ r1_tarski ) )
=> ( ! [I: $i] :
( ( A @ ( I @ m1_subset_1 ) )
=> ( ( H @ ( D @ ( A @ k6_setwiseo ) ) @ ( I @ r2_hidden ) )
=> ( ( I @ ( A @ k2_setwiseo ) @ ( H @ ( A @ k5_setwiseo ) ) @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( I @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( H @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) ) ) ) )
| ( H = k1_xboole_0 ) ) ) )
& ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( A @ k2_setwiseo ) @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( H @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) ) ) )
& ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ( ( C @ ( H @ ( B @ r3_binop_1 ) ) )
=> ( ( k1_xboole_0 @ ( G @ k1_funct_1 ) )
= H ) ) )
& ( F
= ( D @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) ) )
& ( B @ ( A @ k5_finsub_1 @ ( G @ m2_relset_1 ) ) )
& ( B @ ( A @ k5_finsub_1 @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) ) ) )
& ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) ) )
=> ? [G: $i] :
( ! [H: $i] :
( ( A @ k5_finsub_1 @ ( H @ m1_subset_1 ) )
=> ( ( D @ ( H @ r1_tarski ) )
=> ( ! [I: $i] :
( ( A @ ( I @ m1_subset_1 ) )
=> ( ( H @ ( D @ ( A @ k6_setwiseo ) ) @ ( I @ r2_hidden ) )
=> ( ( I @ ( A @ k2_setwiseo ) @ ( H @ ( A @ k5_setwiseo ) ) @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( I @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( H @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) ) ) ) )
| ( H = k1_xboole_0 ) ) ) )
& ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( A @ k2_setwiseo ) @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( H @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) ) ) )
& ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ( ( C @ ( H @ ( B @ r3_binop_1 ) ) )
=> ( ( k1_xboole_0 @ ( G @ k1_funct_1 ) )
= H ) ) )
& ( F
= ( D @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) ) )
& ( B @ ( A @ k5_finsub_1 @ ( G @ m2_relset_1 ) ) )
& ( B @ ( A @ k5_finsub_1 @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) ) ) ) )
| ( ~ ( B @ ( C @ v1_setwiseo ) )
& ( D = k1_xboole_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(668,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(5481,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(1202,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ ( E @ ( D @ ( A @ k4_setwiseo ) ) ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( F @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( B @ k5_setwiseo ) ) @ ( B @ k5_setwiseo ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_setwiseo) ).
thf(8351,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ ( E @ ( D @ ( A @ k4_setwiseo ) ) ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( F @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( B @ k5_setwiseo ) ) @ ( B @ k5_setwiseo ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(321,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k4_relat_1 @ k4_relat_1 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(3787,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k4_relat_1 @ k4_relat_1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(1347,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( B @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_partfun1) ).
thf(9149,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( B @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ m2_relset_1 ) ) )
& ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347]) ).
thf(2390,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k4_relset_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_2) ).
thf(14655,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k4_relset_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2390]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( k1_numbers @ ( B @ m1_subset_1 ) )
& ( k1_numbers @ ( A @ m1_subset_1 ) ) )
=> ( k1_numbers @ ( B @ ( A @ k11_binop_2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_binop_2) ).
thf(2598,plain,
! [A: $i,B: $i] :
( ( ( k1_numbers @ ( B @ m1_subset_1 ) )
& ( k1_numbers @ ( A @ m1_subset_1 ) ) )
=> ( k1_numbers @ ( B @ ( A @ k11_binop_2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(317,axiom,
! [A: $i] :
( ( A @ k1_orders_1 )
= ( k1_xboole_0 @ k1_tarski @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_orders_1) ).
thf(3770,plain,
! [A: $i] :
( ( A @ k1_orders_1 )
= ( k1_xboole_0 @ k1_tarski @ ( A @ k1_zfmisc_1 @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(1505,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( E @ ( F @ r2_hidden ) )
=> ( ( F @ ( C @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_lattice2) ).
thf(9893,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( E @ ( F @ r2_hidden ) )
=> ( ( F @ ( C @ k1_funct_1 ) )
= ( F @ ( D @ k1_funct_1 ) ) ) ) )
=> ( ( E @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505]) ).
thf(1418,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( B @ ( C @ k5_relat_1 ) )
= B )
& ( B @ v2_funct_1 )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( C
= ( A @ k6_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_funct_1) ).
thf(9448,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( B @ ( C @ k5_relat_1 ) )
= B )
& ( B @ v2_funct_1 )
& ( A @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( C
= ( A @ k6_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418]) ).
thf(236,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( B @ k2_finseq_1 @ ( A @ k2_finseq_1 @ r2_wellord2 ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_finseq_1) ).
thf(3390,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ( ( B @ k2_finseq_1 @ ( A @ k2_finseq_1 @ r2_wellord2 ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(1040,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( B @ ( D @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_funct_4) ).
thf(7495,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( B @ ( D @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(582,axiom,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_xboole_1) ).
thf(5058,plain,
! [A: $i] : ( k1_xboole_0 @ ( A @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(2179,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ r1_tarski ) )
& ( F @ ( E @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( H @ ( F @ ( D @ ( B @ k4_zfmisc_1 ) ) ) @ ( G @ ( E @ ( C @ ( A @ k4_zfmisc_1 ) ) ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_mcart_1) ).
thf(13718,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( H @ ( G @ r1_tarski ) )
& ( F @ ( E @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( H @ ( F @ ( D @ ( B @ k4_zfmisc_1 ) ) ) @ ( G @ ( E @ ( C @ ( A @ k4_zfmisc_1 ) ) ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2179]) ).
thf(510,axiom,
! [A: $i] :
( ~ ( ( A @ ( A @ r1_xboole_0 ) )
& ( A != k1_xboole_0 ) )
& ~ ( ( A = k1_xboole_0 )
& ~ ( A @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_xboole_1) ).
thf(4717,plain,
! [A: $i] :
( ~ ( ( A @ ( A @ r1_xboole_0 ) )
& ( A != k1_xboole_0 ) )
& ~ ( ( A = k1_xboole_0 )
& ~ ( A @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(1070,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_partfun1) ).
thf(7597,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ k2_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(833,axiom,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( A @ ( B @ k3_xboole_0 ) @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc28_membered) ).
thf(6346,plain,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( A @ ( B @ k3_xboole_0 ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(1589,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E
= ( D @ ( C @ ( B @ ( A @ a_4_2_relset_2 ) ) ) ) )
=> ( ( C @ ( D @ ( A @ k5_setfam_1 ) @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( E @ ( B @ k8_setfam_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_relset_2) ).
thf(10306,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E
= ( D @ ( C @ ( B @ ( A @ a_4_2_relset_2 ) ) ) ) )
=> ( ( C @ ( D @ ( A @ k5_setfam_1 ) @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( E @ ( B @ k8_setfam_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1589]) ).
thf(1272,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( C @ ( D @ k10_relat_1 ) @ ( E @ r2_hidden ) )
<=> ( ( C @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_2) ).
thf(8732,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ( ( ( C @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ k10_relat_1 ) @ ( E @ r2_hidden ) ) )
& ( ( C @ ( D @ k10_relat_1 ) @ ( E @ r2_hidden ) )
=> ( ( C @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(1421,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r4_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_binop_1) ).
thf(9461,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r4_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( E @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421]) ).
thf(1307,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) ) )
<=> ! [H: $i] :
( ( G @ ( H @ r2_hidden ) )
<=> ~ ( ( H != F )
& ( H != E )
& ( H != D )
& ( H != C )
& ( H != B )
& ( H != A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_enumset1) ).
thf(8896,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ! [H: $i] :
( ( ~ ( ( H != F )
& ( H != E )
& ( H != D )
& ( H != C )
& ( H != B )
& ( H != A ) )
=> ( G @ ( H @ r2_hidden ) ) )
& ( ( G @ ( H @ r2_hidden ) )
=> ~ ( ( H != F )
& ( H != E )
& ( H != D )
& ( H != C )
& ( H != B )
& ( H != A ) ) ) )
=> ( G
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) ) ) )
& ( ( G
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) ) )
=> ! [H: $i] :
( ( ~ ( ( H != F )
& ( H != E )
& ( H != D )
& ( H != C )
& ( H != B )
& ( H != A ) )
=> ( G @ ( H @ r2_hidden ) ) )
& ( ( G @ ( H @ r2_hidden ) )
=> ~ ( ( H != F )
& ( H != E )
& ( H != D )
& ( H != C )
& ( H != B )
& ( H != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(2214,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(13911,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2214]) ).
thf(2169,axiom,
! [A: $i] :
( ( k2_qc_lang1 @ ( A @ m1_subset_1 ) )
=> ( ( A @ k23_qc_lang1 )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k23_qc_lang1) ).
thf(13680,plain,
! [A: $i] :
( ( k2_qc_lang1 @ ( A @ m1_subset_1 ) )
=> ( ( A @ k23_qc_lang1 )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2169]) ).
thf(1610,axiom,
k1_qc_lang1 @ k1_zfmisc_1 @ ( k2_qc_lang1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_qc_lang1) ).
thf(10438,plain,
k1_qc_lang1 @ k1_zfmisc_1 @ ( k2_qc_lang1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1610]) ).
thf(1526,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_filter_2) ).
thf(9990,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( ( B = C )
=> ( C @ ( B @ ( A @ r1_filter_2 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1526]) ).
thf(1451,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_partfun1) ).
thf(9620,plain,
! [A: $i,B: $i,C: $i] :
( ( ( k1_xboole_0 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ v1_relat_1 )
=> ( ( E
= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) )
=> ( ( ( E @ k2_relat_1 )
= ( D @ ( B @ k2_tarski ) ) )
& ( ( E @ k1_relat_1 )
= ( C @ ( A @ k2_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_relat_1) ).
thf(4231,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ v1_relat_1 )
=> ( ( E
= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) )
=> ( ( ( E @ k2_relat_1 )
= ( D @ ( B @ k2_tarski ) ) )
& ( ( E @ k1_relat_1 )
= ( C @ ( A @ k2_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(1075,axiom,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(7619,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(2036,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ k1_orders_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_orders_1) ).
thf(12946,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ( B @ k1_orders_1 @ ( A @ r2_hidden ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ k1_orders_1 @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2036]) ).
thf(735,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_partfun1) ).
thf(5823,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(953,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i] : ( B @ ( B @ ( A @ k9_relat_1 ) @ ( A @ k10_relat_1 ) @ r1_tarski ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t153_funct_1) ).
thf(6908,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i] : ( B @ ( B @ ( A @ k9_relat_1 ) @ ( A @ k10_relat_1 ) @ r1_tarski ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(1222,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ m1_subset_1 ) )
& ( B @ ( A @ k1_fraenkel ) @ ( D @ ( C @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ k1_fraenkel ) @ ( D @ ( C @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_funcsdom ) ) ) ) ) )
= ( F @ ( E @ k1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funcsdom) ).
thf(8455,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ m1_subset_1 ) )
& ( B @ ( A @ k1_fraenkel ) @ ( D @ ( C @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ k1_fraenkel ) @ ( D @ ( C @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_funcsdom ) ) ) ) ) )
= ( F @ ( E @ k1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(856,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k8_relat_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(6465,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k8_relat_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_partfun1) ).
thf(3247,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(241,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ ( B @ k2_funct_1 @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k2_funct_1 @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
thf(3409,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k2_relat_1 @ ( A @ r2_hidden ) )
& ( B @ v2_funct_1 ) )
=> ( ( A
= ( A @ ( B @ ( B @ k2_funct_1 @ k5_relat_1 ) @ k1_funct_1 ) ) )
& ( A
= ( A @ ( B @ k2_funct_1 @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(86,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(2766,plain,
! [A: $i,B: $i] :
~ ( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_functor0 ) ) ) @ v2_funct_2 ) ) )
=> ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v2_funct_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_functor0) ).
thf(2697,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_functor0 ) ) ) @ v2_funct_2 ) ) )
=> ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v2_funct_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(2387,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k7_setfam_1 ) )
= ( C @ ( A @ k7_setfam_1 ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_setfam_1) ).
thf(14634,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k7_setfam_1 ) )
= ( C @ ( A @ k7_setfam_1 ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2387]) ).
thf(1218,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_oppcat_1 ) ) ) )
= ( D @ k2_funct_4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_oppcat_1) ).
thf(8425,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_oppcat_1 ) ) ) )
= ( D @ k2_funct_4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(1161,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_domain_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_domain_1) ).
thf(8090,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_domain_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(1643,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m1_nat_lat ) ) ) )
=> ( B @ ( A @ ( D @ m2_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_nat_lat) ).
thf(10588,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m1_nat_lat ) ) ) )
=> ( B @ ( A @ ( D @ m2_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1643]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( ( k1_numbers @ ( B @ m1_subset_1 ) )
& ( k1_numbers @ ( A @ m1_subset_1 ) ) )
=> ( ( B @ ( A @ k11_binop_2 ) )
= ( A @ ( B @ k11_binop_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k11_binop_2) ).
thf(3064,plain,
! [A: $i,B: $i] :
( ( ( k1_numbers @ ( B @ m1_subset_1 ) )
& ( k1_numbers @ ( A @ m1_subset_1 ) ) )
=> ( ( B @ ( A @ k11_binop_2 ) )
= ( A @ ( B @ k11_binop_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1625,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(10513,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1625]) ).
thf(1565,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g3_lattices ) ) )
= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).
thf(10180,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g3_lattices ) ) )
= ( F @ ( E @ ( D @ g3_lattices ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1565]) ).
thf(1172,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( C @ ( D @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_funct_2) ).
thf(8144,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( A @ ( C @ ( D @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(2262,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k7_setfam_1 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(14116,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k7_setfam_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2262]) ).
thf(1546,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(10075,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1546]) ).
thf(2173,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( D @ ( E @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funcop_1) ).
thf(13693,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( D @ ( E @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2173]) ).
thf(576,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ k2_funct_4 @ k2_funct_4 )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_4) ).
thf(5026,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ k2_funct_4 @ k2_funct_4 )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(1985,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C = D )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_funct_2) ).
thf(12641,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C = D )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1985]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( D
= ( B @ ( C @ k5_funct_5 @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( ( A @ ( D @ k1_funct_1 ) )
= ( B @ ( A @ k4_tarski ) @ ( C @ k1_funct_1 ) ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_funct_5) ).
thf(3364,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( D
= ( B @ ( C @ k5_funct_5 @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( ( A @ ( D @ k1_funct_1 ) )
= ( B @ ( A @ k4_tarski ) @ ( C @ k1_funct_1 ) ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(386,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ( B @ ( A @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_funct_4) ).
thf(4086,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ k1_funct_4 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ( B @ ( A @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(2297,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_mcart_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_mcart_1) ).
thf(14249,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_mcart_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2297]) ).
thf(2018,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_mssubfam) ).
thf(12831,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k8_setfam_1 ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2018]) ).
thf(1516,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ! [C: $i] :
~ ( ( ( C @ k1_tarski @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_funct_1) ).
thf(9942,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ! [C: $i] :
~ ( ( ( C @ k1_tarski @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_wellord2 ) )
<=> ? [C: $i] :
( ( ( C @ k2_relat_1 )
= B )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord2) ).
thf(3083,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( ( C @ k2_relat_1 )
= B )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ r2_wellord2 ) ) )
& ( ( B @ ( A @ r2_wellord2 ) )
=> ? [C: $i] :
( ( ( C @ k2_relat_1 )
= B )
& ( ( C @ k1_relat_1 )
= A )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(2175,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_card_fil ) )
=> ~ ( ( C @ ( B @ ( A @ k1_card_fil ) @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_card_fil) ).
thf(13699,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_card_fil ) )
=> ~ ( ( C @ ( B @ ( A @ k1_card_fil ) @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2175]) ).
thf(2039,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ v1_relat_1 )
=> ( ( C @ k6_relat_1 @ ( D @ k5_relat_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( D @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_relat_1) ).
thf(12962,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( ( D @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) ) )
=> ( C @ k6_relat_1 @ ( D @ k5_relat_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ k6_relat_1 @ ( D @ k5_relat_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2039]) ).
thf(1914,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(12138,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1914]) ).
thf(1465,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( ( C @ k2_funct_4 @ k2_relat_1 )
= ( C @ k2_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_funct_4) ).
thf(9699,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( ( C @ k2_funct_4 @ k2_relat_1 )
= ( C @ k2_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1465]) ).
thf(1285,axiom,
! [A: $i] :
( ( A @ v2_setfam_1 )
<=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( A @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_setfam_1) ).
thf(8796,plain,
! [A: $i] :
( ( ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( A @ ( B @ r2_hidden ) ) )
=> ( A @ v2_setfam_1 ) )
& ( ( A @ v2_setfam_1 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( A @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(1250,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ ( A @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_enumset1) ).
thf(8614,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ ( A @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(1786,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m3_realset1) ).
thf(11368,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1786]) ).
thf(1743,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_realset1) ).
thf(11125,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1743]) ).
thf(723,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(5737,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(2282,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset_1) ).
thf(14185,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( k1_xboole_0 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2282]) ).
thf(624,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ( ~ ( A @ v2_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_yellow21) ).
thf(5249,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ( ~ ( A @ v2_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(2220,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(13932,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2220]) ).
thf(992,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( E @ k1_zfmisc_1 @ ( I @ m1_subset_1 ) )
& ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_8_0_domain_1 ) ) ) ) ) ) ) @ ( A @ r2_hidden ) )
<=> ? [J: $i,K: $i,L: $i,M: $i] :
( ( I @ ( M @ r2_hidden ) )
& ( H @ ( L @ r2_hidden ) )
& ( G @ ( K @ r2_hidden ) )
& ( F @ ( J @ r2_hidden ) )
& ( A
= ( M @ ( L @ ( K @ ( J @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
& ( E @ ( M @ m1_subset_1 ) )
& ( D @ ( L @ m1_subset_1 ) )
& ( C @ ( K @ m1_subset_1 ) )
& ( B @ ( J @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_8_0_domain_1) ).
thf(7193,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ( E @ k1_zfmisc_1 @ ( I @ m1_subset_1 ) )
& ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [J: $i,K: $i,L: $i,M: $i] :
( ( I @ ( M @ r2_hidden ) )
& ( H @ ( L @ r2_hidden ) )
& ( G @ ( K @ r2_hidden ) )
& ( F @ ( J @ r2_hidden ) )
& ( A
= ( M @ ( L @ ( K @ ( J @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
& ( E @ ( M @ m1_subset_1 ) )
& ( D @ ( L @ m1_subset_1 ) )
& ( C @ ( K @ m1_subset_1 ) )
& ( B @ ( J @ m1_subset_1 ) ) )
=> ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_8_0_domain_1 ) ) ) ) ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_8_0_domain_1 ) ) ) ) ) ) ) @ ( A @ r2_hidden ) )
=> ? [J: $i,K: $i,L: $i,M: $i] :
( ( I @ ( M @ r2_hidden ) )
& ( H @ ( L @ r2_hidden ) )
& ( G @ ( K @ r2_hidden ) )
& ( F @ ( J @ r2_hidden ) )
& ( A
= ( M @ ( L @ ( K @ ( J @ ( E @ ( D @ ( C @ ( B @ k5_domain_1 ) ) ) ) ) ) ) ) )
& ( E @ ( M @ m1_subset_1 ) )
& ( D @ ( L @ m1_subset_1 ) )
& ( C @ ( K @ m1_subset_1 ) )
& ( B @ ( J @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(2138,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( B @ ( D @ r2_hidden ) )
<=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_subset_1) ).
thf(13522,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2138]) ).
thf(1719,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_funct_3 ) )
= ( B @ ( A @ k6_relat_1 @ k7_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funct_3) ).
thf(11031,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_funct_3 ) )
= ( B @ ( A @ k6_relat_1 @ k7_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1719]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ( ( k1_numbers @ ( B @ m1_subset_1 ) )
& ( k1_numbers @ ( A @ m1_subset_1 ) ) )
=> ( k1_numbers @ ( B @ ( A @ k12_binop_2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_binop_2) ).
thf(3755,plain,
! [A: $i,B: $i] :
( ( ( k1_numbers @ ( B @ m1_subset_1 ) )
& ( k1_numbers @ ( A @ m1_subset_1 ) ) )
=> ( k1_numbers @ ( B @ ( A @ k12_binop_2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(2120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( D @ ( J @ m1_subset_1 ) )
& ( C @ ( I @ m1_subset_1 ) )
& ( B @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_relset_1 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ~ ( E @ v1_xboole_0 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( E @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_multop_1 ) ) ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_multop_1) ).
thf(13398,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( D @ ( J @ m1_subset_1 ) )
& ( C @ ( I @ m1_subset_1 ) )
& ( B @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m1_relset_1 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ~ ( E @ v1_xboole_0 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( E @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_multop_1 ) ) ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2120]) ).
thf(1316,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( C @ r1_tarski ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_funct_2) ).
thf(8971,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( D @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( C @ r1_tarski ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( C @ ( B @ ( A @ k3_partfun1 ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k3_partfun1 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_partfun1) ).
thf(3802,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( C @ ( B @ ( A @ k3_partfun1 ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k3_partfun1 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(637,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_partfun1) ).
thf(5310,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( B @ ( A @ r1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(1603,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ( ( A
= ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) ) )
<=> ! [F: $i] :
( ( A @ ( F @ r2_hidden ) )
<=> ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_domain_1) ).
thf(10366,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ( ( ! [F: $i] :
( ( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) )
=> ( A @ ( F @ r2_hidden ) ) )
& ( ( A @ ( F @ r2_hidden ) )
=> ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) ) ) )
& ( ( A
= ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) ) )
=> ! [F: $i] :
( ( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) )
=> ( A @ ( F @ r2_hidden ) ) )
& ( ( A @ ( F @ r2_hidden ) )
=> ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1603]) ).
thf(1293,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k4_card_3 @ ( A @ r2_hidden ) )
<=> ( ! [C: $i] :
( ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ ( C @ ( A @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_card_3) ).
thf(8839,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i] :
( ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ ( C @ ( A @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( B @ k4_card_3 @ ( A @ r2_hidden ) ) )
& ( ( B @ k4_card_3 @ ( A @ r2_hidden ) )
=> ( ! [C: $i] :
( ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( C @ ( B @ k1_funct_1 ) @ ( C @ ( A @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(491,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( D @ ( A @ ( C @ k4_funcop_1 ) ) @ ( B @ k5_relat_1 ) )
= ( D @ ( A @ ( B @ k5_relat_1 ) @ ( C @ k4_funcop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funcop_1) ).
thf(4644,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( D @ ( A @ ( C @ k4_funcop_1 ) ) @ ( B @ k5_relat_1 ) )
= ( D @ ( A @ ( B @ k5_relat_1 ) @ ( C @ k4_funcop_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( A @ ( C @ k3_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( A @ ( C @ k3_funct_5 @ k1_funct_1 ) @ v1_relat_1 )
& ( C @ k3_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_funct_5) ).
thf(3225,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( A @ ( C @ k3_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( A @ ( C @ k3_funct_5 @ k1_funct_1 ) @ v1_relat_1 )
& ( C @ k3_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1748,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k7_setfam_1 ) )
= ( B @ ( A @ a_2_0_card_fil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_card_fil) ).
thf(11153,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k7_setfam_1 ) )
= ( B @ ( A @ a_2_0_card_fil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1748]) ).
thf(1596,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_fraenkel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_closure2) ).
thf(10338,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_fraenkel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1596]) ).
thf(1976,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_ordinal1) ).
thf(12577,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
~ ( ( A @ ( F @ r2_hidden ) )
& ( F @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1976]) ).
thf(1522,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B
= ( A @ k1_funct_3 ) )
<=> ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r1_tarski ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ ( A @ k9_relat_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k1_relat_1 @ k1_zfmisc_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_3) ).
thf(9964,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r1_tarski ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ ( A @ k9_relat_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k1_relat_1 @ k1_zfmisc_1 ) ) )
=> ( B
= ( A @ k1_funct_3 ) ) )
& ( ( B
= ( A @ k1_funct_3 ) )
=> ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r1_tarski ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ ( A @ k9_relat_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k1_relat_1 @ k1_zfmisc_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1522]) ).
thf(2280,axiom,
f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s9_domain_1) ).
thf(14180,plain,
f3_s9_domain_1 @ k1_zfmisc_1 @ ( a_0_2_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2280]) ).
thf(414,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ ( A @ ( B @ k4_funcop_1 ) ) )
= ( C @ ( A @ k1_relat_1 @ k2_funcop_1 ) @ ( A @ ( B @ k3_funcop_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funcop_1) ).
thf(4212,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ ( A @ ( B @ k4_funcop_1 ) ) )
= ( C @ ( A @ k1_relat_1 @ k2_funcop_1 ) @ ( A @ ( B @ k3_funcop_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(2374,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k1_funct_7 ) @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_7) ).
thf(14590,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k1_funct_7 ) @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2374]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r1_tarski ) )
=> ( ( ( B @ k2_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) )
= ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) ) )
& ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) )
= ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_sysrel) ).
thf(3183,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ r1_tarski ) )
=> ( ( ( B @ k2_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) )
= ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) ) )
& ( ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) )
= ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(1669,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( D = E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_pua2mss1) ).
thf(10740,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ r2_hidden ) )
& ( E @ ( C @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( D = E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1669]) ).
thf(1480,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( D @ ( F @ ( E @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) )
= ( D @ ( F @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_funcop_1) ).
thf(9782,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( D @ ( F @ ( E @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) )
= ( D @ ( F @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480]) ).
thf(179,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k4_relat_1 )
= ( A @ k4_relat_1 @ ( B @ k4_relat_1 @ k5_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_relat_1) ).
thf(3173,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k4_relat_1 )
= ( A @ k4_relat_1 @ ( B @ k4_relat_1 @ k5_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1629,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ k2_cantor_1 ) @ ( D @ r2_hidden ) )
& ( B @ ( A @ k2_cantor_1 ) @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ k2_cantor_1 ) @ ( D @ ( C @ k3_xboole_0 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_cantor_1) ).
thf(10524,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ k2_cantor_1 ) @ ( D @ r2_hidden ) )
& ( B @ ( A @ k2_cantor_1 ) @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ k2_cantor_1 ) @ ( D @ ( C @ k3_xboole_0 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1629]) ).
thf(1375,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
=> ( ( A @ k3_tarski @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_3) ).
thf(9269,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
=> ( ( A @ k3_tarski @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(1469,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( A @ k1_relat_1 @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_4) ).
thf(9716,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( A @ k1_relat_1 @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469]) ).
thf(2050,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( D @ ( E @ ( C @ k5_funcop_1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ ( E @ ( C @ k5_funcop_1 ) ) @ v1_funct_2 ) ) )
& ( D @ ( E @ ( C @ k5_funcop_1 ) ) @ v1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funcop_1) ).
thf(13026,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( D @ ( E @ ( C @ k5_funcop_1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ ( E @ ( C @ k5_funcop_1 ) ) @ v1_funct_2 ) ) )
& ( D @ ( E @ ( C @ k5_funcop_1 ) ) @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2050]) ).
thf(336,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
=> ( ( A @ ( B @ k4_finseq_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( B @ k4_finseq_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finseq_2) ).
thf(3856,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m2_finseq_1 ) )
=> ( ( A @ ( B @ k4_finseq_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( B @ k4_finseq_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(1656,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) )
<=> ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_mcart_1) ).
thf(10656,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
!= k1_xboole_0 )
=> ( ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) )
& ( ( ( D != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1656]) ).
thf(1217,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k10_relat_1 ) )
= ( A @ k1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t169_relat_1) ).
thf(8422,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ ( A @ k10_relat_1 ) )
= ( A @ k1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(1544,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_subset_1) ).
thf(10069,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1544]) ).
thf(1154,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( ( B @ v1_realset1 )
& ? [C: $i] :
( ? [D: $i] :
( ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) )
& ( A @ ( D @ m1_subset_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) ) )
& ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) )
& ~ ( B @ v1_realset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_realset1) ).
thf(8049,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( ( B @ v1_realset1 )
& ? [C: $i] :
( ? [D: $i] :
( ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) )
& ( A @ ( D @ m1_subset_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) ) )
& ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ( C != D )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) )
& ~ ( B @ v1_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(79,axiom,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( B @ r2_hidden ) )
| ( B @ ( A @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_classes2) ).
thf(2748,plain,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( B @ r2_hidden ) )
| ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(881,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= B )
& ( ( C @ k1_relat_1 )
= B ) )
=> ( ( A @ ( D @ ( C @ k13_funct_3 ) @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) @ ( A @ ( C @ k1_funct_1 ) @ k4_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_funct_3) ).
thf(6592,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= B )
& ( ( C @ k1_relat_1 )
= B ) )
=> ( ( A @ ( D @ ( C @ k13_funct_3 ) @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) @ ( A @ ( C @ k1_funct_1 ) @ k4_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(1687,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( B @ ( A @ ( C @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) )
& ~ ( A @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) )
& ~ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_mcart_1) ).
thf(10819,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( ~ ( B @ ( A @ ( C @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) )
& ~ ( A @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) )
& ~ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1687]) ).
thf(766,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k9_setwiseo @ ( B @ k5_finsub_1 @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_setwiseo) ).
thf(6011,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k9_setwiseo @ ( B @ k5_finsub_1 @ ( A @ k7_setwiseo ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(1970,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
thf(12553,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1970]) ).
thf(1350,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( A @ k15_funct_3 ) @ v2_funct_1 )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_functor0) ).
thf(9169,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( A @ k15_funct_3 ) @ v2_funct_1 )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).
thf(1351,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ? [C: $i] :
( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k3_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_binop_1) ).
thf(9171,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ? [C: $i] :
( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
& ( A @ ( C @ m1_subset_1 ) ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ( C
= ( B @ ( A @ k3_binop_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).
thf(1870,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( C @ ( B @ ( A @ k2_monoid_0 ) ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ ( B @ ( A @ k2_monoid_0 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_monoid_0 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_monoid_0) ).
thf(11901,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( C @ ( B @ ( A @ k2_monoid_0 ) ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ ( B @ ( A @ k2_monoid_0 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_monoid_0 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1870]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_partfun1) ).
thf(2440,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(918,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_lattice2) ).
thf(6756,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ ( D @ k1_funct_4 ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(2066,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_zfmisc_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( A @ ( C @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(13137,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ r1_tarski ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) )
=> ( B
= ( A @ k1_zfmisc_1 ) ) )
& ( ( B
= ( A @ k1_zfmisc_1 ) )
=> ! [C: $i] :
( ( ( A @ ( C @ r1_tarski ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2066]) ).
thf(1034,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( D @ v1_setwiseo ) )
& ( A @ ( D @ v2_binop_1 ) )
& ( A @ ( D @ v1_binop_1 ) )
& ( A @ ( D @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( A @ ( C @ ( G @ m2_relset_1 ) ) )
& ( A @ ( C @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( G @ ( E @ ( F @ ( C @ ( B @ k8_setwiseo ) ) ) @ ( D @ ( A @ ( C @ k7_setwiseo ) ) ) ) )
= ( G @ ( F @ ( A @ ( C @ ( B @ k7_funct_2 ) ) ) ) @ ( E @ ( D @ ( A @ ( B @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_setwiseo) ).
thf(7476,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( D @ v1_setwiseo ) )
& ( A @ ( D @ v2_binop_1 ) )
& ( A @ ( D @ v1_binop_1 ) )
& ( A @ ( D @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( A @ ( C @ ( G @ m2_relset_1 ) ) )
& ( A @ ( C @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( G @ ( E @ ( F @ ( C @ ( B @ k8_setwiseo ) ) ) @ ( D @ ( A @ ( C @ k7_setwiseo ) ) ) ) )
= ( G @ ( F @ ( A @ ( C @ ( B @ k7_funct_2 ) ) ) ) @ ( E @ ( D @ ( A @ ( B @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(2327,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(14362,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2327]) ).
thf(1511,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ! [F: $i,G: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) )
= ( E @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) ) ) )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_partfun1) ).
thf(9925,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ! [F: $i,G: $i] :
( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
=> ( ( G @ ( F @ k4_tarski ) @ ( D @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( E @ k1_funct_1 ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) )
= ( E @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k4_relset_1 ) ) ) ) )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1511]) ).
thf(956,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( C @ ( B @ k1_funct_1 ) @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_pboole) ).
thf(6931,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( C @ ( B @ k1_funct_1 ) @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(612,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
& ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funcop_1) ).
thf(5198,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
& ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(2229,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_cantor_1 ) @ ( B @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_cantor_1) ).
thf(13968,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_cantor_1 ) @ ( B @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2229]) ).
thf(1822,axiom,
( ( k1_numbers @ ( k1_numbers @ ( k31_binop_2 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k31_binop_2 @ v1_funct_2 ) ) )
& ( k31_binop_2 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k31_binop_2) ).
thf(11576,plain,
( ( k1_numbers @ ( k1_numbers @ ( k31_binop_2 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k31_binop_2 @ v1_funct_2 ) ) )
& ( k31_binop_2 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1822]) ).
thf(635,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t155_funct_2) ).
thf(5295,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(1551,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ ( C @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_realset1) ).
thf(10111,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ ( C @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1551]) ).
thf(45,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(2617,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(1679,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(10783,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1679]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
thf(4004,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m2_finseq_1 ) )
=> ( A @ ( C @ m2_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finseq_2) ).
thf(2423,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m2_finseq_1 ) )
=> ( A @ ( C @ m2_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1437,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( B @ ( B @ ( A @ r6_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r6_pboole) ).
thf(9562,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( B @ ( B @ ( A @ r6_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1437]) ).
thf(1906,axiom,
! [A: $i] :
( ( A @ v1_fraenkel )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_fraenkel) ).
thf(12104,plain,
! [A: $i] :
( ( A @ v1_fraenkel )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1906]) ).
thf(1049,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(7527,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_subset_1) ).
thf(4572,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(1371,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( A @ k8_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ ( A @ k8_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_funct_1) ).
thf(9256,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( A @ k8_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ ( A @ k8_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).
thf(1993,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( A @ k1_eqrel_1 @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_toler_1) ).
thf(12677,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( A @ k1_eqrel_1 @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1993]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_pboole) ).
thf(2909,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m3_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(1515,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k6_enumset1 ) ) ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_enumset1) ).
thf(9939,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k6_enumset1 ) ) ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1515]) ).
thf(1590,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) )
=> ( C @ ( B @ ( A @ k7_ens_1 ) ) @ ( D @ ( C @ ( B @ ( A @ ( A @ k1_domain_1 ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( A @ ( A @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_ens_1) ).
thf(10310,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) )
=> ( C @ ( B @ ( A @ k7_ens_1 ) ) @ ( D @ ( C @ ( B @ ( A @ ( A @ k1_domain_1 ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( A @ ( A @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1590]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_relat_1) ).
thf(4438,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(883,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ ( D @ m1_relset_1 ) ) )
& ( C @ k1_zfmisc_1 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k3_cantor_1 ) ) ) ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_cantor_1) ).
thf(6598,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ ( D @ m1_relset_1 ) ) )
& ( C @ k1_zfmisc_1 @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k3_cantor_1 ) ) ) ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_card_fil ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_card_fil) ).
thf(3158,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_card_fil ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(988,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k6_enumset1 ) ) ) ) ) ) ) )
= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_enumset1) ).
thf(7160,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k6_enumset1 ) ) ) ) ) ) ) )
= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(2259,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_finsub_1) ).
thf(14107,plain,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2259]) ).
thf(1813,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k2_funcop_1 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funcop_1) ).
thf(11516,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ ( A @ k2_funcop_1 ) @ v1_funct_2 ) ) )
& ( C @ ( A @ k2_funcop_1 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1813]) ).
thf(1436,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C
= ( A @ ( B @ k5_funct_5 @ k1_funct_1 ) ) )
& ( B @ k5_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( B @ k1_relat_1 @ ( A @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( ( D @ ( C @ k1_funct_1 ) )
= ( A @ ( D @ k4_tarski ) @ ( B @ k1_funct_1 ) ) ) ) )
& ( B @ k2_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ k1_funct_5 @ ( C @ k1_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( A @ k1_tarski @ ( B @ k1_relat_1 @ k1_funct_5 @ k2_zfmisc_1 ) @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ k1_funct_5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_funct_5) ).
thf(9545,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C
= ( A @ ( B @ k5_funct_5 @ k1_funct_1 ) ) )
& ( B @ k5_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( B @ k1_relat_1 @ ( A @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( ( D @ ( C @ k1_funct_1 ) )
= ( A @ ( D @ k4_tarski ) @ ( B @ k1_funct_1 ) ) ) ) )
& ( B @ k2_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ k1_funct_5 @ ( C @ k1_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( A @ k1_tarski @ ( B @ k1_relat_1 @ k1_funct_5 @ k2_zfmisc_1 ) @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ k1_funct_5 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436]) ).
thf(1696,axiom,
! [A: $i] :
( ( a_0_0_yellow_3 @ ( A @ r2_hidden ) )
<=> ? [B: $i,C: $i] :
( ( C @ ( B @ p1_s1_yellow_3 ) )
& ( A
= ( C @ ( B @ f2_s1_yellow_3 ) ) )
& ( f1_s1_yellow_3 @ ( C @ m1_subset_1 ) )
& ( f1_s1_yellow_3 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_0_yellow_3) ).
thf(10862,plain,
! [A: $i] :
( ( ? [B: $i,C: $i] :
( ( C @ ( B @ p1_s1_yellow_3 ) )
& ( A
= ( C @ ( B @ f2_s1_yellow_3 ) ) )
& ( f1_s1_yellow_3 @ ( C @ m1_subset_1 ) )
& ( f1_s1_yellow_3 @ ( B @ m1_subset_1 ) ) )
=> ( a_0_0_yellow_3 @ ( A @ r2_hidden ) ) )
& ( ( a_0_0_yellow_3 @ ( A @ r2_hidden ) )
=> ? [B: $i,C: $i] :
( ( C @ ( B @ p1_s1_yellow_3 ) )
& ( A
= ( C @ ( B @ f2_s1_yellow_3 ) ) )
& ( f1_s1_yellow_3 @ ( C @ m1_subset_1 ) )
& ( f1_s1_yellow_3 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1696]) ).
thf(950,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ? [B: $i,C: $i] : ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_funct_4 @ k1_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_funct_4) ).
thf(6901,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ? [B: $i,C: $i] : ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_funct_4 @ k1_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
<=> ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_partfun1) ).
thf(2729,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( B @ k4_relset_1 ) ) @ ( A @ r2_hidden ) )
=> ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(2063,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ k11_relset_1 ) ) ) @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_relset_1) ).
thf(13122,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) )
=> ( B @ ( D @ ( C @ ( A @ k11_relset_1 ) ) ) @ ( E @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ ( A @ k11_relset_1 ) ) ) @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( B @ ( F @ r2_hidden ) )
& ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( C @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2063]) ).
thf(2129,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_group_6) ).
thf(13444,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
=> ( D = E ) ) ) )
=> ( C @ v2_funct_1 ) )
& ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2129]) ).
thf(2293,axiom,
( ! [A: $i] :
( ( f1_s6_filter_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s6_filter_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s6_filter_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f2_s6_filter_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( f2_s6_filter_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( f2_s6_filter_1 @ ( F @ m1_subset_1 ) )
=> ( F @ ( C @ ( f2_s6_filter_1 @ ( f1_s6_filter_1 @ k1_domain_1 ) ) ) @ ( E @ ( B @ ( f2_s6_filter_1 @ ( f1_s6_filter_1 @ k1_domain_1 ) ) ) @ ( D @ ( A @ ( f2_s6_filter_1 @ ( f1_s6_filter_1 @ k1_domain_1 ) ) ) @ p1_s6_filter_1 ) ) ) ) ) ) ) ) )
=> ! [A: $i] :
( ( f2_s6_filter_1 @ ( f1_s6_filter_1 @ k2_zfmisc_1 ) @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f2_s6_filter_1 @ ( f1_s6_filter_1 @ k2_zfmisc_1 ) @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s6_filter_1 @ ( f1_s6_filter_1 @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ p1_s6_filter_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s6_filter_1) ).
thf(14231,plain,
( ! [A: $i] :
( ( f1_s6_filter_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s6_filter_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s6_filter_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f2_s6_filter_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( f2_s6_filter_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( f2_s6_filter_1 @ ( F @ m1_subset_1 ) )
=> ( F @ ( C @ ( f2_s6_filter_1 @ ( f1_s6_filter_1 @ k1_domain_1 ) ) ) @ ( E @ ( B @ ( f2_s6_filter_1 @ ( f1_s6_filter_1 @ k1_domain_1 ) ) ) @ ( D @ ( A @ ( f2_s6_filter_1 @ ( f1_s6_filter_1 @ k1_domain_1 ) ) ) @ p1_s6_filter_1 ) ) ) ) ) ) ) ) )
=> ! [A: $i] :
( ( f2_s6_filter_1 @ ( f1_s6_filter_1 @ k2_zfmisc_1 ) @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f2_s6_filter_1 @ ( f1_s6_filter_1 @ k2_zfmisc_1 ) @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s6_filter_1 @ ( f1_s6_filter_1 @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ p1_s6_filter_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2293]) ).
thf(895,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( ( A @ k2_relat_1 )
= ( C @ k1_tarski ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_tarski ) ) )
=> ( A
= ( C @ ( B @ k4_tarski ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_pre_circ) ).
thf(6637,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( ( A @ k2_relat_1 )
= ( C @ k1_tarski ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_tarski ) ) )
=> ( A
= ( C @ ( B @ k4_tarski ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(1178,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ m2_relset_1 ) ) )
& ( D @ k2_funct_4 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funct_4) ).
thf(8164,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ m2_relset_1 ) ) )
& ( D @ k2_funct_4 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(826,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ r1_partfun1 ) )
& ( B @ k1_relat_1 @ ( D @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ ( D @ ( C @ k1_funct_4 ) @ k5_relat_1 ) )
= ( B @ ( D @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ k1_funct_4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_4) ).
thf(6314,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ r1_partfun1 ) )
& ( B @ k1_relat_1 @ ( D @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ ( D @ ( C @ k1_funct_4 ) @ k5_relat_1 ) )
= ( B @ ( D @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ k1_funct_4 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(2241,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_tex_2) ).
thf(14020,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2241]) ).
thf(1690,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_binop_1 ) )
=> ( ( E @ ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_funcop_1) ).
thf(10840,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_binop_1 ) )
=> ( ( E @ ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k7_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1690]) ).
thf(168,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k15_funct_3 ) @ k2_funct_4 @ k2_funct_1 )
= ( A @ ( B @ k15_funct_3 ) @ k2_funct_1 @ k2_funct_4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_functor0) ).
thf(3130,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k15_funct_3 ) @ k2_funct_4 @ k2_funct_1 )
= ( A @ ( B @ k15_funct_3 ) @ k2_funct_1 @ k2_funct_4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(776,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
<=> ( ( C @ k1_relat_1 @ ( A @ r2_hidden ) )
| ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_funct_4) ).
thf(6053,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 @ ( A @ r2_hidden ) )
| ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k1_funct_4 ) @ k1_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ k1_funct_4 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( C @ k1_relat_1 @ ( A @ r2_hidden ) )
| ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(678,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B
= ( A @ k6_relat_1 ) )
<=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= C ) )
& ( ( B @ k1_relat_1 )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
thf(5524,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= C ) )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( B
= ( A @ k6_relat_1 ) ) )
& ( ( B
= ( A @ k6_relat_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= C ) )
& ( ( B @ k1_relat_1 )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r2_wellord2 ) )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( C @ ( A @ r2_wellord2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_wellord2) ).
thf(2677,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r2_wellord2 ) )
& ( B @ ( A @ r2_wellord2 ) ) )
=> ( C @ ( A @ r2_wellord2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1408,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(9416,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408]) ).
thf(1753,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ r4_nattra_1 ) ) ) ) ) )
=> ( E @ ( F @ ( D @ ( C @ ( B @ ( A @ r4_nattra_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r4_nattra_1) ).
thf(11179,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ r4_nattra_1 ) ) ) ) ) )
=> ( E @ ( F @ ( D @ ( C @ ( B @ ( A @ r4_nattra_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1753]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_4) ).
thf(4708,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(1919,axiom,
! [A: $i] :
( ( A @ v1_fraenkel )
=> ! [B: $i] :
( ( A @ ( B @ r1_tarski ) )
=> ( B @ v1_fraenkel ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_fraenkel) ).
thf(12168,plain,
! [A: $i] :
( ( A @ v1_fraenkel )
=> ! [B: $i] :
( ( A @ ( B @ r1_tarski ) )
=> ( B @ v1_fraenkel ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1919]) ).
thf(2156,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( D @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(13603,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2156]) ).
thf(2334,axiom,
! [A: $i] :
( ( a_0_1_domain_1 @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ( B @ p1_s8_domain_1 )
& ( A
= ( B @ f3_s8_domain_1 ) )
& ( f1_s8_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_1_domain_1) ).
thf(14388,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ p1_s8_domain_1 )
& ( A
= ( B @ f3_s8_domain_1 ) )
& ( f1_s8_domain_1 @ ( B @ m1_subset_1 ) ) )
=> ( a_0_1_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( a_0_1_domain_1 @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ( B @ p1_s8_domain_1 )
& ( A
= ( B @ f3_s8_domain_1 ) )
& ( f1_s8_domain_1 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2334]) ).
thf(2052,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( A @ r2_hidden ) )
<=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( A
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) )
& ( E @ ( I @ m1_subset_1 ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_domain_1) ).
thf(13041,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ( ( ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( A
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) )
& ( E @ ( I @ m1_subset_1 ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( A @ r2_hidden ) )
=> ? [F: $i] :
( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ( A
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) )
& ( E @ ( I @ m1_subset_1 ) ) )
& ( D @ ( H @ m1_subset_1 ) ) )
& ( C @ ( G @ m1_subset_1 ) ) )
& ( B @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2052]) ).
thf(2109,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funct_5 @ r1_tarski ) )
& ( A @ ( B @ ( A @ k2_zfmisc_1 ) @ k1_funct_5 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_5) ).
thf(13331,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funct_5 @ r1_tarski ) )
& ( A @ ( B @ ( A @ k2_zfmisc_1 ) @ k1_funct_5 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2109]) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( ( B @ v2_membered )
& ( A @ ( B @ r2_hidden ) ) )
=> ( A @ k1_setfam_1 @ v2_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_membered) ).
thf(2904,plain,
! [A: $i,B: $i] :
( ( ( B @ v2_membered )
& ( A @ ( B @ r2_hidden ) ) )
=> ( A @ k1_setfam_1 @ v2_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(1163,axiom,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k9_setwiseo ) )
<=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_binop_1 ) ) ) ) ) )
= ( D @ ( C @ ( A @ k5_setwiseo ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_setwiseo) ).
thf(8095,plain,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_binop_1 ) ) ) ) ) )
= ( D @ ( C @ ( A @ k5_setwiseo ) ) ) ) ) )
=> ( B
= ( A @ k9_setwiseo ) ) )
& ( ( B
= ( A @ k9_setwiseo ) )
=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_binop_1 ) ) ) ) ) )
= ( D @ ( C @ ( A @ k5_setwiseo ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(2077,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_realset1) ).
thf(13201,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2077]) ).
thf(2234,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finsub_1) ).
thf(13989,plain,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2234]) ).
thf(2250,axiom,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ ( A @ k12_funct_3 @ m2_relset_1 ) ) )
& ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ ( A @ k12_funct_3 @ v1_funct_2 ) ) )
& ( A @ k12_funct_3 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_funct_3) ).
thf(14045,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ ( A @ k12_funct_3 @ m2_relset_1 ) ) )
& ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ ( A @ k12_funct_3 @ v1_funct_2 ) ) )
& ( A @ k12_funct_3 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2250]) ).
thf(2043,axiom,
( ! [A: $i] :
( ( f1_s14_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s14_funct_2 ) )
& ( f2_s14_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s14_funct_2) ).
thf(12982,plain,
( ! [A: $i] :
( ( f1_s14_funct_2 @ ( A @ m1_subset_1 ) )
=> ? [B: $i] :
( ( B @ ( A @ p1_s14_funct_2 ) )
& ( f2_s14_funct_2 @ ( B @ m1_subset_1 ) ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s14_funct_2 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ k8_funct_2 ) ) ) @ ( B @ p1_s14_funct_2 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s14_funct_2 @ ( f1_s14_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2043]) ).
thf(1046,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ( ( A @ k3_pua2mss1 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_relset_2) ).
thf(7512,plain,
! [A: $i] :
( ( ( ( A @ k3_pua2mss1 )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( ( A @ k3_pua2mss1 )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(1430,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_sysrel) ).
thf(9502,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430]) ).
thf(1569,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) )
=> ( ( ( C = F )
& ( B = E )
& ( A = D ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_mcart_1) ).
thf(10202,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) )
=> ( ( ( C = F )
& ( B = E )
& ( A = D ) )
| ( C = k1_xboole_0 )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1569]) ).
thf(1236,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ! [E: $i,F: $i] :
( ( ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( ( F @ ( E @ k4_tarski ) @ ( C @ k1_funct_1 ) )
= ( F @ ( E @ k4_tarski ) @ ( D @ k1_funct_1 ) ) ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_3) ).
thf(8531,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ! [E: $i,F: $i] :
( ( ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( ( F @ ( E @ k4_tarski ) @ ( C @ k1_funct_1 ) )
= ( F @ ( E @ k4_tarski ) @ ( D @ k1_funct_1 ) ) ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(201,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_funct_4) ).
thf(3257,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(279,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( k5_numbers @ k1_zfmisc_1 @ ( A @ k4_finseq_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_finseq_1) ).
thf(3607,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( k5_numbers @ k1_zfmisc_1 @ ( A @ k4_finseq_1 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(1442,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k7_relat_1 ) )
= ( B @ ( C @ ( A @ k3_xboole_0 ) @ k2_funcop_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funcop_1) ).
thf(9577,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k7_relat_1 ) )
= ( B @ ( C @ ( A @ k3_xboole_0 ) @ k2_funcop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442]) ).
thf(986,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ ( B @ k5_funcop_1 ) ) )
= ( A @ ( C @ ( A @ k1_relat_1 @ k2_funcop_1 ) @ ( B @ k3_funcop_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_funcop_1) ).
thf(7155,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ ( B @ k5_funcop_1 ) ) )
= ( A @ ( C @ ( A @ k1_relat_1 @ k2_funcop_1 ) @ ( B @ k3_funcop_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(1909,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( E @ ( D @ ( C @ k4_funcop_1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( C @ k4_funcop_1 ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ k4_funcop_1 ) ) @ v1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funcop_1) ).
thf(12119,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( E @ ( D @ ( C @ k4_funcop_1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( C @ k4_funcop_1 ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ k4_funcop_1 ) ) @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1909]) ).
thf(2350,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s2_altcat_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s2_altcat_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_binop_1 ) ) )
= ( C @ ( B @ f3_s2_altcat_1 ) ) ) ) )
& ( f2_s2_altcat_1 @ ( f1_s2_altcat_1 @ k2_zfmisc_1 ) @ ( A @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_altcat_1) ).
thf(14469,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s2_altcat_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s2_altcat_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_binop_1 ) ) )
= ( C @ ( B @ f3_s2_altcat_1 ) ) ) ) )
& ( f2_s2_altcat_1 @ ( f1_s2_altcat_1 @ k2_zfmisc_1 ) @ ( A @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2350]) ).
thf(2090,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_relat_1) ).
thf(13259,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2090]) ).
thf(753,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( ( A @ ( C @ ( B @ k9_funct_3 ) @ k1_funct_3 @ k1_funct_1 ) )
= ( A @ ( C @ ( B @ k9_funct_3 ) @ ( B @ ( C @ ( B @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_borsuk_1) ).
thf(5960,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( ( A @ ( C @ ( B @ k9_funct_3 ) @ k1_funct_3 @ k1_funct_1 ) )
= ( A @ ( C @ ( B @ k9_funct_3 ) @ ( B @ ( C @ ( B @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(1537,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( B @ k1_relat_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_2) ).
thf(10043,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( B @ k1_relat_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537]) ).
thf(2150,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) )
=> ( A @ k2_ens_1 @ ( D @ ( C @ ( B @ ( A @ ( A @ k1_domain_1 ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( A @ ( A @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_ens_1) ).
thf(13579,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C = k1_xboole_0 )
=> ( B = k1_xboole_0 ) )
=> ( A @ k2_ens_1 @ ( D @ ( C @ ( B @ ( A @ ( A @ k1_domain_1 ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( A @ ( A @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2150]) ).
thf(1586,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_setwiseo ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_setwiseo) ).
thf(10289,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_setwiseo ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1586]) ).
thf(308,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_zfmisc_1) ).
thf(3738,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( B @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(1080,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
& ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) )
=> ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_altcat_1 ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_altcat_1) ).
thf(7636,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
& ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) ) )
=> ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_altcat_1 ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(232,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( F @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k8_funct_2 ) ) ) )
= ( D @ ( E @ ( F @ ( C @ ( B @ ( A @ k3_cat_2 ) ) ) @ ( C @ ( A @ k1_fraenkel ) @ ( C @ ( A @ ( B @ k1_cat_2 ) ) ) ) ) @ ( C @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_cat_2) ).
thf(3375,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( F @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k8_funct_2 ) ) ) )
= ( D @ ( E @ ( F @ ( C @ ( B @ ( A @ k3_cat_2 ) ) ) @ ( C @ ( A @ k1_fraenkel ) @ ( C @ ( A @ ( B @ k1_cat_2 ) ) ) ) ) @ ( C @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(338,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ k4_relat_1 )
= ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ k3_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_relat_1) ).
thf(3888,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ k4_relat_1 )
= ( B @ k4_relat_1 @ ( A @ k4_relat_1 @ k3_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(852,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( A @ k2_funct_4 @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_functor0) ).
thf(6454,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( A @ k2_funct_4 @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(332,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_partfun1) ).
thf(3839,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(573,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( D @ ( B @ ( A @ k5_partfun1 ) ) ) )
& ! [E: $i] :
( B
!= ( E @ k1_tarski ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t168_funct_2) ).
thf(5016,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( ( C @ ( B @ ( A @ k5_partfun1 ) ) )
= ( D @ ( B @ ( A @ k5_partfun1 ) ) ) )
& ! [E: $i] :
( B
!= ( E @ k1_tarski ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k7_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).
thf(4503,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k7_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ k7_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) @ k4_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_mcart_1) ).
thf(4577,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) @ k4_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(323,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) )
<=> ( ~ ( C @ ( B @ r2_hidden ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).
thf(3792,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( C @ ( B @ r2_hidden ) )
& ~ ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) ) )
& ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( B @ ( A @ k2_tarski ) ) )
=> ( ~ ( C @ ( B @ r2_hidden ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(746,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_relset_1) ).
thf(5882,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(587,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_enumset1) ).
thf(5095,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B @ ( C @ k5_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( B @ ( C @ k5_funct_5 @ k1_funct_1 ) @ v1_relat_1 )
& ( C @ k5_funct_5 @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_funct_5) ).
thf(3111,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B @ ( C @ k5_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( B @ ( C @ k5_funct_5 @ k1_funct_1 ) @ v1_relat_1 )
& ( C @ k5_funct_5 @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(1268,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( A @ ( C @ ( B @ ( D @ k3_funcop_1 ) ) @ k5_relat_1 ) )
= ( C @ ( B @ ( A @ ( D @ k5_relat_1 ) @ k3_funcop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_funcop_1) ).
thf(8718,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( A @ ( C @ ( B @ ( D @ k3_funcop_1 ) ) @ k5_relat_1 ) )
= ( C @ ( B @ ( A @ ( D @ k5_relat_1 ) @ k3_funcop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_classes2 )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k1_funct_2 ) @ r2_hidden ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_classes2) ).
thf(4017,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_classes2 )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k1_funct_2 ) @ r2_hidden ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(1457,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B
= ( A @ k2_relat_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
thf(9650,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( B
= ( A @ k2_relat_1 ) ) )
& ( ( B
= ( A @ k2_relat_1 ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457]) ).
thf(2158,axiom,
! [A: $i,B: $i] :
( ( A @ k6_partfun1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ k1_funct_5 )
= ( B @ k2_funct_5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_waybel20) ).
thf(13618,plain,
! [A: $i,B: $i] :
( ( A @ k6_partfun1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ k1_funct_5 )
= ( B @ k2_funct_5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2158]) ).
thf(121,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
~ ( A @ k1_relat_1 @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( ( A @ k5_funct_5 )
= k1_xboole_0 )
& ( ( A @ k3_funct_5 )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_5) ).
thf(2894,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
~ ( A @ k1_relat_1 @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( ( A @ k5_funct_5 )
= k1_xboole_0 )
& ( ( A @ k3_funct_5 )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(2051,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_3_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_3_domain_1) ).
thf(13031,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_3_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_3_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2051]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ m2_finseq_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ ( A @ ( k5_numbers @ k1_partfun1 ) ) ) ) ) @ m2_finseq_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_finseq_2) ).
thf(3396,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ m2_finseq_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ ( A @ ( k5_numbers @ k1_partfun1 ) ) ) ) ) @ m2_finseq_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(649,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ( ( B @ ( A @ k1_funct_4 ) )
= ( A @ ( B @ k1_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_4) ).
thf(5400,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k1_funct_4 ) )
= ( A @ ( B @ k1_funct_4 ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= ( A @ ( B @ k1_funct_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(1837,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ! [C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
<=> ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) ) ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( E @ r1_tarski ) )
& ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( E @ ( D @ ( A @ k4_subset_1 ) ) @ r2_hidden ) ) ) ) ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_card_fil) ).
thf(11693,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ! [C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( A @ k3_subset_1 ) @ r2_hidden ) ) ) ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( E @ r1_tarski ) )
& ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( ( C @ ( E @ r2_hidden ) )
& ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( E @ ( D @ ( A @ k4_subset_1 ) ) @ r2_hidden ) ) ) ) ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1837]) ).
thf(1061,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_card_fil ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( C @ ( A @ k3_card_fil ) ) @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( D @ ( B @ ( E @ ( A @ k5_subset_1 ) ) @ r1_tarski ) )
& ( C @ ( E @ r2_hidden ) )
& ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_card_fil) ).
thf(7567,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_card_fil ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( D @ ( B @ ( E @ ( A @ k5_subset_1 ) ) @ r1_tarski ) )
& ( C @ ( E @ r2_hidden ) )
& ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( B @ ( C @ ( A @ k3_card_fil ) ) @ ( D @ r2_hidden ) ) )
& ( ( B @ ( C @ ( A @ k3_card_fil ) ) @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D @ ( B @ ( E @ ( A @ k5_subset_1 ) ) @ r1_tarski ) )
& ( C @ ( E @ r2_hidden ) )
& ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_funct_3) ).
thf(3768,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(277,axiom,
! [A: $i] :
~ ( ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ~ ( B @ k2_finseq_1 @ ( A @ r2_wellord2 ) ) )
& ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_finseq_1) ).
thf(3599,plain,
! [A: $i] :
~ ( ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ~ ( B @ k2_finseq_1 @ ( A @ r2_wellord2 ) ) )
& ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(2304,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k7_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(14286,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k7_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2304]) ).
thf(1715,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_funct_2) ).
thf(11006,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1715]) ).
thf(1892,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( B @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_2) ).
thf(12028,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( B @ ( C @ ( D @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1892]) ).
thf(2177,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(13710,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2177]) ).
thf(1098,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k3_setwiseo ) ) )
= ( B @ ( C @ ( A @ k3_setwiseo ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_setwiseo) ).
thf(7709,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k3_setwiseo ) ) )
= ( B @ ( C @ ( A @ k3_setwiseo ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(231,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_ens_1 ) ) )
= ( C @ ( B @ ( A @ a_3_0_ens_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_ens_1) ).
thf(3372,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_ens_1 ) ) )
= ( C @ ( B @ ( A @ a_3_0_ens_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(366,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_finseq_1 ) )
=> ? [D: $i] :
( ( D @ k4_card_3 @ ( C @ r2_hidden ) )
& ( B @ ( D @ m2_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_pua2mss1) ).
thf(4000,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m2_finseq_1 ) )
=> ? [D: $i] :
( ( D @ k4_card_3 @ ( C @ r2_hidden ) )
& ( B @ ( D @ m2_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(1950,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(12441,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1950]) ).
thf(1561,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_xboole_0 ) )
<=> ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
thf(10155,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( C @ ( B @ r1_xboole_0 ) ) )
& ( ( C @ ( B @ r1_xboole_0 ) )
=> ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1561]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_card_fil ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_card_fil ) @ ( A @ k2_card_fil ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k2_card_fil) ).
thf(3741,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_card_fil ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_card_fil ) @ ( A @ k2_card_fil ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_zfmisc_1) ).
thf(4662,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
| ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(1067,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_setfam_1 ) )
= ( A @ ( B @ k3_setfam_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_setfam_1) ).
thf(7590,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_setfam_1 ) )
= ( A @ ( B @ k3_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(1485,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( D @ k3_funcop_1 ) ) @ ( C @ k5_relat_1 ) )
= ( B @ ( C @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ ( D @ k3_funcop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_funcop_1) ).
thf(9798,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( D @ k3_funcop_1 ) ) @ ( C @ k5_relat_1 ) )
= ( B @ ( C @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ ( D @ k3_funcop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1485]) ).
thf(1791,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_relset_2 ) ) @ m2_relset_1 ) ) )
& ( A @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_relset_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k6_relset_2 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relset_2) ).
thf(11396,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_relset_2 ) ) @ m2_relset_1 ) ) )
& ( A @ k1_zfmisc_1 @ ( B @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_relset_2 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k6_relset_2 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1791]) ).
thf(195,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k4_card_3 @ v1_fraenkel )
& ~ ( A @ k4_card_3 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_card_3) ).
thf(3234,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k4_card_3 @ v1_fraenkel )
& ~ ( A @ k4_card_3 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(1800,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funct_2) ).
thf(11455,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1800]) ).
thf(113,axiom,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_realset1) ).
thf(2859,plain,
? [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(943,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
<=> ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_relat_1) ).
thf(6870,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ ( B @ k9_relat_1 ) )
= k1_xboole_0 )
=> ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(256,axiom,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_classes2) ).
thf(3504,plain,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ ( A @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ k13_funct_3 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) @ ( A @ ( B @ k1_funct_1 ) @ k4_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_3) ).
thf(4283,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ ( A @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ k13_funct_3 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) @ ( A @ ( B @ k1_funct_1 ) @ k4_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(200,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_relat_1) ).
thf(3255,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k4_xboole_0 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ v1_finseq_1 )
<=> ? [B: $i] :
( ( ( A @ k1_relat_1 )
= ( B @ k2_finseq_1 ) )
& ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_finseq_1) ).
thf(2791,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ? [B: $i] :
( ( ( A @ k1_relat_1 )
= ( B @ k2_finseq_1 ) )
& ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) ) )
=> ( A @ v1_finseq_1 ) )
& ( ( A @ v1_finseq_1 )
=> ? [B: $i] :
( ( ( A @ k1_relat_1 )
= ( B @ k2_finseq_1 ) )
& ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(2019,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ r2_hidden ) )
<=> ( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_subset_1) ).
thf(12835,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( ( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) )
=> ( B @ ( E @ r2_hidden ) ) )
& ( ( B @ ( E @ r2_hidden ) )
=> ( ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) ) ) )
=> ( B
= ( D @ ( C @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2019]) ).
thf(1041,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(7497,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1634,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i,F: $i] :
~ ( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
thf(10547,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i,F: $i] :
~ ( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1634]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_partfun1) ).
thf(2789,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(825,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
thf(6312,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(1287,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ v2_funct_1 )
& ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) )
=> ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funct_1) ).
thf(8814,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ v2_funct_1 )
& ( ( A @ ( B @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 ) ) )
=> ( B @ k2_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k5_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k5_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( A @ ( B @ k5_funct_5 @ k1_funct_1 ) @ v1_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_5) ).
thf(3609,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k5_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k5_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( A @ ( B @ k5_funct_5 @ k1_funct_1 ) @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(398,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k1_funct_3 @ k9_relat_1 ) @ ( B @ ( A @ k3_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_3) ).
thf(4159,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k1_funct_3 @ k9_relat_1 ) @ ( B @ ( A @ k3_funct_3 @ k10_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(1920,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_funct_2) ).
thf(12170,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1920]) ).
thf(1474,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( E @ v1_partfun1 ) ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t162_partfun1) ).
thf(9733,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( E @ v1_partfun1 ) ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474]) ).
thf(1226,axiom,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( B @ ( k1_xboole_0 @ ( A @ k5_partfun1 ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t172_partfun1) ).
thf(8470,plain,
! [A: $i,B: $i] :
( ( ( k1_xboole_0 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( ( B @ ( k1_xboole_0 @ ( A @ k5_partfun1 ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(1711,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 )
& ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ a_4_1_yellow_9 ) ) ) @ ( A @ r2_hidden ) )
<=> ? [F: $i,G: $i] :
( ( E @ ( G @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ ( C @ ( B @ k12_mcart_1 ) ) ) ) )
& ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_1_yellow_9) ).
thf(10963,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 )
& ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ( ( ? [F: $i,G: $i] :
( ( E @ ( G @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ ( C @ ( B @ k12_mcart_1 ) ) ) ) )
& ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( C @ ( B @ a_4_1_yellow_9 ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( E @ ( D @ ( C @ ( B @ a_4_1_yellow_9 ) ) ) @ ( A @ r2_hidden ) )
=> ? [F: $i,G: $i] :
( ( E @ ( G @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ ( C @ ( B @ k12_mcart_1 ) ) ) ) )
& ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1711]) ).
thf(1877,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_pcomps_1 @ ( A @ k1_pcomps_1 @ ( C @ m1_relset_1 ) ) )
& ( B @ k1_pcomps_1 @ ( A @ k1_pcomps_1 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k14_borsuk_1 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k14_borsuk_1) ).
thf(11941,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_pcomps_1 @ ( A @ k1_pcomps_1 @ ( C @ m1_relset_1 ) ) )
& ( B @ k1_pcomps_1 @ ( A @ k1_pcomps_1 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k14_borsuk_1 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1877]) ).
thf(1838,axiom,
! [A: $i] :
? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_triang_1) ).
thf(11703,plain,
! [A: $i] :
? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1838]) ).
thf(1037,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k7_relat_1 ) )
= ( A @ k1_relat_1 @ ( B @ k7_relat_1 ) @ k1_relat_1 @ ( A @ k7_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t189_relat_1) ).
thf(7487,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k7_relat_1 ) )
= ( A @ k1_relat_1 @ ( B @ k7_relat_1 ) @ k1_relat_1 @ ( A @ k7_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(1435,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ k1_enumset1 ) ) @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_setwiseo) ).
thf(9543,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ k1_enumset1 ) ) @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435]) ).
thf(1858,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( E @ ( D @ ( C @ m2_relset_1 ) ) )
& ( E @ ( D @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( ( E = k1_xboole_0 )
=> ( D = k1_xboole_0 ) )
& ( B
= ( C @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ ( A @ k1_ens_1 @ ( A @ ( A @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) ) )
& ( A @ ( E @ m1_subset_1 ) ) )
& ( A @ ( D @ m1_subset_1 ) ) )
& ( A @ k1_ens_1 @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_ens_1) ).
thf(11809,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( E @ ( D @ ( C @ m2_relset_1 ) ) )
& ( E @ ( D @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( ( E = k1_xboole_0 )
=> ( D = k1_xboole_0 ) )
& ( B
= ( C @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ ( A @ k1_ens_1 @ ( A @ ( A @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) ) )
& ( A @ ( E @ m1_subset_1 ) ) )
& ( A @ ( D @ m1_subset_1 ) ) )
& ( A @ k1_ens_1 @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1858]) ).
thf(2055,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_0_lattice5 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i,E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ k2_zfmisc_1 ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_lattice5) ).
thf(13060,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i,E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ k2_zfmisc_1 ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_lattice5 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_lattice5 ) @ ( A @ r2_hidden ) )
=> ? [D: $i,E: $i] :
( ( C @ ( E @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( A
= ( E @ ( D @ k2_zfmisc_1 ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2055]) ).
thf(1619,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_functor0 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_functor0 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k1_functor0 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_functor0) ).
thf(10480,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_functor0 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_functor0 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k1_functor0 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1619]) ).
thf(995,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ k6_partfun1 @ ( E @ ( C @ ( B @ ( B @ k8_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( D @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_funcop_1) ).
thf(7223,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ k6_partfun1 @ ( E @ ( C @ ( B @ ( B @ k8_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( D @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(879,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_zfmisc_1) ).
thf(6581,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r1_tarski ) ) )
=> ( B @ ( A @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(1856,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k2_monoid_0 ) ) )
= ( C @ ( B @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_monoid_0) ).
thf(11804,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k2_monoid_0 ) ) )
= ( C @ ( B @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1856]) ).
thf(1927,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_1_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_domain_1) ).
thf(12210,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_1_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1927]) ).
thf(1027,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i] :
~ ( ( B
= ( E @ ( D @ ( C @ k3_mcart_1 ) ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_mcart_1) ).
thf(7440,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i] :
~ ( ( B
= ( E @ ( D @ ( C @ k3_mcart_1 ) ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(307,axiom,
( ( k1_xboole_0 @ k1_setfam_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_setfam_1) ).
thf(3736,plain,
( ( k1_xboole_0 @ k1_setfam_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_card_fil ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k2_card_fil ) @ m2_card_fil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_card_fil) ).
thf(3081,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_card_fil ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ ( A @ k2_card_fil ) @ m2_card_fil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(2366,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k3_subset_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(14572,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k3_subset_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2366]) ).
thf(1106,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C
= ( B @ ( A @ k13_funct_3 ) ) )
<=> ( ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) @ ( D @ ( A @ k1_funct_1 ) @ k4_tarski ) ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_3) ).
thf(7751,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) @ ( D @ ( A @ k1_funct_1 ) @ k4_tarski ) ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) ) ) )
=> ( C
= ( B @ ( A @ k13_funct_3 ) ) ) )
& ( ( C
= ( B @ ( A @ k13_funct_3 ) ) )
=> ( ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) @ ( D @ ( A @ k1_funct_1 ) @ k4_tarski ) ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(59,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ ( A @ r2_wellord2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_card_1) ).
thf(2674,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ ( A @ r2_wellord2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(33,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v5_monoid_0 ) )
<=> ( ( A @ ( B @ v4_monoid_0 ) )
& ( A @ ( B @ v3_monoid_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_monoid_0) ).
thf(2514,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( ( A @ ( B @ v4_monoid_0 ) )
& ( A @ ( B @ v3_monoid_0 ) ) )
=> ( A @ ( B @ v5_monoid_0 ) ) )
& ( ( A @ ( B @ v5_monoid_0 ) )
=> ( ( A @ ( B @ v4_monoid_0 ) )
& ( A @ ( B @ v3_monoid_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1168,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relat_1) ).
thf(8124,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(2146,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_3_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_domain_1) ).
thf(13569,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_3_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2146]) ).
thf(812,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_2 ) @ ( A @ k1_funct_2 ) @ ( D @ r2_hidden ) )
=> ( ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( F @ v1_funct_1 )
& ( F @ v1_relat_1 ) )
=> ! [G: $i,H: $i] :
( ( ( ( H @ ( D @ k10_funct_6 @ k1_funct_1 ) )
= F )
& ( ( G @ ( D @ k1_funct_1 ) )
= E )
& ( B @ ( H @ r2_hidden ) )
& ( A @ ( G @ r2_hidden ) ) )
=> ( ( C @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( C @ ( F @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= B )
& ( ( F @ k1_relat_1 )
= A )
& ( ( G @ ( F @ k1_funct_1 ) )
= ( H @ ( E @ k1_funct_1 ) ) ) ) ) ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_funct_6) ).
thf(6229,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_2 ) @ ( A @ k1_funct_2 ) @ ( D @ r2_hidden ) )
=> ( ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( F @ v1_funct_1 )
& ( F @ v1_relat_1 ) )
=> ! [G: $i,H: $i] :
( ( ( ( H @ ( D @ k10_funct_6 @ k1_funct_1 ) )
= F )
& ( ( G @ ( D @ k1_funct_1 ) )
= E )
& ( B @ ( H @ r2_hidden ) )
& ( A @ ( G @ r2_hidden ) ) )
=> ( ( C @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( C @ ( F @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= B )
& ( ( F @ k1_relat_1 )
= A )
& ( ( G @ ( F @ k1_funct_1 ) )
= ( H @ ( E @ k1_funct_1 ) ) ) ) ) ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(1470,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_xboole_1) ).
thf(9719,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470]) ).
thf(1382,axiom,
! [A: $i,B: $i] :
( ( B @ v1_xboole_0 )
=> ( ( A @ ( B @ k2_funcop_1 ) @ v2_funct_1 )
& ( A @ ( B @ k2_funcop_1 ) @ v1_funct_1 )
& ( A @ ( B @ k2_funcop_1 ) @ v1_relat_1 )
& ( A @ ( B @ k2_funcop_1 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funcop_1) ).
thf(9295,plain,
! [A: $i,B: $i] :
( ( B @ v1_xboole_0 )
=> ( ( A @ ( B @ k2_funcop_1 ) @ v2_funct_1 )
& ( A @ ( B @ k2_funcop_1 ) @ v1_funct_1 )
& ( A @ ( B @ k2_funcop_1 ) @ v1_relat_1 )
& ( A @ ( B @ k2_funcop_1 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382]) ).
thf(1659,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( D @ ( D @ ( C @ ( B @ ( A @ k1_nattra_1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( D @ ( D @ ( C @ ( B @ ( A @ k1_nattra_1 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k1_nattra_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_nattra_1) ).
thf(10700,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( D @ ( D @ ( C @ ( B @ ( A @ k1_nattra_1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( D @ ( D @ ( C @ ( B @ ( A @ k1_nattra_1 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k1_nattra_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1659]) ).
thf(375,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ? [C: $i] :
( ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_partfun1) ).
thf(4032,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ? [C: $i] :
( ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ? [C: $i] :
( ( C @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(1147,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_isocat_2 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_isocat_2 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k1_isocat_2 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_isocat_2) ).
thf(8027,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_isocat_2 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_isocat_2 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k1_isocat_2 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(973,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_partfun1) ).
thf(7041,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k1_relat_1 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(580,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( C @ ( B @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ k2_relat_1 @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_funct_3) ).
thf(5050,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( C @ ( B @ k5_relat_1 ) @ k2_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ k2_relat_1 @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( A @ ( D @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_partfun1) ).
thf(2991,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( D @ k3_partfun1 ) ) @ ( C @ ( A @ ( D @ k3_partfun1 ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(2116,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ ( B @ m1_card_fil ) )
<=> ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k5_subset_1 ) ) @ r2_hidden ) ) ) ) ) )
& ~ ( B @ ( k1_xboole_0 @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_card_fil) ).
thf(13363,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k5_subset_1 ) ) @ r2_hidden ) ) ) ) ) )
& ~ ( B @ ( k1_xboole_0 @ r2_hidden ) ) )
=> ( A @ ( B @ m1_card_fil ) ) )
& ( ( A @ ( B @ m1_card_fil ) )
=> ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k5_subset_1 ) ) @ r2_hidden ) ) ) ) ) )
& ~ ( B @ ( k1_xboole_0 @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2116]) ).
thf(832,axiom,
! [A: $i] :
( ( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ~ ( B @ ( A @ k3_xboole_0 ) @ v1_xboole_0 )
=> ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tex_2) ).
thf(6344,plain,
! [A: $i] :
( ( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ~ ( B @ ( A @ k3_xboole_0 ) @ v1_xboole_0 )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(949,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k1_tarski @ ( B @ ( A @ k1_tarski @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_isocat_2) ).
thf(6898,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ k1_tarski @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k1_tarski @ ( B @ ( A @ k1_tarski @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(2296,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_domain_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_domain_1) ).
thf(14247,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_domain_1 ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2296]) ).
thf(2193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_mcart_1) ).
thf(13809,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2193]) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_funct_1 )
& ( A @ ( B @ k5_relat_1 ) @ v2_relat_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_pre_circ) ).
thf(3590,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_funct_1 )
& ( A @ ( B @ k5_relat_1 ) @ v2_relat_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(1609,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(10435,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1609]) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t154_funct_1) ).
thf(3604,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( ( A @ ( B @ k9_relat_1 ) )
= ( A @ ( B @ k2_funct_1 @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(1162,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ k6_partfun1 @ ( D @ ( B @ ( A @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( D @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funcop_1) ).
thf(8092,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ k6_partfun1 @ ( D @ ( B @ ( A @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( D @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(886,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( D @ v2_binop_1 ) )
& ( A @ ( D @ v1_binop_1 ) )
& ( A @ ( D @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( A @ ( C @ ( G @ m2_relset_1 ) ) )
& ( A @ ( C @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( G @ ( E @ ( F @ ( C @ ( B @ k8_setwiseo ) ) ) @ ( D @ ( A @ ( C @ k7_setwiseo ) ) ) ) )
= ( G @ ( F @ ( A @ ( C @ ( B @ k7_funct_2 ) ) ) ) @ ( E @ ( D @ ( A @ ( B @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_setwiseo) ).
thf(6606,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( D @ v2_binop_1 ) )
& ( A @ ( D @ v1_binop_1 ) )
& ( A @ ( D @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( A @ ( C @ ( G @ m2_relset_1 ) ) )
& ( A @ ( C @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( G @ ( E @ ( F @ ( C @ ( B @ k8_setwiseo ) ) ) @ ( D @ ( A @ ( C @ k7_setwiseo ) ) ) ) )
= ( G @ ( F @ ( A @ ( C @ ( B @ k7_funct_2 ) ) ) ) @ ( E @ ( D @ ( A @ ( B @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(1497,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k9_relat_1 ) @ ( B @ ( A @ ( C @ k7_relat_1 ) @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t161_relat_1) ).
thf(9852,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k9_relat_1 ) @ ( B @ ( A @ ( C @ k7_relat_1 ) @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1497]) ).
thf(489,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( B
= ( A @ k4_card_3 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ! [E: $i] :
( ( A @ k1_relat_1 @ ( E @ r2_hidden ) )
=> ( E @ ( A @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_relat_1 ) )
& ( C = D )
& ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_card_3) ).
thf(4590,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ! [E: $i] :
( ( A @ k1_relat_1 @ ( E @ r2_hidden ) )
=> ( E @ ( A @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_relat_1 ) )
& ( C = D )
& ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ k1_relat_1 @ ( E @ r2_hidden ) )
=> ( E @ ( A @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_relat_1 ) )
& ( C = D )
& ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) ) ) )
=> ( B
= ( A @ k4_card_3 ) ) )
& ( ( B
= ( A @ k4_card_3 ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ! [E: $i] :
( ( A @ k1_relat_1 @ ( E @ r2_hidden ) )
=> ( E @ ( A @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_relat_1 ) )
& ( C = D )
& ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ k1_relat_1 @ ( E @ r2_hidden ) )
=> ( E @ ( A @ k1_funct_1 ) @ ( E @ ( D @ k1_funct_1 ) @ r2_hidden ) ) )
& ( ( D @ k1_relat_1 )
= ( A @ k1_relat_1 ) )
& ( C = D )
& ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(1107,axiom,
! [A: $i,B: $i] :
( ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ k15_funct_3 ) )
= ( B @ ( A @ k2_zfmisc_1 ) @ k6_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_funct_3) ).
thf(7763,plain,
! [A: $i,B: $i] :
( ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ k15_funct_3 ) )
= ( B @ ( A @ k2_zfmisc_1 ) @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(2216,axiom,
( ( ( f4_s22_fraenkel @ v1_finset_1 )
& ( f3_s22_fraenkel @ v1_finset_1 ) )
=> ( a_0_39_fraenkel @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s22_fraenkel) ).
thf(13920,plain,
( ( ( f4_s22_fraenkel @ v1_finset_1 )
& ( f3_s22_fraenkel @ v1_finset_1 ) )
=> ( a_0_39_fraenkel @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2216]) ).
thf(101,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( ( A @ v1_realset1 )
& ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_realset1) ).
thf(2817,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( ( A @ v1_realset1 )
& ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(2136,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k2_funct_5 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funct_5) ).
thf(13492,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( B
= ( A @ k2_funct_5 ) ) )
& ( ( B
= ( A @ k2_funct_5 ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2136]) ).
thf(517,axiom,
( ( k1_xboole_0 @ k4_card_3 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_card_3) ).
thf(4758,plain,
( ( k1_xboole_0 @ k4_card_3 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_xboole_1) ).
thf(4769,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ r1_xboole_0 ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k4_closure2 ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_closure2) ).
thf(2695,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( A @ ( C @ ( B @ ( A @ k4_closure2 ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(2171,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_setfam_1 ) @ r1_tarski ) )
<=> ( C @ ( A @ k7_setfam_1 ) @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_setfam_1) ).
thf(13685,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k7_setfam_1 ) @ ( B @ r1_tarski ) )
=> ( C @ ( B @ ( A @ k7_setfam_1 ) @ r1_tarski ) ) )
& ( ( C @ ( B @ ( A @ k7_setfam_1 ) @ r1_tarski ) )
=> ( C @ ( A @ k7_setfam_1 ) @ ( B @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2171]) ).
thf(1300,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= A )
& ( ( C @ ( B @ ( A @ k4_funct_2 ) ) )
= B ) )
=> ( C
= ( A @ k6_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_funct_2) ).
thf(8872,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= A )
& ( ( C @ ( B @ ( A @ k4_funct_2 ) ) )
= B ) )
=> ( C
= ( A @ k6_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(1805,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ a_2_2_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_domain_1) ).
thf(11483,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) )
= ( B @ ( A @ a_2_2_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1805]) ).
thf(2332,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(14384,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2332]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( C @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( C @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( B @ ( D @ k4_xboole_0 ) @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_closure2) ).
thf(3646,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( C @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( C @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( B @ ( D @ k4_xboole_0 ) @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(1101,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B
= ( A @ k1_relat_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(7719,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( B
= ( A @ k1_relat_1 ) ) )
& ( ( B
= ( A @ k1_relat_1 ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(2159,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ( ( C @ ( D @ r1_tarski ) )
=> ( D = C ) ) )
& ( B @ ( A @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_7) ).
thf(13621,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ( ( C @ ( D @ r1_tarski ) )
=> ( D = C ) ) )
& ( B @ ( A @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2159]) ).
thf(1883,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t154_funct_2) ).
thf(11968,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) ) )
& ( D @ ( C @ r1_partfun1 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1883]) ).
thf(1488,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
<=> ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_realset1) ).
thf(9808,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( B @ ( A @ ( C @ m3_realset1 ) ) ) )
& ( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ! [D: $i] :
( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1488]) ).
thf(1064,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( A @ k1_tarski @ ( B @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( A @ ( B @ ( C @ k4_funcop_1 ) ) @ v1_finseq_1 )
& ( A @ ( B @ ( C @ k4_funcop_1 ) ) @ v1_funct_1 )
& ( A @ ( B @ ( C @ k4_funcop_1 ) ) @ v1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_finseq_2) ).
thf(7579,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( A @ k1_tarski @ ( B @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( A @ ( B @ ( C @ k4_funcop_1 ) ) @ v1_finseq_1 )
& ( A @ ( B @ ( C @ k4_funcop_1 ) ) @ v1_funct_1 )
& ( A @ ( B @ ( C @ k4_funcop_1 ) ) @ v1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(1961,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( A @ k2_ens_1 @ ( B @ k2_ens_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ens_1) ).
thf(12509,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( A @ k2_ens_1 @ ( B @ k2_ens_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1961]) ).
thf(1363,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( k1_xboole_0 @ k1_funct_4 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_4) ).
thf(9224,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( k1_xboole_0 @ k1_funct_4 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).
thf(1210,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_nattra_1 ) ) ) )
= ( D @ ( C @ k7_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_nattra_1) ).
thf(8381,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_nattra_1 ) ) ) )
= ( D @ ( C @ k7_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(192,axiom,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( C @ v1_classes2 )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_classes2) ).
thf(3223,plain,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( C @ v1_classes2 )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(755,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_1) ).
thf(5965,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( B @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ k2_relat_1 @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(2075,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k1_closure2 ) @ k4_subset_1 ) ) @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_closure2) ).
thf(13197,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k1_closure2 ) @ k4_subset_1 ) ) @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2075]) ).
thf(2213,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B
= ( B @ ( A @ a_2_0_relset_2 ) @ k3_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_relset_2) ).
thf(13908,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B
= ( B @ ( A @ a_2_0_relset_2 ) @ k3_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2213]) ).
thf(2359,axiom,
! [A: $i] :
( ( f1_s2_subset_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s2_subset_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( f1_s2_subset_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
<=> ( C @ p1_s2_subset_1 ) ) )
& ! [C: $i] :
( ( f1_s2_subset_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
<=> ( C @ p1_s2_subset_1 ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_subset_1) ).
thf(14508,plain,
! [A: $i] :
( ( f1_s2_subset_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s2_subset_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( f1_s2_subset_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ p1_s2_subset_1 )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C @ p1_s2_subset_1 ) ) ) )
& ! [C: $i] :
( ( f1_s2_subset_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ p1_s2_subset_1 )
=> ( A @ ( C @ r2_hidden ) ) )
& ( ( A @ ( C @ r2_hidden ) )
=> ( C @ p1_s2_subset_1 ) ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2359]) ).
thf(1279,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ k1_realset1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_realset1) ).
thf(8767,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ k1_realset1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( ( A = k1_xboole_0 )
=> ( ( B
= ( A @ k1_setfam_1 ) )
<=> ( B = k1_xboole_0 ) ) )
& ( ( A != k1_xboole_0 )
=> ( ( B
= ( A @ k1_setfam_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(3023,plain,
! [A: $i,B: $i] :
( ( ( A = k1_xboole_0 )
=> ( ( ( B = k1_xboole_0 )
=> ( B
= ( A @ k1_setfam_1 ) ) )
& ( ( B
= ( A @ k1_setfam_1 ) )
=> ( B = k1_xboole_0 ) ) ) )
& ( ( A != k1_xboole_0 )
=> ( ( ! [C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k1_setfam_1 ) ) )
& ( ( B
= ( A @ k1_setfam_1 ) )
=> ! [C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ! [D: $i] :
( ( A @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(2054,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(13054,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( ( D @ ( B @ r1_tarski ) )
& ( C @ ( A @ r1_tarski ) ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2054]) ).
thf(479,axiom,
! [A: $i] :
( ( ( A @ k6_relat_1 @ k2_relat_1 )
= A )
& ( ( A @ k6_relat_1 @ k1_relat_1 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
thf(4558,plain,
! [A: $i] :
( ( ( A @ k6_relat_1 @ k2_relat_1 )
= A )
& ( ( A @ k6_relat_1 @ k1_relat_1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(1358,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_funct_3 @ v1_funct_1 )
& ( A @ k1_funct_3 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_3) ).
thf(9210,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_funct_3 @ v1_funct_1 )
& ( A @ k1_funct_3 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( B @ ( A @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_partfun1) ).
thf(3773,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( B @ ( A @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(687,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_partfun1) ).
thf(5567,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(2254,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k5_setfam_1 ) )
= A )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( C @ k3_tarski ) )
=> ( C @ ( B @ k3_subset_1 ) @ k3_tarski @ ( D @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_borsuk_1) ).
thf(14074,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k5_setfam_1 ) )
= A )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( C @ k3_tarski ) )
=> ( C @ ( B @ k3_subset_1 ) @ k3_tarski @ ( D @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2254]) ).
thf(593,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_finset_1) ).
thf(5118,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(1240,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_4 ) @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_4) ).
thf(8549,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_4 ) @ k2_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(958,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_tarski @ ( A @ k5_partfun1 ) ) )
= ( D @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t164_funct_2) ).
thf(6937,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_tarski @ ( A @ k5_partfun1 ) ) )
= ( D @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(835,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_xboole_1) ).
thf(6357,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( B @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(2891,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(571,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( D @ k13_funct_3 ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ k16_funct_3 ) ) ) ) ) @ ( A @ k12_funct_3 @ k5_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_funct_3) ).
thf(5011,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( D @ k13_funct_3 ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ k16_funct_3 ) ) ) ) ) @ ( A @ k12_funct_3 @ k5_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(1676,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_setwiseo) ).
thf(10770,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1676]) ).
thf(1093,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_mcart_1) ).
thf(7689,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(1431,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ k10_relat_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
thf(9506,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k10_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k10_relat_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431]) ).
thf(867,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
thf(6532,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k1_relat_1 @ ( A @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(693,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] : ( A @ ( B @ ( A @ ( B @ k1_funct_2 ) @ m1_fraenkel ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_fraenkel) ).
thf(5595,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] : ( A @ ( B @ ( A @ ( B @ k1_funct_2 ) @ m1_fraenkel ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(401,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( B @ k2_funcop_1 ) @ ( C @ ( B @ k2_funcop_1 ) @ ( A @ k1_funct_4 ) @ k1_funct_4 ) )
= ( D @ ( B @ k2_funcop_1 ) @ ( A @ k1_funct_4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_7) ).
thf(4171,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( B @ k2_funcop_1 ) @ ( C @ ( B @ k2_funcop_1 ) @ ( A @ k1_funct_4 ) @ k1_funct_4 ) )
= ( D @ ( B @ k2_funcop_1 ) @ ( A @ k1_funct_4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ m1_subset_1 ) )
& ( B @ ( A @ k1_fraenkel ) @ ( D @ ( C @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ k1_fraenkel ) @ ( D @ ( C @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_funcsdom ) ) ) ) ) @ m2_fraenkel ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funcsdom) ).
thf(3208,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ m1_subset_1 ) )
& ( B @ ( A @ k1_fraenkel ) @ ( D @ ( C @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ k1_fraenkel ) @ ( D @ ( C @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_funcsdom ) ) ) ) ) @ m2_fraenkel ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(1352,axiom,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
& ( A @ k1_subset_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_subset_1) ).
thf(9178,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ ( A @ k1_subset_1 @ m1_subset_1 ) )
& ( A @ k1_subset_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).
thf(2381,axiom,
k9_zf_lang @ k1_zfmisc_1 @ ( k2_zfrefle1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfrefle1) ).
thf(14608,plain,
k9_zf_lang @ k1_zfmisc_1 @ ( k2_zfrefle1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2381]) ).
thf(2117,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v2_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ k1_binop_1 ) ) )
= ( E @ ( D @ ( C @ ( B @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_binop_1) ).
thf(13380,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ k1_binop_1 ) ) )
= ( E @ ( D @ ( C @ ( B @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) ) ) ) ) )
=> ( A @ ( B @ v2_binop_1 ) ) )
& ( ( A @ ( B @ v2_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ ( B @ k1_binop_1 ) ) )
= ( E @ ( D @ ( C @ ( B @ k1_binop_1 ) ) @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2117]) ).
thf(1967,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( F @ ( D @ ( B @ k3_zfmisc_1 ) ) @ ( E @ ( C @ ( A @ k3_zfmisc_1 ) ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_mcart_1) ).
thf(12524,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( F @ ( D @ ( B @ k3_zfmisc_1 ) ) @ ( E @ ( C @ ( A @ k3_zfmisc_1 ) ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1967]) ).
thf(533,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k1_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funct_7) ).
thf(4822,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_4 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( A @ k5_relat_1 ) @ ( B @ ( A @ k5_relat_1 ) @ k1_funct_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(1599,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k5_relat_1 ) @ k5_relat_1 ) )
= ( C @ ( B @ k5_relat_1 ) @ ( A @ k5_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_relat_1) ).
thf(10348,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k5_relat_1 ) @ k5_relat_1 ) )
= ( C @ ( B @ k5_relat_1 ) @ ( A @ k5_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1599]) ).
thf(923,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k15_funct_3 ) @ k2_funct_4 @ v2_funct_1 )
=> ( A @ ( B @ k15_funct_3 ) @ v2_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_functor0) ).
thf(6794,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k15_funct_3 ) @ k2_funct_4 @ v2_funct_1 )
=> ( A @ ( B @ k15_funct_3 ) @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(1204,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ v1_partfun1 ) ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_4) ).
thf(8359,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ v1_partfun1 ) ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(1875,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_0_lattice5 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A
= ( C @ ( C @ k2_zfmisc_1 ) ) )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_lattice5) ).
thf(11919,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A
= ( C @ ( C @ k2_zfmisc_1 ) ) )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_lattice5 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_lattice5 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( B @ ( C @ r2_hidden ) )
& ( A
= ( C @ ( C @ k2_zfmisc_1 ) ) )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1875]) ).
thf(1539,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ k4_card_3 @ ( C @ r2_hidden ) )
=> ( B @ ( D @ k5_relat_1 ) @ k4_card_3 @ ( C @ ( D @ k5_relat_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_pre_circ) ).
thf(10051,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ k4_card_3 @ ( C @ r2_hidden ) )
=> ( B @ ( D @ k5_relat_1 ) @ k4_card_3 @ ( C @ ( D @ k5_relat_1 ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1539]) ).
thf(2005,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_subset_1) ).
thf(12759,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2005]) ).
thf(1667,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(10728,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1667]) ).
thf(1704,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_pboole) ).
thf(10938,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1704]) ).
thf(615,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( B @ k4_card_3 @ ( D @ m1_subset_1 ) )
=> ( ( ! [E: $i] :
( ( C @ k1_relat_1 @ ( E @ r2_hidden ) )
=> ( E @ ( B @ k1_funct_1 ) @ ( E @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( B @ k1_relat_1 @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( B @ k4_card_3 @ ( C @ ( D @ k1_funct_4 ) @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_pre_circ) ).
thf(5207,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( B @ k4_card_3 @ ( D @ m1_subset_1 ) )
=> ( ( ! [E: $i] :
( ( C @ k1_relat_1 @ ( E @ r2_hidden ) )
=> ( E @ ( B @ k1_funct_1 ) @ ( E @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( B @ k1_relat_1 @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( B @ k4_card_3 @ ( C @ ( D @ k1_funct_4 ) @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( k5_numbers @ ( B @ m1_subset_1 ) )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k9_funct_7 ) @ v1_funct_1 )
& ( B @ ( A @ k9_funct_7 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_funct_7) ).
thf(2442,plain,
! [A: $i,B: $i] :
( ( ( k5_numbers @ ( B @ m1_subset_1 ) )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k9_funct_7 ) @ v1_funct_1 )
& ( B @ ( A @ k9_funct_7 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( A @ k6_relat_1 @ ( B @ ( A @ k4_xboole_0 ) @ k6_relat_1 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_sysrel) ).
thf(2759,plain,
! [A: $i,B: $i] :
( ( A @ k6_relat_1 @ ( B @ ( A @ k4_xboole_0 ) @ k6_relat_1 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(251,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ r1_tarski ) ) )
& ( ( ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( A @ ( A @ k2_relat_1 @ k6_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_sysrel) ).
thf(3487,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ r1_tarski ) ) )
& ( ( ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( A @ ( A @ k2_relat_1 @ k6_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1155,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k2_funct_4 @ ( A @ k2_funct_4 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_yellow20) ).
thf(8059,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k2_funct_4 @ ( A @ k2_funct_4 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(1428,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funct_4) ).
thf(9496,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428]) ).
thf(2232,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) @ ( A @ k7_setfam_1 ) )
= ( C @ ( A @ k7_setfam_1 ) @ ( B @ ( A @ k7_setfam_1 ) @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_setfam_1) ).
thf(13984,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) @ ( A @ k7_setfam_1 ) )
= ( C @ ( A @ k7_setfam_1 ) @ ( B @ ( A @ k7_setfam_1 ) @ ( A @ k1_zfmisc_1 @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2232]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k2_relat_1 @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ k2_relat_1 @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_partfun1) ).
thf(2457,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k2_relat_1 @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ k2_relat_1 @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(286,axiom,
! [A: $i] : ( A @ k9_setwiseo @ ( A @ k1_setwiseo @ ( A @ k5_finsub_1 @ r3_binop_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_setwiseo) ).
thf(3641,plain,
! [A: $i] : ( A @ k9_setwiseo @ ( A @ k1_setwiseo @ ( A @ k5_finsub_1 @ r3_binop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ ( C @ k1_funct_1 ) @ k1_tarski @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_partfun1) ).
thf(6123,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( A @ ( C @ k1_funct_1 ) @ k1_tarski @ ( C @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( B @ ( C @ k9_funct_7 ) @ m2_relset_1 ) ) )
& ( B @ ( C @ k9_funct_7 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_funct_7) ).
thf(2425,plain,
! [A: $i,B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( B @ ( C @ k9_funct_7 ) @ m2_relset_1 ) ) )
& ( B @ ( C @ k9_funct_7 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1380,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k2_setwiseo ) @ m1_fraenkel ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_fraenkel) ).
thf(9290,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k2_setwiseo ) @ m1_fraenkel ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ ( A @ k2_funcop_1 ) @ k1_funct_1 ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_funcop_1) ).
thf(4273,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( C @ ( A @ k2_funcop_1 ) @ k1_funct_1 ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(1234,axiom,
! [A: $i] :
( ( ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v4_finsub_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v4_finsub_1 )
& ~ ( B @ ( A @ k3_xboole_0 ) @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_finsub_1) ).
thf(8524,plain,
! [A: $i] :
( ( ( A @ v4_finsub_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v4_finsub_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v4_finsub_1 )
& ~ ( B @ ( A @ k3_xboole_0 ) @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(2272,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(14151,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2272]) ).
thf(2016,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k6_relat_1 )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relset_1) ).
thf(12825,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k6_relat_1 )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2016]) ).
thf(763,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_relat_1) ).
thf(5997,plain,
! [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ k1_tarski @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 ) )
=> ( ( B @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 ) )
=> ( ( B @ k2_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_sysrel) ).
thf(3304,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( A @ ( B @ k1_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 ) )
=> ( ( B @ ( B @ k1_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 ) )
=> ( ( B @ k2_relat_1 @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( B @ k5_relat_1 ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(1847,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( A
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) )
& ( D @ ( G @ m1_subset_1 ) ) )
& ( C @ ( F @ m1_subset_1 ) ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_domain_1) ).
thf(11765,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ( ( ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( A
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) )
& ( D @ ( G @ m1_subset_1 ) ) )
& ( C @ ( F @ m1_subset_1 ) ) )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ? [F: $i] :
( ? [G: $i] :
( ( A
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) )
& ( D @ ( G @ m1_subset_1 ) ) )
& ( C @ ( F @ m1_subset_1 ) ) )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1847]) ).
thf(1212,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( A @ k2_setwiseo ) @ ( E @ ( A @ k5_setwiseo ) ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( B @ k5_setwiseo ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_setwiseo) ).
thf(8387,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( A @ k2_setwiseo ) @ ( E @ ( A @ k5_setwiseo ) ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( E @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( B @ k5_setwiseo ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(1933,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
<=> ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k5_subset_1 ) ) @ r2_hidden ) ) ) ) ) )
& ~ ( B @ ( k1_xboole_0 @ r2_hidden ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_card_fil) ).
thf(12278,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k5_subset_1 ) ) @ r2_hidden ) ) ) ) ) )
& ~ ( B @ ( k1_xboole_0 @ r2_hidden ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( A @ ( B @ m1_card_fil ) ) )
& ( ( A @ ( B @ m1_card_fil ) )
=> ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ ( A @ k5_subset_1 ) ) @ r2_hidden ) ) ) ) ) )
& ~ ( B @ ( k1_xboole_0 @ r2_hidden ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1933]) ).
thf(1624,axiom,
! [A: $i] :
( ( ( A @ k1_funct_5 )
= k1_xboole_0 )
<=> ( ( A @ k2_funct_5 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_5) ).
thf(10505,plain,
! [A: $i] :
( ( ( ( A @ k2_funct_5 )
= k1_xboole_0 )
=> ( ( A @ k1_funct_5 )
= k1_xboole_0 ) )
& ( ( ( A @ k1_funct_5 )
= k1_xboole_0 )
=> ( ( A @ k2_funct_5 )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1624]) ).
thf(1104,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t171_partfun1) ).
thf(7746,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(178,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ k1_setfam_1 @ ( A @ k1_setfam_1 @ k3_xboole_0 ) )
= ( B @ ( A @ k3_setfam_1 ) @ k1_setfam_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_setfam_1) ).
thf(3170,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ k1_setfam_1 @ ( A @ k1_setfam_1 @ k3_xboole_0 ) )
= ( B @ ( A @ k3_setfam_1 ) @ k1_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(2212,axiom,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v2_setfam_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] :
( ( C @ v1_finset_1 )
& ~ ( C @ v1_xboole_0 )
& ( B @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_triang_1) ).
thf(13903,plain,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v2_setfam_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] :
( ( C @ v1_finset_1 )
& ~ ( C @ v1_xboole_0 )
& ( B @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2212]) ).
thf(2249,axiom,
! [A: $i] :
( ( A @ v1_fraenkel )
=> ! [B: $i] :
( ( B @ v1_fraenkel )
=> ! [C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
& ( C @ v7_altcat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( E @ ( D @ ( C @ k1_binop_1 ) ) )
= ( D @ ( E @ k5_relat_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_altcat_1) ).
thf(14042,plain,
! [A: $i] :
( ( A @ v1_fraenkel )
=> ! [B: $i] :
( ( B @ v1_fraenkel )
=> ! [C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
& ( C @ v7_altcat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( E @ ( D @ ( C @ k1_binop_1 ) ) )
= ( D @ ( E @ k5_relat_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2249]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= ( D @ ( C @ k10_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_funct_2) ).
thf(6061,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= ( D @ ( C @ k10_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(880,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
<=> ! [D: $i] :
( ( B @ ( A @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_2) ).
thf(6585,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( B @ ( A @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
=> ( C @ ( B @ r1_partfun1 ) ) )
& ( ( C @ ( B @ r1_partfun1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( A @ k4_relset_1 ) ) @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(987,axiom,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_partfun1) ).
thf(7158,plain,
( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(1216,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_funct_3 ) @ ( B @ ( A @ k9_funct_3 ) @ k13_funct_3 ) )
= ( B @ ( A @ k2_zfmisc_1 ) @ k6_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_3) ).
thf(8419,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k10_funct_3 ) @ ( B @ ( A @ k9_funct_3 ) @ k13_funct_3 ) )
= ( B @ ( A @ k2_zfmisc_1 ) @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(1636,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k9_relat_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(10565,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k9_relat_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1636]) ).
thf(1152,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t159_funct_2) ).
thf(8042,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ k1_funct_2 ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(1894,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relset_2) ).
thf(12032,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ k2_relat_1 @ k1_zfmisc_1 @ ( C @ ( A @ k5_relset_2 ) @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1894]) ).
thf(770,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
thf(6024,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_zfmisc_1 ) )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(2306,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B
= ( B @ ( A @ a_2_1_domain_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_domain_1) ).
thf(14290,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B
= ( B @ ( A @ a_2_1_domain_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2306]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_partfun1) ).
thf(3101,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(1452,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( A @ ( A @ ( A @ k3_enumset1 ) ) ) ) )
= ( B @ ( A @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_enumset1) ).
thf(9623,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( A @ ( A @ ( A @ k3_enumset1 ) ) ) ) )
= ( B @ ( A @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k5_finsub_1 @ ( C @ ( B @ ( A @ k5_setwiseo ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setwiseo) ).
thf(2721,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k5_finsub_1 @ ( C @ ( B @ ( A @ k5_setwiseo ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(226,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m2_finseq_1 ) )
=> ( C @ ( D @ ( F @ ( E @ k4_funcop_1 ) ) @ m2_finseq_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_finseq_2) ).
thf(3352,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m2_finseq_1 ) )
=> ( C @ ( D @ ( F @ ( E @ k4_funcop_1 ) ) @ m2_finseq_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(1221,axiom,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(8452,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) )
& ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ ( A @ k4_relset_1 ) ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_partfun1) ).
thf(4337,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) )
& ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( D @ ( B @ ( A @ k4_relset_1 ) ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(1410,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ ( B @ k1_relat_1 @ r1_xboole_0 ) )
& ( C @ ( A @ k1_relat_1 @ r1_tarski ) ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funct_4) ).
thf(9422,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ ( B @ k1_relat_1 @ r1_xboole_0 ) )
& ( C @ ( A @ k1_relat_1 @ r1_tarski ) ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410]) ).
thf(61,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( D @ ( A @ k5_setwiseo ) ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( C @ ( D @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( B @ k5_setwiseo ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_setwiseo) ).
thf(2679,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( D @ ( A @ k5_setwiseo ) ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( C @ ( E @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( C @ ( D @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( B @ k5_setwiseo ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(960,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ~ ( ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ~ ( ! [F: $i] :
( ( B @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( C @ k4_tarski ) @ ( D @ k1_funct_1 ) ) ) )
& ( D @ k2_relat_1 @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= B )
& ( ( C @ ( D @ k3_funct_5 @ k1_funct_1 ) )
= E ) ) )
& ( A @ ( C @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_funct_5) ).
thf(6942,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ~ ( ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ~ ( ! [F: $i] :
( ( B @ ( F @ r2_hidden ) )
=> ( ( F @ ( E @ k1_funct_1 ) )
= ( F @ ( C @ k4_tarski ) @ ( D @ k1_funct_1 ) ) ) )
& ( D @ k2_relat_1 @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= B )
& ( ( C @ ( D @ k3_funct_5 @ k1_funct_1 ) )
= E ) ) )
& ( A @ ( C @ r2_hidden ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(2085,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_4) ).
thf(13240,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2085]) ).
thf(1576,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_filter_1) ).
thf(10236,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1576]) ).
thf(1591,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ r1_realset1 ) ) )
<=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_realset1) ).
thf(10317,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ r1_realset1 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_realset1 ) ) )
=> ! [D: $i] :
( ( C @ ( C @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( C @ ( D @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1591]) ).
thf(1111,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_funct_3 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k1_funct_3 @ k1_funct_1 ) )
= ( A @ ( B @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_3) ).
thf(7783,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_funct_3 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k1_funct_3 @ k1_funct_1 ) )
= ( A @ ( B @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(705,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funcop_1) ).
thf(5671,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ k6_funcop_1 ) ) ) ) @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ ( B @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(1700,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ? [C: $i] :
( ( C @ v1_fraenkel )
& ( C @ v1_finset_1 )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( C @ v1_xboole_0 )
& ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_closure2) ).
thf(10910,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ? [C: $i] :
( ( C @ v1_fraenkel )
& ( C @ v1_finset_1 )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( C @ v1_xboole_0 )
& ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700]) ).
thf(467,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( B @ ( A @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_enumset1) ).
thf(4498,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( B @ ( A @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_relset_2 ) ) ) )
= ( D @ k1_tarski @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relset_2) ).
thf(4369,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k3_relset_2 ) ) ) )
= ( D @ k1_tarski @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(1987,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k9_funct_3 ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k9_funct_3 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k9_funct_3 ) @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_funct_3) ).
thf(12651,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k9_funct_3 ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k9_funct_3 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k9_funct_3 ) @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1987]) ).
thf(1083,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_ens_1 @ ( A @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( A @ k2_ens_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_ens_1) ).
thf(7643,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_ens_1 @ ( A @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( A @ k2_ens_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_cat_2 ) ) ) )
= ( D @ k3_funct_5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_cat_2) ).
thf(3155,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_cat_2 ) ) ) )
= ( D @ k3_funct_5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1444,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_eqrel_1 ) )
=> ! [D: $i] :
( ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( B @ ( E @ r2_hidden ) )
=> ( E @ ( D @ k1_funct_1 ) @ ( E @ r1_tarski ) ) )
=> ! [E: $i] :
( ( B @ ( E @ m2_finseq_1 ) )
=> ! [F: $i] :
( ( C @ ( F @ m2_finseq_1 ) )
=> ( ( F @ k4_card_3 @ ( E @ k4_card_3 @ r1_tarski ) )
<=> ( ( D @ ( E @ ( C @ ( B @ ( B @ ( k5_numbers @ k1_partfun1 ) ) ) ) ) )
= F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_pua2mss1) ).
thf(9592,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_eqrel_1 ) )
=> ! [D: $i] :
( ( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( B @ ( E @ r2_hidden ) )
=> ( E @ ( D @ k1_funct_1 ) @ ( E @ r1_tarski ) ) )
=> ! [E: $i] :
( ( B @ ( E @ m2_finseq_1 ) )
=> ! [F: $i] :
( ( C @ ( F @ m2_finseq_1 ) )
=> ( ( ( ( D @ ( E @ ( C @ ( B @ ( B @ ( k5_numbers @ k1_partfun1 ) ) ) ) ) )
= F )
=> ( F @ k4_card_3 @ ( E @ k4_card_3 @ r1_tarski ) ) )
& ( ( F @ k4_card_3 @ ( E @ k4_card_3 @ r1_tarski ) )
=> ( ( D @ ( E @ ( C @ ( B @ ( B @ ( k5_numbers @ k1_partfun1 ) ) ) ) ) )
= F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444]) ).
thf(196,axiom,
! [A: $i] :
( ( A @ k5_finsub_1 @ ( A @ k1_setwiseo @ m1_subset_1 ) )
& ( A @ k1_setwiseo @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setwiseo) ).
thf(3238,plain,
! [A: $i] :
( ( A @ k5_finsub_1 @ ( A @ k1_setwiseo @ m1_subset_1 ) )
& ( A @ k1_setwiseo @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(622,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
thf(5244,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(1811,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k3_funcsdom ) ) )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funcsdom) ).
thf(11508,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ k3_funcsdom ) ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1811]) ).
thf(1912,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k5_setfam_1 ) @ ( A @ k2_subset_1 @ ( A @ k6_subset_1 ) ) )
= ( B @ ( A @ k7_setfam_1 ) @ ( A @ k6_setfam_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_setfam_1) ).
thf(12131,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k5_setfam_1 ) @ ( A @ k2_subset_1 @ ( A @ k6_subset_1 ) ) )
= ( B @ ( A @ k7_setfam_1 ) @ ( A @ k6_setfam_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1912]) ).
thf(640,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( B @ ( F @ m2_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) )
= ( F @ ( B @ ( A @ k10_funct_3 ) @ k5_relat_1 ) @ ( E @ ( B @ ( A @ k9_funct_3 ) @ k5_relat_1 ) @ k13_funct_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_funct_3) ).
thf(5325,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( B @ ( F @ m2_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) )
= ( F @ ( B @ ( A @ k10_funct_3 ) @ k5_relat_1 ) @ ( E @ ( B @ ( A @ k9_funct_3 ) @ k5_relat_1 ) @ k13_funct_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(2263,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s4_altcat_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s4_altcat_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f3_s4_altcat_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_multop_1 ) ) ) )
= ( D @ ( C @ ( B @ f4_s4_altcat_1 ) ) ) ) ) ) )
& ( f3_s4_altcat_1 @ ( f2_s4_altcat_1 @ ( f1_s4_altcat_1 @ k3_zfmisc_1 ) ) @ ( A @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_altcat_1) ).
thf(14119,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s4_altcat_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f2_s4_altcat_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( f3_s4_altcat_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_multop_1 ) ) ) )
= ( D @ ( C @ ( B @ f4_s4_altcat_1 ) ) ) ) ) ) )
& ( f3_s4_altcat_1 @ ( f2_s4_altcat_1 @ ( f1_s4_altcat_1 @ k3_zfmisc_1 ) ) @ ( A @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2263]) ).
thf(2133,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(13467,plain,
! [A: $i,B: $i] :
( ( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2133]) ).
thf(1123,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( D @ k2_relat_1 )
= B )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 ) )
=> ( ( ( E @ v2_funct_1 )
& ( D @ v2_funct_1 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_funct_2) ).
thf(7837,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( ( D @ k2_relat_1 )
= B )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v2_funct_1 ) )
=> ( ( ( E @ v2_funct_1 )
& ( D @ v2_funct_1 ) )
| ( ( B != k1_xboole_0 )
& ( C = k1_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(1584,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ~ ( ! [E: $i,F: $i] :
~ ( ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) )
& ( C
= ( F @ ( E @ k4_tarski ) ) ) )
& ( D @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relset_1) ).
thf(10279,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ~ ( ! [E: $i,F: $i] :
~ ( ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) )
& ( C
= ( F @ ( E @ k4_tarski ) ) ) )
& ( D @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1584]) ).
thf(860,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( B @ ( A @ k7_relat_1 ) @ ( A @ k1_funct_4 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_funct_4) ).
thf(6500,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( B @ ( A @ k7_relat_1 ) @ ( A @ k1_funct_4 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(1895,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ~ ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ k13_funct_3 ) @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ k13_funct_3 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ k13_funct_3 ) @ v1_funct_1 ) )
& ( ( C = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_funct_3) ).
thf(12034,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ~ ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ k13_funct_3 ) @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ k13_funct_3 ) @ v1_funct_2 ) ) )
& ( E @ ( D @ k13_funct_3 ) @ v1_funct_1 ) )
& ( ( C = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1895]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( B @ ( C @ ( A @ k3_xboole_0 ) @ ( D @ k3_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_partfun1) ).
thf(3515,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ ( D @ k3_partfun1 ) ) @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( B @ ( C @ ( A @ k3_xboole_0 ) @ ( D @ k3_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(941,axiom,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( B @ k1_relat_1 @ r2_hidden ) ) )
=> ( A @ ( B @ k4_card_3 @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_yellow_6) ).
thf(6866,plain,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( B @ k1_relat_1 @ r2_hidden ) ) )
=> ( A @ ( B @ k4_card_3 @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(804,axiom,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(6197,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(1390,axiom,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_subset_1) ).
thf(9322,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= ( A @ k1_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390]) ).
thf(205,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( F @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k8_funct_2 ) ) ) )
= ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ k2_cat_2 ) ) ) @ ( C @ ( B @ k1_fraenkel ) @ ( C @ ( B @ ( A @ k1_cat_2 ) ) ) ) ) @ ( C @ ( B @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_cat_2) ).
thf(3270,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( F @ ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k8_funct_2 ) ) ) )
= ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ k2_cat_2 ) ) ) @ ( C @ ( B @ k1_fraenkel ) @ ( C @ ( B @ ( A @ k1_cat_2 ) ) ) ) ) @ ( C @ ( B @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(2088,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k10_cat_2 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k10_cat_2 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_cat_2) ).
thf(13253,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k10_cat_2 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k10_cat_2 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2088]) ).
thf(2166,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ k2_funct_5 @ r1_tarski ) )
& ( B @ ( A @ k1_funct_5 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_funct_5) ).
thf(13670,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ k2_funct_5 @ r1_tarski ) )
& ( B @ ( A @ k1_funct_5 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2166]) ).
thf(2132,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k5_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_subset_1) ).
thf(13464,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k5_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2132]) ).
thf(1528,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) @ ( D @ ( A @ k1_funct_1 ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_funcop_1) ).
thf(10000,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) @ ( D @ ( A @ k1_funct_1 ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1528]) ).
thf(1001,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_relat_1) ).
thf(7255,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k1_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(1923,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(12182,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1923]) ).
thf(2189,axiom,
~ ( k3_qc_lang1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_qc_lang1) ).
thf(13794,plain,
~ ( k3_qc_lang1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2189]) ).
thf(2152,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ~ ( F @ v1_xboole_0 )
=> ! [G: $i] :
( ( ( E @ ( B @ ( A @ k2_zfmisc_1 ) @ ( G @ m2_relset_1 ) ) )
& ( E @ ( B @ ( A @ k2_zfmisc_1 ) @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ! [H: $i] :
( ( ( F @ ( D @ ( C @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( F @ ( D @ ( C @ k2_zfmisc_1 ) @ ( H @ v1_funct_2 ) ) )
& ( H @ v1_funct_1 ) )
=> ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( H @ ( G @ k3_funct_4 ) @ m2_relset_1 ) ) )
& ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( H @ ( G @ k3_funct_4 ) @ v1_funct_2 ) ) )
& ( H @ ( G @ k3_funct_4 ) @ v1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_4) ).
thf(13588,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ~ ( F @ v1_xboole_0 )
=> ! [G: $i] :
( ( ( E @ ( B @ ( A @ k2_zfmisc_1 ) @ ( G @ m2_relset_1 ) ) )
& ( E @ ( B @ ( A @ k2_zfmisc_1 ) @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ! [H: $i] :
( ( ( F @ ( D @ ( C @ k2_zfmisc_1 ) @ ( H @ m2_relset_1 ) ) )
& ( F @ ( D @ ( C @ k2_zfmisc_1 ) @ ( H @ v1_funct_2 ) ) )
& ( H @ v1_funct_1 ) )
=> ( ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( H @ ( G @ k3_funct_4 ) @ m2_relset_1 ) ) )
& ( F @ ( E @ k2_zfmisc_1 ) @ ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( H @ ( G @ k3_funct_4 ) @ v1_funct_2 ) ) )
& ( H @ ( G @ k3_funct_4 ) @ v1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2152]) ).
thf(1536,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v1_setwiseo ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_binop_1 ) @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= C )
& ( ( C @ ( B @ ( A @ k3_binop_1 ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_setwiseo) ).
thf(10037,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v1_setwiseo ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_binop_1 ) @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= C )
& ( ( C @ ( B @ ( A @ k3_binop_1 ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1536]) ).
thf(58,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_funct_1) ).
thf(2669,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(2211,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ~ ( ( C @ ( E @ r2_hidden ) )
<=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_7_domain_1) ).
thf(13888,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_7_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ~ ( ( ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2211]) ).
thf(300,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_relat_1 )
=> ( A @ k2_relat_1 @ v1_setfam_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_pboole) ).
thf(3710,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_relat_1 )
=> ( A @ k2_relat_1 @ v1_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
thf(4958,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(1466,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ r1_xboole_0 ) )
=> ( ~ ( F @ ( C @ r1_xboole_0 ) )
& ~ ( E @ ( B @ r1_xboole_0 ) )
& ~ ( D @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_mcart_1) ).
thf(9702,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ r1_xboole_0 ) )
=> ( ~ ( F @ ( C @ r1_xboole_0 ) )
& ~ ( E @ ( B @ r1_xboole_0 ) )
& ~ ( D @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466]) ).
thf(1785,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_2_domain_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_domain_1) ).
thf(11365,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( C @ ( B @ ( A @ a_3_2_domain_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1785]) ).
thf(396,axiom,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v1_binop_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_setwiseo) ).
thf(4154,plain,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v1_binop_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(112,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_partfun1 ) ) )
= ( B @ ( A @ ( C @ k8_relat_1 ) @ k7_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_partfun1) ).
thf(2856,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_partfun1 ) ) )
= ( B @ ( A @ ( C @ k8_relat_1 ) @ k7_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_xboole_1) ).
thf(4176,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k3_xboole_0 ) @ ( C @ ( A @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(499,axiom,
! [A: $i] :
( ( k1_numbers @ ( A @ m1_subset_1 ) )
=> ( ( A @ k8_binop_2 @ k8_binop_2 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k8_binop_2) ).
thf(4667,plain,
! [A: $i] :
( ( k1_numbers @ ( A @ m1_subset_1 ) )
=> ( ( A @ k8_binop_2 @ k8_binop_2 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(97,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_orders_1 ) )
=> ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_orders_1) ).
thf(2802,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_orders_1 ) )
=> ( ( A @ k3_tarski @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k3_tarski @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(711,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_partfun1) ).
thf(5689,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ k1_tarski @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(1032,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( D @ ( C @ ( C @ ( B @ ( B @ ( A @ ( A @ k16_funct_3 ) ) ) ) ) @ ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ ( A @ k2_zfmisc_1 ) @ ( F @ m1_functor0 ) ) ) ) ) )
& ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m1_pboole ) )
& ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_pboole ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_functor0 ) ) ) ) ) )
= ( F @ k2_funct_4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_functor0) ).
thf(7470,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( D @ ( C @ ( C @ ( B @ ( B @ ( A @ ( A @ k16_funct_3 ) ) ) ) ) @ ( B @ ( B @ k2_zfmisc_1 ) @ ( A @ ( A @ k2_zfmisc_1 ) @ ( F @ m1_functor0 ) ) ) ) ) )
& ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m1_pboole ) )
& ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_pboole ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_functor0 ) ) ) ) ) )
= ( F @ k2_funct_4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(1548,axiom,
a_0_0_pre_circ @ v1_finset_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_pre_circ) ).
thf(10098,plain,
a_0_0_pre_circ @ v1_finset_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1548]) ).
thf(885,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_relat_1) ).
thf(6604,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(800,axiom,
! [A: $i] :
( ( A @ k12_funct_3 )
= ( A @ k6_partfun1 @ ( A @ k6_partfun1 @ k13_funct_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funcop_1) ).
thf(6184,plain,
! [A: $i] :
( ( A @ k12_funct_3 )
= ( A @ k6_partfun1 @ ( A @ k6_partfun1 @ k13_funct_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(2198,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_qc_lang1) ).
thf(13836,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( C @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2198]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_card_fil ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k3_card_fil ) ) @ m1_subset_1 ) )
& ~ ( C @ ( B @ ( A @ k3_card_fil ) ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_card_fil) ).
thf(3586,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_card_fil ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k3_card_fil ) ) @ m1_subset_1 ) )
& ~ ( C @ ( B @ ( A @ k3_card_fil ) ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(913,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ k1_enumset1 ) ) @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_subset_1) ).
thf(6737,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ k1_enumset1 ) ) @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(471,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_relat_1) ).
thf(4509,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(1504,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_zfmisc_1) ).
thf(9890,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ r2_hidden ) )
& ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504]) ).
thf(854,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k3_multop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k4_mcart_1 ) ) ) @ ( A @ k1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_multop_1) ).
thf(6460,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ k3_multop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ k4_mcart_1 ) ) ) @ ( A @ k1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(2251,axiom,
! [A: $i] :
( ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_zfmisc_1 ) @ ( A @ k9_setwiseo @ m2_relset_1 ) ) )
& ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_zfmisc_1 ) @ ( A @ k9_setwiseo @ v1_funct_2 ) ) )
& ( A @ k9_setwiseo @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_setwiseo) ).
thf(14053,plain,
! [A: $i] :
( ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_zfmisc_1 ) @ ( A @ k9_setwiseo @ m2_relset_1 ) ) )
& ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ ( A @ k5_finsub_1 @ k2_zfmisc_1 ) @ ( A @ k9_setwiseo @ v1_funct_2 ) ) )
& ( A @ k9_setwiseo @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2251]) ).
thf(1900,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B
= ( A @ k6_relat_1 ) )
<=> ! [C: $i,D: $i] :
( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
<=> ( ( C = D )
& ( A @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
thf(12064,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ! [C: $i,D: $i] :
( ( ( ( C = D )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( ( C = D )
& ( A @ ( C @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k6_relat_1 ) ) )
& ( ( B
= ( A @ k6_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( ( ( C = D )
& ( A @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
& ( ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( ( C = D )
& ( A @ ( C @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1900]) ).
thf(629,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r2_hidden ) )
=> ( E @ ( D @ r1_tarski ) ) )
& ( C @ ( D @ r2_hidden ) ) )
& ( C != k1_xboole_0 )
& ( B @ ( C @ r1_tarski ) ) )
& ( ( B @ k3_tarski )
= ( A @ k3_tarski ) )
& ( A @ ( B @ r1_tarski ) ) )
& ( A @ v6_ordinal1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_card_3) ).
thf(5267,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r2_hidden ) )
=> ( E @ ( D @ r1_tarski ) ) )
& ( C @ ( D @ r2_hidden ) ) )
& ( C != k1_xboole_0 )
& ( B @ ( C @ r1_tarski ) ) )
& ( ( B @ k3_tarski )
= ( A @ k3_tarski ) )
& ( A @ ( B @ r1_tarski ) ) )
& ( A @ v6_ordinal1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(2386,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ k2_funct_5 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_yellow_3) ).
thf(14632,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ k2_funct_5 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2386]) ).
thf(2024,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ( ( D @ ( C @ r2_hidden ) )
=> ( D
= ( C @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_borsuk_1) ).
thf(12882,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) )
=> ( ( D @ ( C @ r2_hidden ) )
=> ( D
= ( C @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2024]) ).
thf(809,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tex_2 ) )
<=> ( B
!= ( A @ k3_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tex_2) ).
thf(6216,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( ( B
!= ( A @ k3_tarski ) )
=> ( A @ ( B @ v1_tex_2 ) ) )
& ( ( A @ ( B @ v1_tex_2 ) )
=> ( B
!= ( A @ k3_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(1512,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_relat_1) ).
thf(9931,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ m2_pua2mss1 ) )
<=> ( ( B @ v2_funct_1 )
& ( A @ ( B @ k2_relat_1 @ m1_eqrel_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pua2mss1) ).
thf(2824,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ v2_funct_1 )
& ( A @ ( B @ k2_relat_1 @ m1_eqrel_1 ) ) )
=> ( A @ ( B @ m2_pua2mss1 ) ) )
& ( ( A @ ( B @ m2_pua2mss1 ) )
=> ( ( B @ v2_funct_1 )
& ( A @ ( B @ k2_relat_1 @ m1_eqrel_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(784,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ ( C @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
thf(6087,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) @ ( C @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_setfam_1 ) )
= ( B @ k1_setfam_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(3133,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_setfam_1 ) )
= ( B @ k1_setfam_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(1641,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ( ! [F: $i] :
( ( A @ ( F @ r2_hidden ) )
<=> ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_domain_1) ).
thf(10579,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ( ! [F: $i] :
( ( ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) )
=> ( A @ ( F @ r2_hidden ) ) )
& ( ( A @ ( F @ r2_hidden ) )
=> ? [G: $i] :
( ? [H: $i] :
( ? [I: $i] :
( ? [J: $i] :
( ( F
= ( J @ ( I @ ( H @ ( G @ k4_mcart_1 ) ) ) ) )
& ( E @ ( J @ m1_subset_1 ) ) )
& ( D @ ( I @ m1_subset_1 ) ) )
& ( C @ ( H @ m1_subset_1 ) ) )
& ( B @ ( G @ m1_subset_1 ) ) ) ) )
=> ( A
= ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1641]) ).
thf(1973,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( C @ ( E @ ( D @ k4_tarski ) @ ( F @ k1_funct_1 ) @ r2_hidden ) )
| ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_funct_2) ).
thf(12562,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( C @ ( E @ ( D @ k4_tarski ) @ ( F @ k1_funct_1 ) @ r2_hidden ) )
| ( C = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1973]) ).
thf(1227,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ r1_tarski ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_lattice2) ).
thf(8473,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ r1_tarski ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(1043,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
=> ( A @ ( B @ r1_partfun1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_partfun1) ).
thf(7504,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
=> ( A @ ( B @ r1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(765,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_zfmisc_1) ).
thf(6004,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A != k1_xboole_0 )
& ( A
!= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(1290,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k1_funct_4 ) @ ( C @ ( A @ k1_funct_4 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_pre_circ) ).
thf(8826,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k1_funct_4 ) @ ( C @ ( A @ k1_funct_4 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290]) ).
thf(1499,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k5_subset_1 ) ) @ k3_tarski )
= ( D @ k3_tarski @ ( C @ k3_tarski @ k3_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_borsuk_1) ).
thf(9857,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k5_subset_1 ) ) @ k3_tarski )
= ( D @ k3_tarski @ ( C @ k3_tarski @ k3_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499]) ).
thf(1653,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t151_funct_2) ).
thf(10621,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1653]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(2812,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_xboole_1) ).
thf(2632,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
=> ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ( B @ v2_membered )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v2_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_membered) ).
thf(4541,plain,
! [A: $i,B: $i] :
( ( B @ v2_membered )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v2_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(2069,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) @ r1_tarski ) )
& ( B @ ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_relat_1) ).
thf(13164,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) @ r1_tarski ) )
& ( B @ ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2069]) ).
thf(1710,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( G @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) ) ) )
=> ( F
= ( E @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funcop_1) ).
thf(10957,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( G @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) ) ) )
=> ( F
= ( E @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1710]) ).
thf(2299,axiom,
! [A: $i] :
( ( a_0_0_pre_circ @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ( B @ p1_s1_pre_circ )
& ( A
= ( B @ f2_s1_pre_circ ) )
& ( f1_s1_pre_circ @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_0_pre_circ) ).
thf(14262,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ p1_s1_pre_circ )
& ( A
= ( B @ f2_s1_pre_circ ) )
& ( f1_s1_pre_circ @ ( B @ m1_subset_1 ) ) )
=> ( a_0_0_pre_circ @ ( A @ r2_hidden ) ) )
& ( ( a_0_0_pre_circ @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ( B @ p1_s1_pre_circ )
& ( A
= ( B @ f2_s1_pre_circ ) )
& ( f1_s1_pre_circ @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2299]) ).
thf(451,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_enumset1) ).
thf(4420,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(1005,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_partfun1) ).
thf(7275,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(2219,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_eqrel_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
thf(13930,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_eqrel_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2219]) ).
thf(1503,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
thf(9888,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1503]) ).
thf(722,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
<=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(5730,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) )
=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(1176,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( F @ v1_funct_1 )
& ( F @ v1_relat_1 ) )
=> ( ( ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ k1_relat_1 @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( F @ ( E @ k3_funct_4 ) @ k1_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funct_4) ).
thf(8156,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( F @ v1_funct_1 )
& ( F @ v1_relat_1 ) )
=> ( ( ( D @ ( C @ k2_zfmisc_1 ) @ ( F @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ k1_relat_1 @ r1_tarski ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( F @ ( E @ k3_funct_4 ) @ k1_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(2314,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m3_realset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m3_realset1) ).
thf(14311,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m3_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2314]) ).
thf(481,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ k13_funct_3 ) )
= ( B @ ( A @ k13_funct_3 ) @ ( C @ k5_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_funct_3) ).
thf(4569,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ ( A @ ( C @ k5_relat_1 ) @ k13_funct_3 ) )
= ( B @ ( A @ k13_funct_3 ) @ ( C @ k5_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(1896,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ ( A @ ( k1_xboole_0 @ v1_funct_2 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_functor0) ).
thf(12049,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) )
& ( k1_xboole_0 @ ( A @ ( k1_xboole_0 @ v1_funct_2 ) ) )
& ( k1_xboole_0 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1896]) ).
thf(1808,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(11498,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1808]) ).
thf(2204,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) )
=> ( D
= ( E @ ( F @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funcop_1) ).
thf(13857,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) )
=> ( D
= ( E @ ( F @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2204]) ).
thf(2107,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k1_cantor_1 ) @ ( A @ g1_pre_topc ) @ ( B @ m1_cantor_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_cantor_1) ).
thf(13323,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k1_cantor_1 ) @ ( A @ g1_pre_topc ) @ ( B @ m1_cantor_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2107]) ).
thf(937,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_lattice2) ).
thf(6849,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( E @ ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_funct_4 ) )
= E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(383,axiom,
? [A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(4064,plain,
? [A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(1494,axiom,
( ( k1_numbers @ ( k33_binop_2 @ v1_setwiseo ) )
& ( k1_numbers @ ( k33_binop_2 @ v2_binop_1 ) )
& ( k1_numbers @ ( k33_binop_2 @ v1_binop_1 ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k33_binop_2 @ v1_funct_2 ) ) )
& ( k33_binop_2 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_binop_2) ).
thf(9830,plain,
( ( k1_numbers @ ( k33_binop_2 @ v1_setwiseo ) )
& ( k1_numbers @ ( k33_binop_2 @ v2_binop_1 ) )
& ( k1_numbers @ ( k33_binop_2 @ v1_binop_1 ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k33_binop_2 @ v1_funct_2 ) ) )
& ( k33_binop_2 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1494]) ).
thf(1654,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( A @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( B @ ( C @ m1_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_cat_1 ) ) ) ) ) )
= ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ g1_cat_1 ) ) ) ) ) ) )
=> ( ( F = L )
& ( E = K )
& ( D = J )
& ( C = I )
& ( B = H )
& ( A = G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_cat_1) ).
thf(10628,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( A @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( B @ ( D @ m1_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( B @ ( C @ m1_relset_1 ) ) )
& ( A @ ( B @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_cat_1 ) ) ) ) ) )
= ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ g1_cat_1 ) ) ) ) ) ) )
=> ( ( F = L )
& ( E = K )
& ( D = J )
& ( C = I )
& ( B = H )
& ( A = G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1654]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ r2_hidden ) )
=> ( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funcop_1) ).
thf(4264,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ r2_hidden ) )
=> ( ( C @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(1121,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( D @ k4_tarski ) @ ( F @ k4_tarski ) @ k20_mcart_1 )
= E )
& ( ( E @ ( D @ k4_tarski ) @ ( F @ k4_tarski ) @ k19_mcart_1 )
= D )
& ( ( C @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) @ k18_mcart_1 )
= B )
& ( ( C @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) @ k17_mcart_1 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_mcart_1) ).
thf(7820,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( D @ k4_tarski ) @ ( F @ k4_tarski ) @ k20_mcart_1 )
= E )
& ( ( E @ ( D @ k4_tarski ) @ ( F @ k4_tarski ) @ k19_mcart_1 )
= D )
& ( ( C @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) @ k18_mcart_1 )
= B )
& ( ( C @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) @ k17_mcart_1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t161_funct_2) ).
thf(3932,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ ( C @ k3_partfun1 ) ) @ ( B @ ( A @ k5_partfun1 ) ) )
= ( C @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(695,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ( C @ ( B @ r1_partfun1 ) )
& ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_funct_2) ).
thf(5599,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ? [C: $i] :
( ( C @ ( B @ r1_partfun1 ) )
& ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(1373,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ v1_setfam_1 ) )
=> ( ( C @ k4_card_3 @ v1_fraenkel )
& ~ ( C @ k4_card_3 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_card_3) ).
thf(9263,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( B @ v1_setfam_1 ) )
=> ( ( C @ k4_card_3 @ v1_fraenkel )
& ~ ( C @ k4_card_3 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373]) ).
thf(15,axiom,
! [A: $i] :
~ ( ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ~ ( B @ ( A @ r2_wellord2 ) ) )
& ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_card_1) ).
thf(2446,plain,
! [A: $i] :
~ ( ! [B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ~ ( B @ ( A @ r2_wellord2 ) ) )
& ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_enumset1) ).
thf(4277,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(1908,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i] :
( ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_0_domain_1) ).
thf(12111,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i] :
( ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_0_domain_1 @ ( A @ r2_hidden ) )
=> ? [C: $i] :
( ( A = C )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1908]) ).
thf(972,axiom,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ k2_relat_1 )
= k1_xboole_0 )
& ( ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ k1_relat_1 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funcop_1) ).
thf(7033,plain,
! [A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ k2_relat_1 )
= k1_xboole_0 )
& ( ( A @ ( k1_xboole_0 @ k2_funcop_1 ) @ k1_relat_1 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(2003,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ k2_funct_5 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_yellow_3) ).
thf(12755,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ k2_funct_5 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2003]) ).
thf(1749,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_partfun1) ).
thf(11156,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( B = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1749]) ).
thf(83,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i,C: $i] :
( ( B @ ( C @ m2_finseq_1 ) )
=> ( ( C @ k4_finseq_1 @ ( A @ r2_hidden ) )
=> ( B @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finseq_2) ).
thf(2757,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i,C: $i] :
( ( B @ ( C @ m2_finseq_1 ) )
=> ( ( C @ k4_finseq_1 @ ( A @ r2_hidden ) )
=> ( B @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1705,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ a_4_1_relset_2 ) ) ) @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_relset_2) ).
thf(10942,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ a_4_1_relset_2 ) ) ) @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1705]) ).
thf(1088,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_relset_1 ) ) )
= ( C @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
thf(7664,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_relset_1 ) ) )
= ( C @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( B @ k3_partfun1 ) ) @ ( A @ ( A @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t162_funct_2) ).
thf(3165,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( B @ k3_partfun1 ) ) @ ( A @ ( A @ k5_partfun1 ) ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(1056,axiom,
? [A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_setfam_1) ).
thf(7551,plain,
? [A: $i] :
( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(1668,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r2_relat_2 ) )
<=> ! [C: $i] :
~ ( ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_2) ).
thf(10732,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i] :
~ ( ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r2_relat_2 ) ) )
& ( ( B @ ( A @ r2_relat_2 ) )
=> ! [C: $i] :
~ ( ( A @ ( C @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1668]) ).
thf(2164,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(13653,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2164]) ).
thf(1821,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m1_filter_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( B @ ( E @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_filter_1) ).
thf(11569,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( B @ ( E @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) )
=> ( B @ ( A @ ( C @ m1_filter_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m1_filter_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) )
=> ( B @ ( E @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1821]) ).
thf(916,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_funcop_1 ) @ ( C @ ( A @ k2_funcop_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_funct_4) ).
thf(6747,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k2_funcop_1 ) @ ( C @ ( A @ k2_funcop_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( D @ ( A @ ( E @ m1_relset_1 ) ) )
& ( D @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( C @ ( B @ ( D @ m1_fraenkel ) ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( D @ ( C @ ( B @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_cat_2 ) ) ) ) ) @ m2_fraenkel ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_cat_2) ).
thf(2785,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( D @ ( A @ ( E @ m1_relset_1 ) ) )
& ( D @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( C @ ( B @ ( D @ m1_fraenkel ) ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( D @ ( C @ ( B @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_cat_2 ) ) ) ) ) @ m2_fraenkel ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1086,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( A @ k2_relat_1 @ k8_relat_1 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t126_relat_1) ).
thf(7654,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ ( A @ k2_relat_1 @ k8_relat_1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ k1_setfam_1 )
= ( B @ ( A @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_setfam_1) ).
thf(2593,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ k1_setfam_1 )
= ( B @ ( A @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(539,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) )
=> ( C
= ( C @ ( B @ k6_domain_1 ) @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k3_funct_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_borsuk_1) ).
thf(4850,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) )
=> ( C
= ( C @ ( B @ k6_domain_1 ) @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k3_funct_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(1832,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g1_vectsp_1 ) ) )
= ( F @ ( E @ ( D @ g1_vectsp_1 ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_vectsp_1) ).
thf(11640,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ g1_vectsp_1 ) ) )
= ( F @ ( E @ ( D @ g1_vectsp_1 ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1832]) ).
thf(666,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ r4_nattra_1 ) ) ) ) ) )
<=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( G @ ( F @ k1_funct_1 ) ) ) )
& ( A = C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_nattra_1) ).
thf(5466,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( G @ ( F @ k1_funct_1 ) ) ) )
& ( A = C ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ r4_nattra_1 ) ) ) ) ) ) )
& ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ r4_nattra_1 ) ) ) ) ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( G @ ( F @ k1_funct_1 ) ) ) )
& ( A = C ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(1148,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ ( B @ ( C @ ( A @ k9_funcop_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k9_funcop_1 ) ) ) @ k4_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funcop_1) ).
thf(8032,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ ( B @ ( C @ ( A @ k9_funcop_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k9_funcop_1 ) ) ) @ k4_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1129,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( B @ ( A @ k15_funct_3 ) @ v2_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_isocat_1) ).
thf(7869,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( B @ ( A @ k15_funct_3 ) @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(511,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_funct_2) ).
thf(4726,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_partfun1 ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k4_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(3861,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k4_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k4_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(1943,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( F @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
!= E ) )
& ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( G @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
=> ( ( F @ ( E @ ( C @ ( A @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( C @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_borsuk_1) ).
thf(12381,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ~ ( ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( F @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
!= E ) )
& ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( G @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) ) )
=> ( ( F @ ( E @ ( C @ ( A @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( C @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1943]) ).
thf(2015,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_lopclset) ).
thf(12821,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2015]) ).
thf(978,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) )
& ( B @ ( C @ v3_binop_1 ) ) )
=> ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) ) )
<=> ? [G: $i] :
( ! [H: $i] :
( ( A @ k5_finsub_1 @ ( H @ m1_subset_1 ) )
=> ( ( D @ ( H @ r1_tarski ) )
=> ( ! [I: $i] :
( ( A @ ( I @ m1_subset_1 ) )
=> ( ( D @ ( I @ r2_hidden ) )
=> ( ( I @ ( A @ k2_setwiseo ) @ ( H @ ( A @ k5_setwiseo ) ) @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( I @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( H @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) ) ) ) )
| ( H = k1_xboole_0 ) ) ) )
& ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( A @ k2_setwiseo ) @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( H @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) ) ) )
& ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ( ( C @ ( H @ ( B @ r3_binop_1 ) ) )
=> ( ( k1_xboole_0 @ ( G @ k1_funct_1 ) )
= H ) ) )
& ( F
= ( D @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) ) )
& ( B @ ( A @ k5_finsub_1 @ ( G @ m2_relset_1 ) ) )
& ( B @ ( A @ k5_finsub_1 @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) ) ) )
| ( ~ ( B @ ( C @ v1_setwiseo ) )
& ( D = k1_xboole_0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_setwiseo) ).
thf(7066,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) )
& ( B @ ( C @ v3_binop_1 ) ) )
=> ( ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( ? [G: $i] :
( ! [H: $i] :
( ( A @ k5_finsub_1 @ ( H @ m1_subset_1 ) )
=> ( ( D @ ( H @ r1_tarski ) )
=> ( ! [I: $i] :
( ( A @ ( I @ m1_subset_1 ) )
=> ( ( D @ ( I @ r2_hidden ) )
=> ( ( I @ ( A @ k2_setwiseo ) @ ( H @ ( A @ k5_setwiseo ) ) @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( I @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( H @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) ) ) ) )
| ( H = k1_xboole_0 ) ) ) )
& ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( A @ k2_setwiseo ) @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( H @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) ) ) )
& ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ( ( C @ ( H @ ( B @ r3_binop_1 ) ) )
=> ( ( k1_xboole_0 @ ( G @ k1_funct_1 ) )
= H ) ) )
& ( F
= ( D @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) ) )
& ( B @ ( A @ k5_finsub_1 @ ( G @ m2_relset_1 ) ) )
& ( B @ ( A @ k5_finsub_1 @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) ) ) )
& ( ( F
= ( E @ ( D @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) ) )
=> ? [G: $i] :
( ! [H: $i] :
( ( A @ k5_finsub_1 @ ( H @ m1_subset_1 ) )
=> ( ( D @ ( H @ r1_tarski ) )
=> ( ! [I: $i] :
( ( A @ ( I @ m1_subset_1 ) )
=> ( ( D @ ( I @ r2_hidden ) )
=> ( ( I @ ( A @ k2_setwiseo ) @ ( H @ ( A @ k5_setwiseo ) ) @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( I @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( H @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) ) ) ) )
| ( H = k1_xboole_0 ) ) ) )
& ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( A @ k2_setwiseo ) @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( H @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) ) ) )
& ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ( ( C @ ( H @ ( B @ r3_binop_1 ) ) )
=> ( ( k1_xboole_0 @ ( G @ k1_funct_1 ) )
= H ) ) )
& ( F
= ( D @ ( G @ ( B @ ( A @ k5_finsub_1 @ k8_funct_2 ) ) ) ) )
& ( B @ ( A @ k5_finsub_1 @ ( G @ m2_relset_1 ) ) )
& ( B @ ( A @ k5_finsub_1 @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) ) ) ) )
| ( ~ ( B @ ( C @ v1_setwiseo ) )
& ( D = k1_xboole_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k9_relat_1 ) @ ( B @ k4_relat_1 @ k9_relat_1 ) @ ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t163_relat_1) ).
thf(2461,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k9_relat_1 ) @ ( B @ k4_relat_1 @ k9_relat_1 ) @ ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
=> ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funcop_1 ) @ k5_funct_5 )
= ( C @ ( A @ k2_funcop_1 ) @ ( B @ k2_funcop_1 ) ) )
& ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funcop_1 ) @ k3_funct_5 )
= ( C @ ( B @ k2_funcop_1 ) @ ( A @ k2_funcop_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_6) ).
thf(2974,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 )
=> ( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funcop_1 ) @ k5_funct_5 )
= ( C @ ( A @ k2_funcop_1 ) @ ( B @ k2_funcop_1 ) ) )
& ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funcop_1 ) @ k3_funct_5 )
= ( C @ ( B @ k2_funcop_1 ) @ ( A @ k2_funcop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(1681,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(10792,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1681]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ r6_pboole ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r6_pboole) ).
thf(4684,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( ( B = C )
=> ( C @ ( B @ ( A @ r6_pboole ) ) ) )
& ( ( C @ ( B @ ( A @ r6_pboole ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(2135,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( A @ ( F @ m2_relset_1 ) ) )
& ( C @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( C @ ( A @ ( G @ m2_relset_1 ) ) )
& ( C @ ( A @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) )
= ( G @ ( E @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) ) )
=> ( ( F = G )
& ( D = E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_funct_3) ).
thf(13486,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( A @ ( F @ m2_relset_1 ) ) )
& ( C @ ( A @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( C @ ( A @ ( G @ m2_relset_1 ) ) )
& ( C @ ( A @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) )
= ( G @ ( E @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) ) )
=> ( ( F = G )
& ( D = E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2135]) ).
thf(961,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ k7_relat_1 ) @ k2_relat_1 @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_funct_1) ).
thf(6956,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ k7_relat_1 ) @ k2_relat_1 @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(1814,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k5_finsub_1 @ ( C @ ( B @ ( A @ k3_setwiseo ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_setwiseo) ).
thf(11521,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k5_finsub_1 @ ( C @ ( B @ ( A @ k3_setwiseo ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1814]) ).
thf(126,axiom,
! [A: $i] : ( A @ k3_tarski @ ( A @ k1_setfam_1 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_setfam_1) ).
thf(2911,plain,
! [A: $i] : ( A @ k3_tarski @ ( A @ k1_setfam_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(1192,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(8280,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(1346,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_finset_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_finset_1) ).
thf(9143,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ v1_finset_1 )
& ~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).
thf(1818,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ r4_nattra_1 ) ) ) ) ) )
<=> ( E = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r4_nattra_1) ).
thf(11558,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( ( E = F )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ r4_nattra_1 ) ) ) ) ) ) )
& ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ r4_nattra_1 ) ) ) ) ) )
=> ( E = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1818]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_zfmisc_1) ).
thf(2620,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1971,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_subset_1) ).
thf(12556,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_subset_1 ) ) @ ( A @ k3_subset_1 ) )
= ( C @ ( B @ ( A @ k3_subset_1 ) @ ( A @ k4_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1971]) ).
thf(171,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( A @ k2_finseq_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ) )
& ( ( C @ k3_finseq_1 )
= A )
& ( ( B @ k3_finseq_1 )
= A ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_finseq_2) ).
thf(3142,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ! [D: $i] :
( ( k5_numbers @ ( k1_numbers @ ( D @ m2_subset_1 ) ) )
=> ( ( A @ k2_finseq_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) ) )
& ( ( C @ k3_finseq_1 )
= A )
& ( ( B @ k3_finseq_1 )
= A ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(1058,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k15_funct_3 ) @ v1_funct_1 )
& ( B @ ( A @ k15_funct_3 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k15_funct_3) ).
thf(7558,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k15_funct_3 ) @ v1_funct_1 )
& ( B @ ( A @ k15_funct_3 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(1921,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(12178,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1921]) ).
thf(673,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ v2_funct_1 )
<=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ( ( ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( H @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) ) )
=> ( ( G = H )
& ( E = F ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yellow18) ).
thf(5495,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ( ( ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( H @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) ) )
=> ( ( G = H )
& ( E = F ) ) ) ) ) ) )
=> ( D @ v2_funct_1 ) )
& ( ( D @ v2_funct_1 )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ( ( ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( H @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) ) )
=> ( ( G = H )
& ( E = F ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(1320,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) )
= ( D @ ( C @ k10_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k11_relset_1) ).
thf(8990,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k11_relset_1 ) ) ) )
= ( D @ ( C @ k10_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).
thf(2200,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ r2_hidden ) )
=> ( B @ ( A @ ( C @ ( B @ k6_funct_3 ) @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funct_3) ).
thf(13840,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ r2_hidden ) )
=> ( B @ ( A @ ( C @ ( B @ k6_funct_3 ) @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2200]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ k4_closure2 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k4_closure2 ) ) @ v2_relat_1 )
& ( C @ ( B @ ( A @ k4_closure2 ) ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_closure2) ).
thf(2770,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ k4_closure2 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k4_closure2 ) ) @ v2_relat_1 )
& ( C @ ( B @ ( A @ k4_closure2 ) ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1752,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r1_tarski ) ) )
=> ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r1_tarski ) )
| ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_mssubfam) ).
thf(11173,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
=> ( D @ ( B @ r1_tarski ) ) )
=> ( ( C @ ( A @ k8_setfam_1 ) @ ( B @ r1_tarski ) )
| ( C = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1752]) ).
thf(2206,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
=> ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_tex_2) ).
thf(13867,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
=> ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2206]) ).
thf(1559,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ k7_pboole ) ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_pboole) ).
thf(10147,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( A @ ( D @ ( C @ ( B @ ( A @ k7_pboole ) ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1559]) ).
thf(816,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ r1_tarski ) )
<=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(6255,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) )
=> ( B @ k1_tarski @ ( A @ r1_tarski ) ) )
& ( ( B @ k1_tarski @ ( A @ r1_tarski ) )
=> ( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(1955,axiom,
( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k36_binop_2 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k36_binop_2 @ v1_funct_2 ) ) )
& ( k36_binop_2 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k36_binop_2) ).
thf(12460,plain,
( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k36_binop_2 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k36_binop_2 @ v1_funct_2 ) ) )
& ( k36_binop_2 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1955]) ).
thf(2153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ k5_finsub_1 @ ( D @ ( C @ ( B @ ( A @ k10_setwiseo ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_setwiseo) ).
thf(13593,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ k5_finsub_1 @ ( D @ ( C @ ( B @ ( A @ k10_setwiseo ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2153]) ).
thf(1072,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k3_funct_2 ) ) ) )
= ( C @ k3_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_borsuk_1) ).
thf(7603,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k3_funct_2 ) ) ) )
= ( C @ k3_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(878,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ r1_partfun1 ) )
<=> ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_partfun1) ).
thf(6574,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
=> ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
=> ( B @ ( A @ r1_partfun1 ) ) )
& ( ( B @ ( A @ r1_partfun1 ) )
=> ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(2161,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r4_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_binop_1) ).
thf(13630,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r4_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ k1_binop_1 ) ) @ ( D @ ( B @ k1_binop_1 ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) @ ( E @ ( D @ ( B @ k1_binop_1 ) ) @ ( C @ k1_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2161]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_setwiseo ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setwiseo) ).
thf(2401,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k6_setwiseo ) ) )
= ( C @ ( B @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(617,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t169_funct_2) ).
thf(5216,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(887,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( C @ ( D @ k1_relat_1 @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( D @ k1_relat_1 @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_msualg_1) ).
thf(6609,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( C @ ( D @ k1_relat_1 @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( D @ k1_relat_1 @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(1035,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k8_relat_1 ) @ ( B @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_relat_1) ).
thf(7479,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k8_relat_1 ) @ ( B @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(1723,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ k1_funct_3 @ m2_relset_1 ) ) )
& ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ k1_funct_3 @ v1_funct_2 ) ) )
& ( C @ k1_funct_3 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_3) ).
thf(11041,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ k1_funct_3 @ m2_relset_1 ) ) )
& ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ k1_funct_3 @ v1_funct_2 ) ) )
& ( C @ k1_funct_3 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1723]) ).
thf(1969,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_5_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ~ ( C @ ( E @ r2_hidden ) )
<=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_5_domain_1) ).
thf(12534,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
=> ~ ( C @ ( E @ r2_hidden ) ) )
& ( ~ ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_5_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_5_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ( D @ ( E @ r2_hidden ) )
=> ~ ( C @ ( E @ r2_hidden ) ) )
& ( ~ ( C @ ( E @ r2_hidden ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1969]) ).
thf(893,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ v2_funct_1 )
=> ( B @ ( A @ k3_funct_3 @ k10_relat_1 ) @ ( B @ ( A @ k1_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_funct_3) ).
thf(6628,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ v2_funct_1 )
=> ( B @ ( A @ k3_funct_3 @ k10_relat_1 ) @ ( B @ ( A @ k1_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(1901,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_partfun1) ).
thf(12086,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1901]) ).
thf(1702,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( k1_xboole_0 @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_relset_1) ).
thf(10925,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( k1_xboole_0 @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1702]) ).
thf(1848,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_relset_1) ).
thf(11775,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ ( k1_xboole_0 @ ( C @ m2_relset_1 ) ) )
=> ( C = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1848]) ).
thf(1956,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_relat_1) ).
thf(12465,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( D @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k5_relat_1 ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1956]) ).
thf(2111,axiom,
! [A: $i] :
( ( A @ k5_finsub_1 @ ( A @ ( A @ k11_setwiseo @ m2_relset_1 ) ) )
& ( A @ k5_finsub_1 @ ( A @ ( A @ k11_setwiseo @ v1_funct_2 ) ) )
& ( A @ k11_setwiseo @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_setwiseo) ).
thf(13339,plain,
! [A: $i] :
( ( A @ k5_finsub_1 @ ( A @ ( A @ k11_setwiseo @ m2_relset_1 ) ) )
& ( A @ k5_finsub_1 @ ( A @ ( A @ k11_setwiseo @ v1_funct_2 ) ) )
& ( A @ k11_setwiseo @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2111]) ).
thf(810,axiom,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_setfam_1) ).
thf(6223,plain,
! [A: $i] :
( ~ ( A @ v2_setfam_1 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(1741,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finset_1) ).
thf(11113,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_finset_1 )
& ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1741]) ).
thf(445,axiom,
! [A: $i] : ( A @ k9_setwiseo @ ( A @ k9_setwiseo @ ( A @ k5_finsub_1 @ k3_binop_1 ) @ ( A @ k5_finsub_1 @ r3_binop_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_setwiseo) ).
thf(4362,plain,
! [A: $i] : ( A @ k9_setwiseo @ ( A @ k9_setwiseo @ ( A @ k5_finsub_1 @ k3_binop_1 ) @ ( A @ k5_finsub_1 @ r3_binop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( C @ ( B @ k1_closure2 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E
= ( D @ k1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( A @ ( E @ ( C @ ( B @ k4_closure2 ) ) @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) @ k1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_closure2) ).
thf(6816,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( C @ ( B @ k1_closure2 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E
= ( D @ k1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( A @ ( E @ ( C @ ( B @ k4_closure2 ) ) @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) @ k1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(689,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m2_relset_1 ) ) )
& ( A @ ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( A @ ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( G @ m2_relset_1 ) ) )
& ( A @ ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ! [H: $i,I: $i,J: $i,K: $i] :
( ( ( E @ ( K @ r2_hidden ) )
& ( D @ ( J @ r2_hidden ) )
& ( C @ ( I @ r2_hidden ) )
& ( B @ ( H @ r2_hidden ) ) )
=> ( ( K @ ( J @ ( I @ ( H @ k4_mcart_1 ) ) ) @ ( F @ k1_funct_1 ) )
= ( K @ ( J @ ( I @ ( H @ k4_mcart_1 ) ) ) @ ( G @ k1_funct_1 ) ) ) )
=> ( F = G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_multop_1) ).
thf(5575,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ m2_relset_1 ) ) )
& ( A @ ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( A @ ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( G @ m2_relset_1 ) ) )
& ( A @ ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ! [H: $i,I: $i,J: $i,K: $i] :
( ( ( E @ ( K @ r2_hidden ) )
& ( D @ ( J @ r2_hidden ) )
& ( C @ ( I @ r2_hidden ) )
& ( B @ ( H @ r2_hidden ) ) )
=> ( ( K @ ( J @ ( I @ ( H @ k4_mcart_1 ) ) ) @ ( F @ k1_funct_1 ) )
= ( K @ ( J @ ( I @ ( H @ k4_mcart_1 ) ) ) @ ( G @ k1_funct_1 ) ) ) )
=> ( F = G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(2392,axiom,
( ( ! [A: $i] :
( ( f1_s23_fraenkel @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s23_fraenkel @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s23_fraenkel @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ p1_s23_fraenkel ) )
& ( B @ ( A @ p1_s23_fraenkel ) ) )
=> ( C @ ( A @ p1_s23_fraenkel ) ) ) ) ) )
& ! [A: $i] :
( ( f1_s23_fraenkel @ ( A @ m1_subset_1 ) )
=> ( A @ ( A @ p1_s23_fraenkel ) ) ) )
=> ! [A: $i] :
( ( f1_s23_fraenkel @ ( A @ m1_subset_1 ) )
=> ~ ( ! [B: $i] :
( ( f1_s23_fraenkel @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( f1_s23_fraenkel @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ p1_s23_fraenkel ) )
& ( f2_s23_fraenkel @ ( C @ r2_hidden ) ) )
=> ( C @ ( B @ p1_s23_fraenkel ) ) ) )
& ( A @ ( B @ p1_s23_fraenkel ) )
& ( f2_s23_fraenkel @ ( B @ r2_hidden ) ) ) )
& ( f2_s23_fraenkel @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s23_fraenkel) ).
thf(14660,plain,
( ( ! [A: $i] :
( ( f1_s23_fraenkel @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s23_fraenkel @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s23_fraenkel @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ p1_s23_fraenkel ) )
& ( B @ ( A @ p1_s23_fraenkel ) ) )
=> ( C @ ( A @ p1_s23_fraenkel ) ) ) ) ) )
& ! [A: $i] :
( ( f1_s23_fraenkel @ ( A @ m1_subset_1 ) )
=> ( A @ ( A @ p1_s23_fraenkel ) ) ) )
=> ! [A: $i] :
( ( f1_s23_fraenkel @ ( A @ m1_subset_1 ) )
=> ~ ( ! [B: $i] :
( ( f1_s23_fraenkel @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( f1_s23_fraenkel @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( C @ p1_s23_fraenkel ) )
& ( f2_s23_fraenkel @ ( C @ r2_hidden ) ) )
=> ( C @ ( B @ p1_s23_fraenkel ) ) ) )
& ( A @ ( B @ p1_s23_fraenkel ) )
& ( f2_s23_fraenkel @ ( B @ r2_hidden ) ) ) )
& ( f2_s23_fraenkel @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2392]) ).
thf(1338,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( C @ ( A @ k1_funct_2 ) )
= k1_xboole_0 )
& ( ( C @ ( B @ k1_funct_2 ) )
!= k1_xboole_0 )
& ( ( B @ ( A @ k1_funct_2 ) )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_altcat_1) ).
thf(9106,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( C @ ( A @ k1_funct_2 ) )
= k1_xboole_0 )
& ( ( C @ ( B @ k1_funct_2 ) )
!= k1_xboole_0 )
& ( ( B @ ( A @ k1_funct_2 ) )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ k3_pua2mss1 )
= ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_relset_2) ).
thf(2752,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ k3_pua2mss1 )
= ( B @ k3_pua2mss1 @ ( A @ k3_pua2mss1 @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1944,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( E @ m1_eqrel_1 ) )
& ( B @ ( D @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ a_4_0_pua2mss1 ) ) ) @ ( A @ r2_hidden ) )
<=> ? [F: $i,G: $i] :
( ( A
= ( G @ ( F @ ( C @ ( B @ k12_mcart_1 ) ) ) ) )
& ( E @ ( C @ k1_zfmisc_1 @ ( G @ m2_subset_1 ) ) )
& ( D @ ( B @ k1_zfmisc_1 @ ( F @ m2_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_0_pua2mss1) ).
thf(12409,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( E @ m1_eqrel_1 ) )
& ( B @ ( D @ m1_eqrel_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [F: $i,G: $i] :
( ( A
= ( G @ ( F @ ( C @ ( B @ k12_mcart_1 ) ) ) ) )
& ( E @ ( C @ k1_zfmisc_1 @ ( G @ m2_subset_1 ) ) )
& ( D @ ( B @ k1_zfmisc_1 @ ( F @ m2_subset_1 ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ a_4_0_pua2mss1 ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( E @ ( D @ ( C @ ( B @ a_4_0_pua2mss1 ) ) ) @ ( A @ r2_hidden ) )
=> ? [F: $i,G: $i] :
( ( A
= ( G @ ( F @ ( C @ ( B @ k12_mcart_1 ) ) ) ) )
& ( E @ ( C @ k1_zfmisc_1 @ ( G @ m2_subset_1 ) ) )
& ( D @ ( B @ k1_zfmisc_1 @ ( F @ m2_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1944]) ).
thf(2008,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( E @ ( D @ ( C @ k3_funcop_1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( C @ k3_funcop_1 ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ k3_funcop_1 ) ) @ v1_funct_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_funcop_1) ).
thf(12765,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( E @ ( D @ ( C @ k3_funcop_1 ) ) @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ ( D @ ( C @ k3_funcop_1 ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ k3_funcop_1 ) ) @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2008]) ).
thf(215,axiom,
! [A: $i] : ( A @ ( A @ ( A @ k6_partfun1 @ v2_funct_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_functor1) ).
thf(3310,plain,
! [A: $i] : ( A @ ( A @ ( A @ k6_partfun1 @ v2_funct_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(1744,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_0_card_fil ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( D @ ( B @ k3_subset_1 ) @ r2_hidden ) )
& ( A = D )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_card_fil) ).
thf(11130,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ ( B @ k3_subset_1 ) @ r2_hidden ) )
& ( A = D )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_card_fil ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_card_fil ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( D @ ( B @ k3_subset_1 ) @ r2_hidden ) )
& ( A = D )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1744]) ).
thf(1262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_mcart_1) ).
thf(8676,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k1_tarski @ ( B @ k1_tarski @ ( A @ k1_tarski @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k4_mcart_1 ) ) ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(505,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) )
= ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_relat_1) ).
thf(4703,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k7_relat_1 ) )
= ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(1606,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( k9_zf_lang @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k9_zf_lang @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ r1_zfrefle1 ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( B @ ( A @ r1_zfrefle1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfrefle1) ).
thf(10424,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( k9_zf_lang @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k9_zf_lang @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ r1_zfrefle1 ) )
& ( C @ ( B @ r1_tarski ) ) )
=> ( B @ ( A @ r1_zfrefle1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1606]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
| ( A @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(3512,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r1_tarski ) )
| ( A @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(1934,axiom,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc8_finseq_1) ).
thf(12308,plain,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1934]) ).
thf(771,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_finseq_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_funct_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finseq_1) ).
thf(6027,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_finseq_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_funct_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( A @ k3_pua2mss1 @ ( B @ m2_finseq_1 ) )
=> ? [C: $i] :
( ( ( B @ k4_card_3 )
= ( C @ k1_tarski ) )
& ( A @ ( C @ m2_finseq_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_pua2mss1) ).
thf(3178,plain,
! [A: $i,B: $i] :
( ( A @ k3_pua2mss1 @ ( B @ m2_finseq_1 ) )
=> ? [C: $i] :
( ( ( B @ k4_card_3 )
= ( C @ k1_tarski ) )
& ( A @ ( C @ m2_finseq_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1937,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ k1_funct_2 ) @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_2) ).
thf(12341,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ k1_funct_2 ) @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1937]) ).
thf(888,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ k10_funct_3 ) @ ( E @ ( C @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( B @ k10_funct_3 ) @ ( D @ ( C @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ ( C @ ( A @ r4_nattra_1 ) ) ) ) ) )
& ( C @ ( B @ k9_funct_3 ) @ ( E @ ( B @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( B @ k9_funct_3 ) @ ( D @ ( B @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_funct_2 ) ) ) ) @ ( B @ ( A @ ( B @ ( A @ r4_nattra_1 ) ) ) ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_isocat_2) ).
thf(6614,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( C @ ( B @ k10_funct_3 ) @ ( E @ ( C @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( B @ k10_funct_3 ) @ ( D @ ( C @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ ( C @ ( A @ r4_nattra_1 ) ) ) ) ) )
& ( C @ ( B @ k9_funct_3 ) @ ( E @ ( B @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( B @ k9_funct_3 ) @ ( D @ ( B @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k7_funct_2 ) ) ) ) @ ( B @ ( A @ ( B @ ( A @ r4_nattra_1 ) ) ) ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(2079,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finset_1) ).
thf(13208,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A @ v6_ordinal1 )
& ( A != k1_xboole_0 )
& ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2079]) ).
thf(1807,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_subset_1) ).
thf(11493,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r2_hidden ) ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1807]) ).
thf(1149,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k4_card_3 @ v1_fraenkel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_card_3) ).
thf(8035,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k4_card_3 @ v1_fraenkel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(557,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_domain_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_mcart_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_domain_1) ).
thf(4965,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( H @ m1_subset_1 ) )
& ( C @ ( G @ m1_subset_1 ) )
& ( B @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_domain_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_mcart_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(1623,axiom,
! [A: $i] :
~ ( ! [B: $i,C: $i] :
~ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
& ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funct_4) ).
thf(10499,plain,
! [A: $i] :
~ ( ! [B: $i,C: $i] :
~ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
& ! [B: $i] :
~ ( ! [C: $i,D: $i] :
( B
!= ( D @ ( C @ k4_tarski ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1623]) ).
thf(1783,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).
thf(11361,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1783]) ).
thf(140,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k4_relat_1 @ v1_relat_1 )
& ( A @ k4_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(2984,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k4_relat_1 @ v1_relat_1 )
& ( A @ k4_relat_1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(2342,axiom,
! [A: $i] :
( ( a_0_2_domain_1 @ ( A @ r2_hidden ) )
<=> ? [B: $i,C: $i] :
( ( C @ ( B @ p1_s9_domain_1 ) )
& ( A
= ( C @ ( B @ f4_s9_domain_1 ) ) )
& ( f2_s9_domain_1 @ ( C @ m1_subset_1 ) )
& ( f1_s9_domain_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_2_domain_1) ).
thf(14427,plain,
! [A: $i] :
( ( ? [B: $i,C: $i] :
( ( C @ ( B @ p1_s9_domain_1 ) )
& ( A
= ( C @ ( B @ f4_s9_domain_1 ) ) )
& ( f2_s9_domain_1 @ ( C @ m1_subset_1 ) )
& ( f1_s9_domain_1 @ ( B @ m1_subset_1 ) ) )
=> ( a_0_2_domain_1 @ ( A @ r2_hidden ) ) )
& ( ( a_0_2_domain_1 @ ( A @ r2_hidden ) )
=> ? [B: $i,C: $i] :
( ( C @ ( B @ p1_s9_domain_1 ) )
& ( A
= ( C @ ( B @ f4_s9_domain_1 ) ) )
& ( f2_s9_domain_1 @ ( C @ m1_subset_1 ) )
& ( f1_s9_domain_1 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2342]) ).
thf(464,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B
= ( A @ k3_funct_3 ) )
<=> ( ! [C: $i] :
( ( A @ k2_relat_1 @ ( C @ r1_tarski ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ ( A @ k10_relat_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 @ k1_zfmisc_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funct_3) ).
thf(4481,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ! [C: $i] :
( ( A @ k2_relat_1 @ ( C @ r1_tarski ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ ( A @ k10_relat_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 @ k1_zfmisc_1 ) ) )
=> ( B
= ( A @ k3_funct_3 ) ) )
& ( ( B
= ( A @ k3_funct_3 ) )
=> ( ! [C: $i] :
( ( A @ k2_relat_1 @ ( C @ r1_tarski ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ ( A @ k10_relat_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ k2_relat_1 @ k1_zfmisc_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(921,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
| ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
thf(6785,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
| ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( B @ ( A @ k4_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k4_xboole_0 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc38_membered) ).
thf(2506,plain,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( B @ ( A @ k4_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k4_xboole_0 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(2192,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( D @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) @ ( D @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_2) ).
thf(13806,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ ( D @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( B @ ( C @ k1_funct_1 ) @ ( D @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2192]) ).
thf(975,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ k1_enumset1 ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_finset_1) ).
thf(7049,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ k1_enumset1 ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(1314,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( A @ k1_tarski ) )
=> ( ( B @ k2_relat_1 )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_1) ).
thf(8965,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= ( A @ k1_tarski ) )
=> ( ( B @ k2_relat_1 )
= ( A @ ( B @ k1_funct_1 ) @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314]) ).
thf(1592,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_relat_1) ).
thf(10322,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ! [D: $i] :
( ( D @ v1_relat_1 )
=> ( ( ( B @ ( A @ r1_tarski ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( B @ ( D @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1592]) ).
thf(1364,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_filter_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_filter_1) ).
thf(9227,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_filter_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(984,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ ( B @ k5_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t122_relat_1) ).
thf(7151,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ ( B @ k5_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(129,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k5_funct_5 )
= ( A @ k2_funct_4 @ k3_funct_5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_5) ).
thf(2927,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k5_funct_5 )
= ( A @ k2_funct_4 @ k3_funct_5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1866,axiom,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
thf(11872,plain,
! [A: $i,B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
~ ( ( C @ ( D @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1866]) ).
thf(907,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( ( A @ ( C @ ( B @ k1_funct_4 ) @ k5_relat_1 ) )
= ( A @ ( C @ k5_relat_1 ) @ ( A @ ( B @ k5_relat_1 ) @ k1_funct_4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_funct_7) ).
thf(6719,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( ( A @ ( C @ ( B @ k1_funct_4 ) @ k5_relat_1 ) )
= ( A @ ( C @ k5_relat_1 ) @ ( A @ ( B @ k5_relat_1 ) @ k1_funct_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(1614,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k1_cantor_1 ) )
= ( k1_xboole_0 @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_yellow_9) ).
thf(10456,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k1_cantor_1 ) )
= ( k1_xboole_0 @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1614]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_partfun1) ).
thf(3009,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C @ ( A @ ( D @ k1_funct_1 ) @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) )
& ( D @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ k3_partfun1 ) ) @ k1_funct_1 ) )
= ( A @ ( D @ k1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(2034,axiom,
( ( f2_s21_fraenkel @ v1_finset_1 )
=> ( a_0_38_fraenkel @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s21_fraenkel) ).
thf(12922,plain,
( ( f2_s21_fraenkel @ v1_finset_1 )
=> ( a_0_38_fraenkel @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2034]) ).
thf(1627,axiom,
! [A: $i] :
( ( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ~ ( B @ v1_realset1 )
& ~ ( B @ v1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc7_tex_2) ).
thf(10517,plain,
! [A: $i] :
( ( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ~ ( B @ v1_realset1 )
& ~ ( B @ v1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1627]) ).
thf(1651,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k6_partfun1 @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( B @ ( A @ k6_partfun1 @ ( A @ ( A @ k8_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_closure2) ).
thf(10617,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( C @ ( A @ k6_partfun1 @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( B @ ( A @ k6_partfun1 @ ( A @ ( A @ k8_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1651]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k1_relset_2 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_relset_2) ).
thf(4426,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k1_relset_2 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(413,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( E @ ( B @ r5_binop_1 ) ) )
& ( D @ ( C @ ( A @ r5_binop_1 ) ) ) )
<=> ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r5_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_filter_1) ).
thf(4207,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r5_binop_1 ) ) )
=> ( ( F @ ( E @ ( B @ r5_binop_1 ) ) )
& ( D @ ( C @ ( A @ r5_binop_1 ) ) ) ) )
& ( ( ( F @ ( E @ ( B @ r5_binop_1 ) ) )
& ( D @ ( C @ ( A @ r5_binop_1 ) ) ) )
=> ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r5_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(1926,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k7_pboole ) ) ) )
= ( D @ ( C @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_pboole) ).
thf(12207,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_pboole ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k7_pboole ) ) ) )
= ( D @ ( C @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1926]) ).
thf(2096,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( A @ r1_lattice2 ) ) )
& ( F
= ( B @ ( D @ k1_realset1 ) ) )
& ( E
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( F @ ( E @ ( B @ r1_lattice2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_filter_2) ).
thf(13278,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( A @ r1_lattice2 ) ) )
& ( F
= ( B @ ( D @ k1_realset1 ) ) )
& ( E
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( F @ ( E @ ( B @ r1_lattice2 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2096]) ).
thf(2285,axiom,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s11_funct_2 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
!= ( B @ f7_s11_funct_2 ) )
& ( B != f4_s11_funct_2 )
& ( B != f3_s11_funct_2 ) ) )
& ( ( f4_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f6_s11_funct_2 )
& ( ( f3_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f5_s11_funct_2 )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s11_funct_2) ).
thf(14190,plain,
( ( f3_s11_funct_2 != f4_s11_funct_2 )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s11_funct_2 @ ( B @ m1_subset_1 ) )
=> ~ ( ( ( B @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
!= ( B @ f7_s11_funct_2 ) )
& ( B != f4_s11_funct_2 )
& ( B != f3_s11_funct_2 ) ) )
& ( ( f4_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f6_s11_funct_2 )
& ( ( f3_s11_funct_2 @ ( A @ ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ k8_funct_2 ) ) ) )
= f5_s11_funct_2 )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s11_funct_2 @ ( f1_s11_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2285]) ).
thf(828,axiom,
! [A: $i] :
( ( A @ k20_mcart_1 )
= ( A @ k2_mcart_1 @ k2_mcart_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_mcart_1) ).
thf(6320,plain,
! [A: $i] :
( ( A @ k20_mcart_1 )
= ( A @ k2_mcart_1 @ k2_mcart_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(679,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( E @ ( B @ r4_binop_1 ) ) )
& ( D @ ( C @ ( A @ r4_binop_1 ) ) ) )
<=> ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r4_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_filter_1) ).
thf(5538,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r4_binop_1 ) ) )
=> ( ( F @ ( E @ ( B @ r4_binop_1 ) ) )
& ( D @ ( C @ ( A @ r4_binop_1 ) ) ) ) )
& ( ( ( F @ ( E @ ( B @ r4_binop_1 ) ) )
& ( D @ ( C @ ( A @ r4_binop_1 ) ) ) )
=> ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r4_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(947,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
=> ( ( ( B @ ( A @ k6_partfun1 @ ( A @ ( A @ ( A @ ( A @ k7_relset_1 ) ) ) ) ) )
= B )
& ( ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ ( A @ ( A @ k7_relset_1 ) ) ) ) ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_funct_2) ).
thf(6890,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
=> ( ( ( B @ ( A @ k6_partfun1 @ ( A @ ( A @ ( A @ ( A @ k7_relset_1 ) ) ) ) ) )
= B )
& ( ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ ( A @ ( A @ k7_relset_1 ) ) ) ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(690,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_relat_1) ).
thf(5587,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( C @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(2070,axiom,
( ! [A: $i] :
( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s13_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s13_funct_2 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s13_funct_2) ).
thf(13168,plain,
( ! [A: $i] :
( ( f1_s13_funct_2 @ ( A @ m1_subset_1 ) )
=> ( f2_s13_funct_2 @ ( A @ f3_s13_funct_2 @ m1_subset_1 ) ) )
=> ? [A: $i] :
( ! [B: $i] :
( ( f1_s13_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s13_funct_2 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s13_funct_2 @ ( f1_s13_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2070]) ).
thf(1038,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_partfun1) ).
thf(7490,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_partfun1) ).
thf(3193,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( k1_xboole_0 @ k3_partfun1 ) ) @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1888,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ ( B @ k9_relat_1 ) @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finset_1) ).
thf(12021,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ v1_finset_1 )
=> ( A @ ( B @ k9_relat_1 ) @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1888]) ).
thf(2265,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k12_mcart_1) ).
thf(14126,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) )
= ( D @ ( C @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2265]) ).
thf(1834,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A = k1_xboole_0 )
=> ( ( A @ ( B @ m1_eqrel_1 ) )
<=> ( B = k1_xboole_0 ) ) )
& ( ( A != k1_xboole_0 )
=> ( ( A @ ( B @ m1_eqrel_1 ) )
<=> ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r1_xboole_0 ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( C != k1_xboole_0 ) ) ) )
& ( ( B @ ( A @ k5_setfam_1 ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_eqrel_1) ).
thf(11654,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A = k1_xboole_0 )
=> ( ( ( B = k1_xboole_0 )
=> ( A @ ( B @ m1_eqrel_1 ) ) )
& ( ( A @ ( B @ m1_eqrel_1 ) )
=> ( B = k1_xboole_0 ) ) ) )
& ( ( A != k1_xboole_0 )
=> ( ( ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r1_xboole_0 ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( C != k1_xboole_0 ) ) ) )
& ( ( B @ ( A @ k5_setfam_1 ) )
= A ) )
=> ( A @ ( B @ m1_eqrel_1 ) ) )
& ( ( A @ ( B @ m1_eqrel_1 ) )
=> ( ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( B @ ( C @ r2_hidden ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ~ ( D @ ( C @ r1_xboole_0 ) )
& ( C != D )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( C != k1_xboole_0 ) ) ) )
& ( ( B @ ( A @ k5_setfam_1 ) )
= A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1834]) ).
thf(1136,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ v4_finsub_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finsub_1) ).
thf(7896,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ v4_finsub_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(1008,axiom,
~ ( k5_numbers @ v1_finset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_card_4) ).
thf(7296,plain,
~ ( k5_numbers @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(1726,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k1_closure2 ) @ k7_subset_1 ) ) @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_closure2) ).
thf(11062,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k1_closure2 ) @ k7_subset_1 ) ) @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1726]) ).
thf(820,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( C @ k10_relat_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( C @ ( D @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ k2_relat_1 @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
thf(6276,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( C @ ( D @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ k2_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ r2_hidden ) ) )
& ( ( B @ ( C @ k10_relat_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( B @ ( D @ r2_hidden ) )
& ( C @ ( D @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( C @ k2_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(2239,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( D @ ( F @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) ) ) )
=> ( D @ ( C @ ( E @ ( B @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_setwiseo) ).
thf(14012,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ r2_hidden ) )
=> ( D @ ( F @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) ) ) )
=> ( D @ ( C @ ( E @ ( B @ ( A @ k2_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2239]) ).
thf(2325,axiom,
! [A: $i] :
( ( a_0_0_card_fil @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ( B @ p1_s1_card_fil )
& ( A = B )
& ( f1_s1_card_fil @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_0_card_fil) ).
thf(14349,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ p1_s1_card_fil )
& ( A = B )
& ( f1_s1_card_fil @ ( B @ m1_subset_1 ) ) )
=> ( a_0_0_card_fil @ ( A @ r2_hidden ) ) )
& ( ( a_0_0_card_fil @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ( B @ p1_s1_card_fil )
& ( A = B )
& ( f1_s1_card_fil @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2325]) ).
thf(1567,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relset_2) ).
thf(10191,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567]) ).
thf(485,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( B @ ( A @ k6_pralg_1 ) @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_pralg_1) ).
thf(4580,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( B @ ( A @ k6_pralg_1 ) @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(1141,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i] :
~ ( ( B
= ( F @ ( E @ ( D @ ( C @ k4_mcart_1 ) ) ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_mcart_1) ).
thf(7975,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i,F: $i] :
~ ( ( B
= ( F @ ( E @ ( D @ ( C @ k4_mcart_1 ) ) ) ) )
& ( ( A @ ( D @ r2_hidden ) )
| ( A @ ( C @ r2_hidden ) ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(2203,axiom,
! [A: $i] :
( ( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( B @ v1_realset1 )
& ~ ( B @ v1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_tex_2) ).
thf(13852,plain,
! [A: $i] :
( ( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( B @ v1_realset1 )
& ~ ( B @ v1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2203]) ).
thf(1372,axiom,
? [A: $i] :
( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_realset1) ).
thf(9259,plain,
? [A: $i] :
( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).
thf(1621,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( D @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ( F @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( E @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A @ ( F @ m1_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_setwiseo) ).
thf(10488,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ? [F: $i] :
( ( F @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( E @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A @ ( F @ m1_subset_1 ) ) )
=> ( C @ ( D @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( E @ r2_hidden ) ) )
& ( ( C @ ( D @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( F @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( E @ r2_hidden ) )
& ( D @ ( F @ r2_hidden ) )
& ( A @ ( F @ m1_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1621]) ).
thf(1009,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( D
= ( C @ ( B @ ( A @ k5_partfun1 ) ) ) )
<=> ! [E: $i] :
( ( D @ ( E @ r2_hidden ) )
<=> ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_partfun1) ).
thf(7298,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ! [E: $i] :
( ( ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( ( D @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) ) ) )
=> ( D
= ( C @ ( B @ ( A @ k5_partfun1 ) ) ) ) )
& ( ( D
= ( C @ ( B @ ( A @ k5_partfun1 ) ) ) )
=> ! [E: $i] :
( ( ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( ( D @ ( E @ r2_hidden ) )
=> ? [F: $i] :
( ( F @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( F @ v1_partfun1 ) ) )
& ( F = E )
& ( B @ ( A @ ( F @ m2_relset_1 ) ) )
& ( F @ v1_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(175,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_finseq_1 )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m2_finseq_1 ) )
=> ( ( E
= ( G @ ( D @ ( F @ k5_funcop_1 ) ) ) )
=> ( ( E @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_finseq_2) ).
thf(3161,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_finseq_1 )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m2_finseq_1 ) )
=> ( ( E
= ( G @ ( D @ ( F @ k5_funcop_1 ) ) ) )
=> ( ( E @ k3_finseq_1 )
= ( G @ k3_finseq_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(1286,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( ( C @ ( D @ r1_tarski ) )
| ( C @ ( D @ r1_xboole_0 ) ) ) ) )
=> ( C
= ( C @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k3_funct_2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_borsuk_1) ).
thf(8804,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
=> ( ( C @ ( D @ r1_tarski ) )
| ( C @ ( D @ r1_xboole_0 ) ) ) ) )
=> ( C
= ( C @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k3_funct_2 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(514,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( D @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funcop_1) ).
thf(4735,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( D @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(1579,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( B @ v1_xboole_0 ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( A @ ( B @ m1_subset_1 ) )
<=> ( A @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(10249,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_xboole_0 )
=> ( ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xboole_0 ) ) ) )
& ( ~ ( A @ v1_xboole_0 )
=> ( ( ( A @ ( B @ r2_hidden ) )
=> ( A @ ( B @ m1_subset_1 ) ) )
& ( ( A @ ( B @ m1_subset_1 ) )
=> ( A @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1579]) ).
thf(899,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ k1_funct_4 ) )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_closure3) ).
thf(6659,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_pboole ) )
=> ( ( C @ ( B @ k1_funct_4 ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(1492,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_domain_1) ).
thf(9826,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1492]) ).
thf(1059,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_setwiseo ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_setwiseo) ).
thf(7562,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k2_setwiseo ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(1052,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funcop_1) ).
thf(7539,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( B @ ( A @ k2_funcop_1 ) @ k10_relat_1 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(1731,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_zfmisc_1) ).
thf(11077,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1731]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
<=> ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(2878,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ r2_hidden ) )
=> ( ( A != C )
& ( B @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_xboole_1) ).
thf(2503,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ ( A @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1167,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k4_tarski ) @ ( C @ ( A @ k4_tarski ) @ k2_tarski ) ) )
& ( ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( C @ ( A @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_zfmisc_1) ).
thf(8116,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_tarski @ ( B @ ( A @ k2_tarski ) @ k2_zfmisc_1 ) )
= ( C @ ( B @ k4_tarski ) @ ( C @ ( A @ k4_tarski ) @ k2_tarski ) ) )
& ( ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k2_zfmisc_1 ) )
= ( C @ ( A @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(803,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_realset1 ) @ v1_funct_1 )
& ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_realset1) ).
thf(6191,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_realset1 ) @ v1_funct_1 )
& ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(750,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t157_funct_1) ).
thf(5952,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( C @ k1_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(1229,axiom,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_zfmisc_1) ).
thf(8505,plain,
! [A: $i,B: $i] :
~ ( ( A = B )
& ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(430,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k5_setfam_1 ) @ ( C @ k9_relat_1 ) )
= ( C @ ( B @ ( A @ a_3_0_relset_2 ) ) @ k3_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_2) ).
thf(4292,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k5_setfam_1 ) @ ( C @ k9_relat_1 ) )
= ( C @ ( B @ ( A @ a_3_0_relset_2 ) ) @ k3_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(1283,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ k4_funcop_1 ) ) )
= ( A @ ( C @ ( B @ k1_relat_1 @ k2_funcop_1 ) @ ( B @ k13_funct_3 ) @ k5_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funcop_1) ).
thf(8789,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ k4_funcop_1 ) ) )
= ( A @ ( C @ ( B @ k1_relat_1 @ k2_funcop_1 ) @ ( B @ k13_funct_3 ) @ k5_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(1405,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) )
=> ( ( A @ ( C @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_funcop_1) ).
thf(9408,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) )
=> ( ( A @ ( C @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405]) ).
thf(2277,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(14175,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k4_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2277]) ).
thf(2338,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k2_cat_5 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_cat_5) ).
thf(14406,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k2_cat_5 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2338]) ).
thf(2343,axiom,
! [A: $i] :
( ( A @ v1_fraenkel )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_fraenkel ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_altcat_1) ).
thf(14438,plain,
! [A: $i] :
( ( A @ v1_fraenkel )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_fraenkel ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2343]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) )
= ( D @ ( C @ k3_funct_4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_filter_1) ).
thf(4566,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) )
= ( D @ ( C @ k3_funct_4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(541,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( B @ k1_domain_1 ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ k6_domain_1 ) @ ( C @ k6_partfun1 @ ( D @ ( C @ ( B @ ( C @ ( A @ k16_funct_3 ) ) ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_funct_2 ) ) ) )
= ( F @ ( C @ k6_domain_1 ) @ ( E @ ( B @ k6_domain_1 ) @ ( D @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( C @ ( A @ k12_mcart_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_borsuk_1) ).
thf(4859,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( B @ k1_domain_1 ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ k6_domain_1 ) @ ( C @ k6_partfun1 @ ( D @ ( C @ ( B @ ( C @ ( A @ k16_funct_3 ) ) ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k3_funct_2 ) ) ) )
= ( F @ ( C @ k6_domain_1 ) @ ( E @ ( B @ k6_domain_1 ) @ ( D @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( C @ ( A @ k12_mcart_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(1164,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( E @ ( B @ r1_lattice2 ) ) )
& ( D @ ( C @ ( A @ r1_lattice2 ) ) ) )
<=> ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_lattice2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_filter_1) ).
thf(8106,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_lattice2 ) ) )
=> ( ( F @ ( E @ ( B @ r1_lattice2 ) ) )
& ( D @ ( C @ ( A @ r1_lattice2 ) ) ) ) )
& ( ( ( F @ ( E @ ( B @ r1_lattice2 ) ) )
& ( D @ ( C @ ( A @ r1_lattice2 ) ) ) )
=> ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_lattice2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(350,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(3921,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(2360,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relset_2) ).
thf(14530,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2360]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_relat_1) ).
thf(2846,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( B @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ k1_enumset1 ) ) @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_setwiseo) ).
thf(4113,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ k1_enumset1 ) ) @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k3_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k3_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( A @ ( B @ k3_funct_5 @ k1_funct_1 ) @ v1_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_5) ).
thf(3278,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k3_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k3_funct_5 @ k1_funct_1 ) @ v1_funct_1 )
& ( A @ ( B @ k3_funct_5 @ k1_funct_1 ) @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(717,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ ( A @ k1_tarski @ m1_card_fil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_card_fil) ).
thf(5710,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ ( A @ k1_tarski @ m1_card_fil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(2130,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k8_funct_2 ) ) ) )
= ( F @ ( E @ ( C @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ k4_tarski ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funct_3) ).
thf(13454,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ ( E @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k8_funct_2 ) ) ) )
= ( F @ ( E @ ( C @ ( A @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ k4_tarski ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2130]) ).
thf(1366,axiom,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( B @ ( A @ k2_funcop_1 ) @ k2_relat_1 )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funcop_1) ).
thf(9232,plain,
! [A: $i,B: $i] :
( ( A != k1_xboole_0 )
=> ( ( B @ ( A @ k2_funcop_1 ) @ k2_relat_1 )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ v2_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_partfun1) ).
thf(7137,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( C @ v2_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(1377,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) )
= ( F @ ( E @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_relset_1) ).
thf(9276,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) )
= ( F @ ( E @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377]) ).
thf(727,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k1_yellow_3 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_3) ).
thf(5763,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k1_yellow_3 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(1304,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ k10_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t168_relat_1) ).
thf(8885,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k10_relat_1 ) )
= ( A @ ( B @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ k10_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).
thf(2294,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(14240,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2294]) ).
thf(849,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m2_card_fil ) )
=> ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_card_fil) ).
thf(6440,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m2_card_fil ) )
=> ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(563,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_xboole_0 ) )
& ( C @ ( B @ r1_xboole_0 ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_subset_1) ).
thf(4986,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( C @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k3_subset_1 ) @ r1_xboole_0 ) )
& ( C @ ( B @ r1_xboole_0 ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(1355,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( C @ ( B @ ( A @ k3_realset1 ) ) )
= ( B @ ( C @ k1_realset1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_realset1) ).
thf(9202,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_realset1 ) ) )
=> ( ( C @ ( B @ ( A @ k3_realset1 ) ) )
= ( B @ ( C @ k1_realset1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).
thf(794,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k2_ens_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_ens_1 ) ) @ ( D @ r2_hidden ) )
=> ( D
= ( D @ k2_mcart_1 @ ( C @ ( B @ ( A @ ( A @ k1_domain_1 ) ) ) @ k4_tarski ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_ens_1) ).
thf(6132,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k2_ens_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k7_ens_1 ) ) @ ( D @ r2_hidden ) )
=> ( D
= ( D @ k2_mcart_1 @ ( C @ ( B @ ( A @ ( A @ k1_domain_1 ) ) ) @ k4_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(2073,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_funct_3 ) ) @ m2_relset_1 ) ) )
& ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_funct_3 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_funct_3 ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_3) ).
thf(13189,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_funct_3 ) ) @ m2_relset_1 ) ) )
& ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k2_funct_3 ) ) @ v1_funct_2 ) ) )
& ( C @ ( B @ ( A @ k2_funct_3 ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2073]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m2_fraenkel ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_fraenkel) ).
thf(3849,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m2_fraenkel ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(805,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_orders_1) ).
thf(6202,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(1388,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_partfun1) ).
thf(9317,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388]) ).
thf(1816,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_2) ).
thf(11540,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
=> ( ( ( C @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
| ( ( A != k1_xboole_0 )
& ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1816]) ).
thf(596,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_zfmisc_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_zfmisc_1) ).
thf(5125,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( D @ ( A @ k2_zfmisc_1 ) @ k3_xboole_0 ) )
= ( C @ ( A @ k2_zfmisc_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(647,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( A @ ( k1_xboole_0 @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_partfun1) ).
thf(5388,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( B @ k2_relat_1 )
= k1_xboole_0 )
& ( ( B @ ( A @ ( k1_xboole_0 @ k4_relset_1 ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(1695,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_subset_1) ).
thf(10856,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1695]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(3214,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(1468,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k13_funct_3 ) )
= ( C @ ( D @ k13_funct_3 ) ) )
& ( ( D @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( ( B = C )
& ( A = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_funct_3) ).
thf(9710,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( B @ ( A @ k13_funct_3 ) )
= ( C @ ( D @ k13_funct_3 ) ) )
& ( ( D @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( ( B = C )
& ( A = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468]) ).
thf(1519,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( B @ k5_funcop_1 ) ) @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ ( D @ ( B @ k5_funcop_1 ) ) @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) @ ( D @ ( B @ k1_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_funcop_1) ).
thf(9953,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( B @ k5_funcop_1 ) ) @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ ( D @ ( B @ k5_funcop_1 ) ) @ k1_funct_1 ) )
= ( C @ ( A @ k1_funct_1 ) @ ( D @ ( B @ k1_binop_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1519]) ).
thf(1628,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(10521,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1628]) ).
thf(1127,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_relat_1) ).
thf(7864,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
=> ( ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(1766,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ r1_tarski ) )
& ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_funct_5) ).
thf(11230,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ r1_tarski ) )
& ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1766]) ).
thf(132,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ k5_funct_5 @ m2_relset_1 ) ) )
& ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ k5_funct_5 @ v1_funct_2 ) ) )
& ( D @ k5_funct_5 @ v1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_cat_2) ).
thf(2942,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ k5_funct_5 @ m2_relset_1 ) ) )
& ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ k5_funct_5 @ v1_funct_2 ) ) )
& ( D @ k5_funct_5 @ v1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1007,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v5_monoid_0 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ? [F: $i] :
( ( ( C @ ( F @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D )
& ( ( E @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D )
& ( A @ ( F @ m1_subset_1 ) ) )
& ( A @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_monoid_0) ).
thf(7283,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ? [F: $i] :
( ( ( C @ ( F @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D )
& ( ( E @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D )
& ( A @ ( F @ m1_subset_1 ) ) )
& ( A @ ( E @ m1_subset_1 ) ) ) ) )
=> ( A @ ( B @ v5_monoid_0 ) ) )
& ( ( A @ ( B @ v5_monoid_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ? [F: $i] :
( ( ( C @ ( F @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D )
& ( ( E @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D )
& ( A @ ( F @ m1_subset_1 ) ) )
& ( A @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(2376,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_pcomps_1 @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pcomps_1) ).
thf(14594,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_pcomps_1 @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2376]) ).
thf(579,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) )
= ( A @ ( C @ k10_relat_1 ) @ ( B @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t181_relat_1) ).
thf(5047,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) )
= ( A @ ( C @ k10_relat_1 ) @ ( B @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(2311,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( E @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ a_6_0_relset_2 ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s8_domain_1__e1_46__relset_2) ).
thf(14304,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( E @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ a_6_0_relset_2 ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2311]) ).
thf(1683,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(10797,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1683]) ).
thf(1328,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k1_funct_2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_funct_2) ).
thf(9022,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) ) ) )
=> ( C
= ( B @ ( A @ k1_funct_2 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_funct_2 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ k2_relat_1 @ r1_tarski ) )
& ( ( E @ k1_relat_1 )
= A )
& ( D = E )
& ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).
thf(1930,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_realset1) ).
thf(12266,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k1_funct_1 ) @ r2_hidden ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1930]) ).
thf(2032,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_cantor_1 ) @ ( A @ k1_cantor_1 ) @ ( A @ g1_pre_topc ) @ ( B @ m2_cantor_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_cantor_1) ).
thf(12918,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k2_cantor_1 ) @ ( A @ k1_cantor_1 ) @ ( A @ g1_pre_topc ) @ ( B @ m2_cantor_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2032]) ).
thf(1270,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( E @ ( B @ r6_binop_1 ) ) )
& ( D @ ( C @ ( A @ r6_binop_1 ) ) ) )
<=> ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r6_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_filter_1) ).
thf(8725,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r6_binop_1 ) ) )
=> ( ( F @ ( E @ ( B @ r6_binop_1 ) ) )
& ( D @ ( C @ ( A @ r6_binop_1 ) ) ) ) )
& ( ( ( F @ ( E @ ( B @ r6_binop_1 ) ) )
& ( D @ ( C @ ( A @ r6_binop_1 ) ) ) )
=> ( F @ ( D @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( E @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r6_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(2382,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( C @ ( B @ ( A @ k3_cat_5 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_cat_5) ).
thf(14609,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( C @ ( B @ ( A @ k3_cat_5 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2382]) ).
thf(789,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(6120,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(1097,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( D @ ( C @ k7_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_partfun1) ).
thf(7705,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_partfun1 ) ) ) )
= ( D @ ( C @ k7_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(1281,axiom,
! [A: $i] :
( ( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( A = k34_binop_2 )
<=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k1_numbers @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k10_binop_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_binop_2) ).
thf(8772,plain,
! [A: $i] :
( ( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k1_numbers @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k10_binop_2 ) ) ) ) )
=> ( A = k34_binop_2 ) )
& ( ( A = k34_binop_2 )
=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k1_numbers @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k10_binop_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(1959,axiom,
( k5_urysohn1
= ( k2_urysohn1 @ ( k4_urysohn1 @ ( k1_urysohn1 @ ( k1_numbers @ k4_subset_1 ) ) @ ( k1_numbers @ k4_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_urysohn1) ).
thf(12502,plain,
( k5_urysohn1
= ( k2_urysohn1 @ ( k4_urysohn1 @ ( k1_urysohn1 @ ( k1_numbers @ k4_subset_1 ) ) @ ( k1_numbers @ k4_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1959]) ).
thf(114,axiom,
( ( k1_xboole_0 @ k10_funct_6 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_funct_6) ).
thf(2863,plain,
( ( k1_xboole_0 @ k10_funct_6 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(1778,axiom,
( ( k4_urysohn1 @ v2_membered )
& ( k4_urysohn1 @ v1_membered )
& ~ ( k4_urysohn1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_urysohn1) ).
thf(11329,plain,
( ( k4_urysohn1 @ v2_membered )
& ( k4_urysohn1 @ v1_membered )
& ~ ( k4_urysohn1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1778]) ).
thf(1484,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( ( C @ ( B @ k13_funct_3 ) )
= ( C @ ( B @ k15_funct_3 ) @ ( A @ k12_funct_3 @ k5_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_funct_3) ).
thf(9794,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( ( C @ ( B @ k13_funct_3 ) )
= ( C @ ( B @ k15_funct_3 ) @ ( A @ k12_funct_3 @ k5_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1484]) ).
thf(697,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_tarski @ v1_setfam_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_setfam_1) ).
thf(5607,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k1_tarski @ v1_setfam_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(2329,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( A @ a_1_2_domain_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_domain_1) ).
thf(14374,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( A @ a_1_2_domain_1 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2329]) ).
thf(444,axiom,
! [A: $i] :
( ( A @ v1_realset1 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_yellow13) ).
thf(4360,plain,
! [A: $i] :
( ( A @ v1_realset1 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(675,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( D @ ( A @ ( E @ m1_relset_1 ) ) )
& ( D @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( C @ ( B @ ( D @ m1_fraenkel ) ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_cat_2 ) ) ) ) ) )
= ( F @ ( E @ k1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_cat_2) ).
thf(5514,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( D @ ( A @ ( E @ m1_relset_1 ) ) )
& ( D @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( C @ ( B @ ( D @ m1_fraenkel ) ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_cat_2 ) ) ) ) ) )
= ( F @ ( E @ k1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(1632,axiom,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_zfmisc_1) ).
thf(10540,plain,
! [A: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1632]) ).
thf(1348,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
<=> ? [B: $i] :
( ( A
= ( B @ k2_relat_1 ) )
& ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_finseq_1) ).
thf(9153,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( A
= ( B @ k2_relat_1 ) )
& ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ v1_finset_1 ) )
& ( ( A @ v1_finset_1 )
=> ? [B: $i] :
( ( A
= ( B @ k2_relat_1 ) )
& ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).
thf(1446,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( ( C @ k2_funct_4 @ k2_funct_4 )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funct_4) ).
thf(9606,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) )
=> ( ( C @ k2_funct_4 @ k2_funct_4 )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446]) ).
thf(817,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( D @ v1_partfun1 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_partfun1) ).
thf(6266,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ r1_partfun1 ) )
& ( B @ ( A @ ( D @ v1_partfun1 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(667,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_relat_1) ).
thf(5478,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(2321,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k1_relset_2 ) ) )
= ( B @ ( C @ ( A @ k1_relset_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k1_relset_2) ).
thf(14336,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k1_relset_2 ) ) )
= ( B @ ( C @ ( A @ k1_relset_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2321]) ).
thf(447,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( D @ ( A @ k3_setwiseo ) ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( E @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( B @ k5_setwiseo ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_setwiseo) ).
thf(4366,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( C @ ( E @ ( D @ ( A @ k3_setwiseo ) ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( E @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( B @ k5_setwiseo ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(1306,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) )
= C )
& ( ( C @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ ( A @ k7_relset_1 ) ) ) ) ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_2) ).
thf(8890,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) )
= C )
& ( ( C @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ ( A @ k7_relset_1 ) ) ) ) ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).
thf(1897,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_yellow_3 ) ) ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yellow_3) ).
thf(12056,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_yellow_3 ) ) ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1897]) ).
thf(1986,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( A @ k1_domain_1 ) ) ) @ ( C @ k6_partfun1 @ ( D @ ( C @ ( B @ ( C @ ( A @ k16_funct_3 ) ) ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k8_funct_2 ) ) ) )
= ( F @ ( E @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( B @ k1_domain_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_borsuk_1) ).
thf(12648,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( C @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( A @ k1_domain_1 ) ) ) @ ( C @ k6_partfun1 @ ( D @ ( C @ ( B @ ( C @ ( A @ k16_funct_3 ) ) ) ) ) @ ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k8_funct_2 ) ) ) )
= ( F @ ( E @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( B @ k1_domain_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1986]) ).
thf(343,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( ( A @ ( k1_xboole_0 @ k9_funct_7 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funct_7) ).
thf(3904,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ( ( A @ ( k1_xboole_0 @ k9_funct_7 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(550,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( ( A @ v2_funct_1 )
& ( B @ v2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_funct_1) ).
thf(4922,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( ( B @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( A @ ( B @ k5_relat_1 ) @ v2_funct_1 ) )
=> ( ( A @ v2_funct_1 )
& ( B @ v2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(2240,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_cantor_1 ) @ ( A @ k2_cantor_1 ) @ ( A @ k1_cantor_1 ) )
= ( B @ ( A @ k2_cantor_1 ) @ ( A @ k1_cantor_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_yellow_9) ).
thf(14017,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k1_cantor_1 ) @ ( A @ k2_cantor_1 ) @ ( A @ k1_cantor_1 ) )
= ( B @ ( A @ k2_cantor_1 ) @ ( A @ k1_cantor_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2240]) ).
thf(669,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ ( A @ ( A @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_enumset1) ).
thf(5484,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ ( A @ ( A @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(932,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funct_1) ).
thf(6826,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k2_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(2098,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
thf(13285,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2098]) ).
thf(692,axiom,
! [A: $i] :
( ( k1_numbers @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k7_metric_1 @ ( k1_numbers @ ( k1_numbers @ k1_metric_1 ) ) ) ) )
= ( A @ ( B @ ( k7_metric_1 @ ( k1_numbers @ ( k1_numbers @ k1_metric_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_metric_1) ).
thf(5592,plain,
! [A: $i] :
( ( k1_numbers @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k7_metric_1 @ ( k1_numbers @ ( k1_numbers @ k1_metric_1 ) ) ) ) )
= ( A @ ( B @ ( k7_metric_1 @ ( k1_numbers @ ( k1_numbers @ k1_metric_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(2012,axiom,
! [A: $i] : ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ k6_relat_1 @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_relset_1) ).
thf(12807,plain,
! [A: $i] : ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ k6_relat_1 @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2012]) ).
thf(759,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( A @ k3_pua2mss1 @ ( C @ k9_relat_1 ) @ ( A @ k3_pua2mss1 @ ( B @ k9_relat_1 ) @ k3_xboole_0 ) @ ( A @ k3_pua2mss1 @ ( C @ ( B @ k3_xboole_0 ) @ k9_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_relset_2) ).
thf(5980,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( A @ k3_pua2mss1 @ ( C @ k9_relat_1 ) @ ( A @ k3_pua2mss1 @ ( B @ k9_relat_1 ) @ k3_xboole_0 ) @ ( A @ k3_pua2mss1 @ ( C @ ( B @ k3_xboole_0 ) @ k9_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(974,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k5_funcop_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k5_funcop_1 ) ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_funcop_1) ).
thf(7045,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k5_funcop_1 ) ) @ v1_funct_1 )
& ( C @ ( B @ ( A @ k5_funcop_1 ) ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(2091,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) )
= ( B @ ( B @ ( B @ k3_zfmisc_1 ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_mcart_1) ).
thf(13261,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) )
= ( B @ ( B @ ( B @ k3_zfmisc_1 ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2091]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_enumset1) ).
thf(4641,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k5_enumset1 ) ) ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ k3_enumset1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(720,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] : ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(5721,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ r1_xboole_0 ) )
& ? [C: $i] : ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ k3_xboole_0 ) @ ( C @ r2_hidden ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(102,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k1_funct_1 ) @ ( B @ ( A @ k3_pralg_3 ) @ k10_relat_1 ) )
= ( A @ k4_card_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_yellow17) ).
thf(2821,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( B @ ( A @ k1_funct_1 ) @ ( B @ ( A @ k3_pralg_3 ) @ k10_relat_1 ) )
= ( A @ k4_card_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1477,axiom,
! [A: $i] : ( A @ k5_finsub_1 @ v4_finsub_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
thf(9766,plain,
! [A: $i] : ( A @ k5_finsub_1 @ v4_finsub_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477]) ).
thf(559,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ k6_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( B @ r1_tarski ) )
& ( B
= ( C @ ( A @ ( B @ k4_relset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_relset_1) ).
thf(4971,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ k6_relat_1 @ r1_tarski ) )
=> ( ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( B @ r1_tarski ) )
& ( B
= ( C @ ( A @ ( B @ k4_relset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(1429,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ r1_tarski ) )
=> ( ( B = D )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_funct_4) ).
thf(9499,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ r1_tarski ) )
=> ( ( B = D )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429]) ).
thf(2178,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(13713,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2178]) ).
thf(435,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ ( D @ ( B @ ( A @ k3_mcart_1 ) ) @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_mcart_1) ).
thf(4324,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ ( B @ k2_tarski ) @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( D @ ( C @ ( A @ k3_mcart_1 ) ) @ ( D @ ( B @ ( A @ k3_mcart_1 ) ) @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(1206,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
=> ( ( ( ( D @ k2_relat_1 )
= A )
& ( C @ v2_funct_1 ) )
| ( B = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_funct_2) ).
thf(8364,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
=> ( ( ( ( D @ k2_relat_1 )
= A )
& ( C @ v2_funct_1 ) )
| ( B = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(1517,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_finset_1) ).
thf(9948,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_enumset1 ) ) ) ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517]) ).
thf(882,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_orders_1) ).
thf(6596,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ k1_orders_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(1562,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ r4_waybel_4 ) ) )
<=> ( ! [D: $i] :
~ ( ( C @ ( B @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( D != B )
& ( A @ ( D @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d26_waybel_4) ).
thf(10159,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( ! [D: $i] :
~ ( ( C @ ( B @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( D != B )
& ( A @ ( D @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
=> ( C @ ( B @ ( A @ r4_waybel_4 ) ) ) )
& ( ( C @ ( B @ ( A @ r4_waybel_4 ) ) )
=> ( ! [D: $i] :
~ ( ( C @ ( B @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( D != B )
& ( A @ ( D @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562]) ).
thf(1196,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(8295,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ k3_tarski @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(1118,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( k1_xboole_0 @ ( B @ v1_partfun1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_partfun1) ).
thf(7811,plain,
! [A: $i,B: $i] :
( ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( k1_xboole_0 @ ( B @ v1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(1066,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_zfmisc_1) ).
thf(7586,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_setwiseo ) ) )
= ( B @ ( C @ ( A @ k5_setwiseo ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_setwiseo) ).
thf(2888,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_setwiseo ) ) )
= ( B @ ( C @ ( A @ k5_setwiseo ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1423,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k2_funct_3 ) ) )
= ( C @ k1_funct_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_3) ).
thf(9473,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k2_funct_3 ) ) )
= ( C @ k1_funct_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1423]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k3_funct_3 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k3_funct_3 @ k1_funct_1 ) )
= ( A @ ( B @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_funct_3) ).
thf(2831,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k3_funct_3 @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ k3_funct_3 @ k1_funct_1 ) )
= ( A @ ( B @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1988,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_filter_1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_filter_1) ).
thf(12659,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_filter_1 ) ) )
=> ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1988]) ).
thf(1151,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) ) )
=> ( ( A @ ( B @ k3_funct_3 @ k10_relat_1 ) @ k3_tarski )
= ( A @ k3_tarski @ ( B @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_funct_3) ).
thf(8039,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ r1_tarski ) ) )
=> ( ( A @ ( B @ k3_funct_3 @ k10_relat_1 ) @ k3_tarski )
= ( A @ k3_tarski @ ( B @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(2196,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(13823,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2196]) ).
thf(400,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ v1_realset1 )
<=> ? [B: $i] :
( ( A
= ( B @ ( A @ k6_domain_1 ) ) )
& ( A @ ( B @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tex_2) ).
thf(4164,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( ? [B: $i] :
( ( A
= ( B @ ( A @ k6_domain_1 ) ) )
& ( A @ ( B @ m1_subset_1 ) ) )
=> ( A @ v1_realset1 ) )
& ( ( A @ v1_realset1 )
=> ? [B: $i] :
( ( A
= ( B @ ( A @ k6_domain_1 ) ) )
& ( A @ ( B @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( A @ ( B @ k2_zfmisc_1 ) @ ( C @ k4_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_sysrel) ).
thf(2656,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( A @ ( B @ k2_zfmisc_1 ) @ ( C @ k4_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1091,axiom,
! [A: $i] :
( ( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( A = k33_binop_2 )
<=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k1_numbers @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k9_binop_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_binop_2) ).
thf(7672,plain,
! [A: $i] :
( ( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k1_numbers @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k9_binop_2 ) ) ) ) )
=> ( A = k33_binop_2 ) )
& ( ( A = k33_binop_2 )
=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k1_numbers @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k9_binop_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(709,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_enumset1 ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_subset_1) ).
thf(5684,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_enumset1 ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(1571,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D @ k2_relat_1 @ ( C @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_isocat_2) ).
thf(10218,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D @ k2_relat_1 @ ( C @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1571]) ).
thf(2247,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_funct_7 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_7) ).
thf(14036,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( B @ ( A @ k1_funct_7 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2247]) ).
thf(2300,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_subset_1) ).
thf(14272,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2300]) ).
thf(1249,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_funct_1) ).
thf(8612,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( A @ ( C @ k9_relat_1 ) @ ( C @ ( B @ k5_relat_1 ) @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(1924,axiom,
k5_numbers @ ( k5_numbers @ ( k1_numbers @ ( k1_numbers @ k12_mcart_1 ) ) ) @ ( k1_qc_lang1 @ r1_tarski ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_qc_lang1) ).
thf(12187,plain,
k5_numbers @ ( k5_numbers @ ( k1_numbers @ ( k1_numbers @ k12_mcart_1 ) ) ) @ ( k1_qc_lang1 @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1924]) ).
thf(1860,axiom,
! [A: $i,B: $i] :
( ~ ( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
& ( ( A @ ( B @ k2_zfmisc_1 ) )
= k1_xboole_0 )
& ( A = k1_xboole_0 ) )
=> ( ( ( B @ ( A @ k2_zfmisc_1 ) @ k2_funct_5 )
= B )
& ( ( A @ ( B @ k2_zfmisc_1 ) @ k1_funct_5 )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funct_5) ).
thf(11823,plain,
! [A: $i,B: $i] :
( ~ ( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
& ( ( A @ ( B @ k2_zfmisc_1 ) )
= k1_xboole_0 )
& ( A = k1_xboole_0 ) )
=> ( ( ( B @ ( A @ k2_zfmisc_1 ) @ k2_funct_5 )
= B )
& ( ( A @ ( B @ k2_zfmisc_1 ) @ k1_funct_5 )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1860]) ).
thf(2185,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_subset_1) ).
thf(13769,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2185]) ).
thf(1538,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_2) ).
thf(10048,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538]) ).
thf(729,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_lattice2) ).
thf(5767,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) @ k1_relat_1 )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(656,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_pboole ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_pboole ) )
=> ! [H: $i] :
( ( G @ ( F @ ( E @ ( C @ ( B @ ( H @ m1_functor0 ) ) ) ) ) )
=> ( G @ ( F @ ( D @ ( B @ ( A @ k7_pboole ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ ( H @ ( D @ ( B @ ( A @ k7_pboole ) ) ) @ m1_functor0 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_functor0) ).
thf(5431,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_pboole ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_pboole ) )
=> ! [H: $i] :
( ( G @ ( F @ ( E @ ( C @ ( B @ ( H @ m1_functor0 ) ) ) ) ) )
=> ( G @ ( F @ ( D @ ( B @ ( A @ k7_pboole ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ ( H @ ( D @ ( B @ ( A @ k7_pboole ) ) ) @ m1_functor0 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(1714,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r7_relat_2 ) )
<=> ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ~ ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_2) ).
thf(10994,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ~ ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r7_relat_2 ) ) )
& ( ( B @ ( A @ r7_relat_2 ) )
=> ! [C: $i,D: $i] :
~ ( ~ ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) )
& ~ ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1714]) ).
thf(2380,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_subset_1 ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(14604,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_subset_1 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2380]) ).
thf(1359,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ k1_fraenkel ) @ ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_funcsdom ) ) ) ) @ m2_fraenkel ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_funcsdom) ).
thf(9214,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ ( B @ k1_fraenkel ) @ ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_funcsdom ) ) ) ) @ m2_fraenkel ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).
thf(1165,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( D @ ( A @ k7_relat_1 ) )
= ( D @ ( B @ k7_relat_1 ) ) )
=> ( ( D @ ( A @ ( C @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) )
= ( D @ ( B @ ( C @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_funcop_1) ).
thf(8111,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( D @ ( A @ k7_relat_1 ) )
= ( D @ ( B @ k7_relat_1 ) ) )
=> ( ( D @ ( A @ ( C @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) )
= ( D @ ( B @ ( C @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(1611,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_zfmisc_1) ).
thf(10439,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1611]) ).
thf(1709,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ v1_funct_2 ) ) )
& ( D @ k2_funct_4 @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_funct_4) ).
thf(10952,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ m2_relset_1 ) ) )
& ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ k2_funct_4 @ v1_funct_2 ) ) )
& ( D @ k2_funct_4 @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1709]) ).
thf(1003,axiom,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k5_finsub_1 @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B
= ( A @ k11_setwiseo ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ k1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_setwiseo) ).
thf(7264,plain,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ k5_finsub_1 @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ k1_tarski ) ) )
=> ( B
= ( A @ k11_setwiseo ) ) )
& ( ( B
= ( A @ k11_setwiseo ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= ( C @ k1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(1208,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_pre_circ) ).
thf(8377,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k1_funct_4 ) @ ( A @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(2168,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_binop_1 ) ) )
= ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_binop_1) ).
thf(13677,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ k1_binop_1 ) ) )
= ( C @ ( B @ k4_tarski ) @ ( A @ k1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2168]) ).
thf(1997,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( C @ ( D @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_mssubfam) ).
thf(12720,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C @ ( B @ r1_tarski ) )
& ( D @ ( B @ r2_hidden ) ) )
=> ( C @ ( D @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1997]) ).
thf(206,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( k5_numbers @ ( C @ m2_relset_1 ) ) )
& ( B @ ( k5_numbers @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ k2_finseq_1 @ ( C @ ( B @ ( k5_numbers @ k2_partfun1 ) ) ) @ m2_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_finseq_2) ).
thf(3273,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( k5_numbers @ ( C @ m2_relset_1 ) ) )
& ( B @ ( k5_numbers @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( A @ k2_finseq_1 @ ( C @ ( B @ ( k5_numbers @ k2_partfun1 ) ) ) @ m2_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(2058,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_2) ).
thf(13089,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2058]) ).
thf(1910,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ k5_setfam_1 ) @ ( B @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_mssubfam) ).
thf(12124,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ k5_setfam_1 ) @ ( B @ ( A @ k8_setfam_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1910]) ).
thf(1219,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t176_orders_1) ).
thf(8428,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( B @ ( C @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( D @ ( C @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(1963,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k17_domain_1 ) ) ) )
= ( D @ k20_mcart_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k17_domain_1) ).
thf(12514,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k17_domain_1 ) ) ) )
= ( D @ k20_mcart_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1963]) ).
thf(1541,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ k2_funct_5 @ ( B @ k9_relat_1 ) @ ( C @ ( B @ ( A @ k15_funct_3 ) @ k9_relat_1 ) @ k2_funct_5 @ r1_tarski ) )
& ( C @ k1_funct_5 @ ( A @ k9_relat_1 ) @ ( C @ ( B @ ( A @ k15_funct_3 ) @ k9_relat_1 ) @ k1_funct_5 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_waybel20) ).
thf(10055,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ k2_funct_5 @ ( B @ k9_relat_1 ) @ ( C @ ( B @ ( A @ k15_funct_3 ) @ k9_relat_1 ) @ k2_funct_5 @ r1_tarski ) )
& ( C @ k1_funct_5 @ ( A @ k9_relat_1 ) @ ( C @ ( B @ ( A @ k15_funct_3 ) @ k9_relat_1 ) @ k1_funct_5 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1541]) ).
thf(223,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k4_finseq_1 )
= ( A @ k1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_finseq_1) ).
thf(3344,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k4_finseq_1 )
= ( A @ k1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(2145,axiom,
! [A: $i] :
( ( ( k1_numbers @ ( k1_numbers @ ( A @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( A = k31_binop_2 )
<=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ k8_funct_2 ) ) ) )
= ( B @ k7_binop_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_binop_2) ).
thf(13560,plain,
! [A: $i] :
( ( ( k1_numbers @ ( k1_numbers @ ( A @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ k8_funct_2 ) ) ) )
= ( B @ k7_binop_2 ) ) )
=> ( A = k31_binop_2 ) )
& ( ( A = k31_binop_2 )
=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ k8_funct_2 ) ) ) )
= ( B @ k7_binop_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2145]) ).
thf(684,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_card_fil) ).
thf(5555,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(1774,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( B @ ( A @ k3_binop_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_binop_1) ).
thf(11297,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( B @ ( A @ k3_binop_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1774]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ! [F: $i,G: $i,H: $i,I: $i] :
~ ( ( A
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) )
& ( E @ ( I @ r2_hidden ) )
& ( D @ ( H @ r2_hidden ) )
& ( C @ ( G @ r2_hidden ) )
& ( B @ ( F @ r2_hidden ) ) )
& ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_mcart_1) ).
thf(4222,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ! [F: $i,G: $i,H: $i,I: $i] :
~ ( ( A
= ( I @ ( H @ ( G @ ( F @ k4_mcart_1 ) ) ) ) )
& ( E @ ( I @ r2_hidden ) )
& ( D @ ( H @ r2_hidden ) )
& ( C @ ( G @ r2_hidden ) )
& ( B @ ( F @ r2_hidden ) ) )
& ( E @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(1662,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ m2_relset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_relset_1) ).
thf(10717,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( A @ r1_tarski ) )
=> ( C @ ( B @ ( A @ m2_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1662]) ).
thf(1089,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_relat_1) ).
thf(7667,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( A @ ( B @ ( C @ k7_relat_1 ) @ k7_relat_1 ) )
= ( A @ ( C @ k7_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(1113,axiom,
k1_numbers @ k1_zfmisc_1 @ ( k5_numbers @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_numbers) ).
thf(7796,plain,
k1_numbers @ k1_zfmisc_1 @ ( k5_numbers @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(1558,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ r3_binop_1 ) ) )
& ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_binop_1) ).
thf(10144,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( B @ ( D @ ( A @ r3_binop_1 ) ) )
& ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1558]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_relat_1) ).
thf(2429,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1917,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_sysrel) ).
thf(12160,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k6_relat_1 @ ( A @ k6_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1917]) ).
thf(1185,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( ( B @ ( C @ ( A @ k4_funct_2 ) ) )
= B ) )
=> ( C
= ( A @ k6_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_funct_2) ).
thf(8216,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( ( B @ ( C @ ( A @ k4_funct_2 ) ) )
= B ) )
=> ( C
= ( A @ k6_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(1945,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(12419,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1945]) ).
thf(983,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m2_card_fil ) )
=> ( B @ ( k1_xboole_0 @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_card_fil) ).
thf(7149,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m2_card_fil ) )
=> ( B @ ( k1_xboole_0 @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(2188,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( A @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( A = B )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_zfmisc_1) ).
thf(13791,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= ( A @ ( B @ k2_zfmisc_1 ) ) )
=> ( ( A = B )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2188]) ).
thf(822,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_binop_1) ).
thf(6298,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) )
=> ( B @ ( C @ ( A @ r3_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r3_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(1133,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
thf(7879,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k2_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(791,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_funct_3 )
= ( B @ k1_funct_3 @ ( A @ k1_funct_3 @ k5_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funct_3) ).
thf(6125,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_funct_3 )
= ( B @ k1_funct_3 @ ( A @ k1_funct_3 @ k5_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(614,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( ( B @ ( A @ k1_funct_2 ) @ v1_fraenkel )
& ( B @ ( A @ k1_funct_2 ) @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_fraenkel) ).
thf(5203,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( ( B @ ( A @ k1_funct_2 ) @ v1_fraenkel )
& ( B @ ( A @ k1_funct_2 ) @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(762,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( D @ ( F @ ( C @ ( B @ k8_funct_2 ) ) ) @ ( C @ k6_domain_1 ) @ ( F @ ( E @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ k3_funct_2 ) ) ) @ ( D @ ( B @ k6_domain_1 ) @ ( E @ ( B @ ( A @ k3_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_borsuk_1) ).
thf(5995,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( D @ ( F @ ( C @ ( B @ k8_funct_2 ) ) ) @ ( C @ k6_domain_1 ) @ ( F @ ( E @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( C @ ( A @ k3_funct_2 ) ) ) @ ( D @ ( B @ k6_domain_1 ) @ ( E @ ( B @ ( A @ k3_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(2045,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(12995,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2045]) ).
thf(2105,axiom,
f1_s10_fraenkel @ ( a_0_18_fraenkel @ r1_tarski ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s10_fraenkel) ).
thf(13320,plain,
f1_s10_fraenkel @ ( a_0_18_fraenkel @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2105]) ).
thf(167,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v2_relat_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ k4_card_3 )
= ( B @ k4_card_3 ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_pua2mss1) ).
thf(3127,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v2_relat_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ k4_card_3 )
= ( B @ k4_card_3 ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1235,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k2_ens_1 )
= ( A @ a_1_1_ens_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ens_1) ).
thf(8528,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ k2_ens_1 )
= ( A @ a_1_1_ens_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(1770,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ k5_setfam_1 ) @ k9_relat_1 ) )
= ( D @ ( C @ ( B @ ( A @ a_4_3_relset_2 ) ) ) @ k3_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_relset_2) ).
thf(11257,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ k5_setfam_1 ) @ k9_relat_1 ) )
= ( D @ ( C @ ( B @ ( A @ a_4_3_relset_2 ) ) ) @ k3_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1770]) ).
thf(440,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_relat_1) ).
thf(4351,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(799,axiom,
! [A: $i] :
( ( A @ v1_realset1 )
<=> ~ ( ! [B: $i] :
( A
!= ( B @ k1_tarski ) )
& ~ ( A @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_realset1) ).
thf(6174,plain,
! [A: $i] :
( ( ~ ( ! [B: $i] :
( A
!= ( B @ k1_tarski ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ v1_realset1 ) )
& ( ( A @ v1_realset1 )
=> ~ ( ! [B: $i] :
( A
!= ( B @ k1_tarski ) )
& ~ ( A @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(329,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ k4_tarski ) @ ( D @ ( C @ ( B @ ( A @ k1_isocat_2 ) ) ) @ k1_funct_1 ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ k1_fraenkel ) @ ( C @ ( B @ ( A @ k1_cat_2 ) ) ) ) ) @ ( C @ ( B @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_isocat_2) ).
thf(3828,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ k4_tarski ) @ ( D @ ( C @ ( B @ ( A @ k1_isocat_2 ) ) ) @ k1_funct_1 ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ k1_fraenkel ) @ ( C @ ( B @ ( A @ k1_cat_2 ) ) ) ) ) @ ( C @ ( B @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(680,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ v1_funct_1 )
& ( B @ ( A @ k1_funct_4 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_4) ).
thf(5543,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k1_funct_4 ) @ v1_funct_1 )
& ( B @ ( A @ k1_funct_4 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(1012,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_relat_1) ).
thf(7351,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( A @ ( A @ ( B @ k7_relat_1 ) @ k1_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_3) ).
thf(2701,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(848,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k1_relat_1 @ v1_relat_1 )
& ( A @ k1_relat_1 @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(6436,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ k1_relat_1 @ v1_relat_1 )
& ( A @ k1_relat_1 @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
<=> ( ( B @ ( A @ k4_xboole_0 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(2486,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ k4_xboole_0 ) )
= A )
=> ( B @ ( A @ r1_xboole_0 ) ) )
& ( ( B @ ( A @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(528,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k3_funct_4 ) @ v1_funct_1 )
& ( B @ ( A @ k3_funct_4 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_funct_4) ).
thf(4800,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k3_funct_4 ) @ v1_funct_1 )
& ( B @ ( A @ k3_funct_4 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(1720,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_ordinal1) ).
thf(11034,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( A @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1720]) ).
thf(2269,axiom,
! [A: $i] :
? [B: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tex_2) ).
thf(14143,plain,
! [A: $i] :
? [B: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2269]) ).
thf(1532,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ~ ( ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( B @ ( A @ r1_tarski ) ) )
& ? [B: $i] :
( ( B @ k2_finseq_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
& ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finseq_1) ).
thf(10012,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ~ ( ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( B @ ( A @ r1_tarski ) ) )
& ? [B: $i] :
( ( B @ k2_finseq_1 @ ( A @ k1_relat_1 @ r1_tarski ) )
& ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1532]) ).
thf(1277,axiom,
! [A: $i,B: $i] :
( ( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ k2_mcart_1 @ v1_funct_1 )
& ( B @ k2_mcart_1 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ens_1) ).
thf(8757,plain,
! [A: $i,B: $i] :
( ( ( A @ k2_ens_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ k2_mcart_1 @ v1_funct_1 )
& ( B @ k2_mcart_1 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(2291,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( E @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_relset_2) ).
thf(14226,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( E @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( E @ ( D @ ( B @ ( A @ k8_relset_2 ) ) ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2291]) ).
thf(2279,axiom,
k1_numbers @ k1_zfmisc_1 @ ( k2_urysohn1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_urysohn1) ).
thf(14179,plain,
k1_numbers @ k1_zfmisc_1 @ ( k2_urysohn1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2279]) ).
thf(1977,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k9_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_relat_1) ).
thf(12580,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k9_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1977]) ).
thf(1649,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k7_setfam_1 ) @ ( B @ ( A @ k7_setfam_1 ) @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_setfam_1) ).
thf(10613,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k7_setfam_1 ) @ ( B @ ( A @ k7_setfam_1 ) @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1649]) ).
thf(1692,axiom,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(10846,plain,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1692]) ).
thf(1020,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(7398,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(661,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( D @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_funct_4) ).
thf(5450,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ k1_funct_4 ) @ m2_relset_1 ) ) )
& ( D @ ( C @ k1_funct_4 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(1462,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_4) ).
thf(9690,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_funcop_1 ) @ ( B @ ( A @ k2_funcop_1 ) @ r1_tarski ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462]) ).
thf(807,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(6206,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(1413,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k8_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_relat_1) ).
thf(9435,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k8_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k6_relat_1 @ r1_tarski ) )
=> ( B @ k4_relat_1 @ ( A @ k6_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_sysrel) ).
thf(2468,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k6_relat_1 @ r1_tarski ) )
=> ( B @ k4_relat_1 @ ( A @ k6_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( ( A @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t161_funct_1) ).
thf(5277,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( ( A @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(1949,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k5_finsub_1 @ ( D @ ( C @ ( B @ ( A @ k4_setwiseo ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_setwiseo) ).
thf(12439,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k5_finsub_1 @ ( D @ ( C @ ( B @ ( A @ k4_setwiseo ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1949]) ).
thf(560,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( D @ ( E @ r2_hidden ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ( E
= ( G @ ( F @ ( B @ ( A @ k12_mcart_1 ) ) ) ) )
& ( B @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) ) )
& ( A @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) ) )
& ( C @ ( E @ r1_tarski ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k10_funct_3 ) @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski @ ( D @ ( B @ ( A @ k9_funct_3 ) @ k1_funct_3 @ k9_relat_1 ) @ k1_setfam_1 @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_borsuk_1) ).
thf(4976,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ! [E: $i] :
( ( D @ ( E @ r2_hidden ) )
=> ( ? [F: $i] :
( ? [G: $i] :
( ( E
= ( G @ ( F @ ( B @ ( A @ k12_mcart_1 ) ) ) ) )
& ( B @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) ) )
& ( A @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) ) )
& ( C @ ( E @ r1_tarski ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k10_funct_3 ) @ k1_funct_3 @ k9_relat_1 ) @ k3_tarski @ ( D @ ( B @ ( A @ k9_funct_3 ) @ k1_funct_3 @ k9_relat_1 ) @ k1_setfam_1 @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(2336,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ k5_subset_1 ) ) @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( B @ k5_subset_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_relset_2) ).
thf(14400,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ k5_subset_1 ) ) @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= ( E @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) @ ( B @ k5_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2336]) ).
thf(2167,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( k1_numbers @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k1_metric_1 ) ) ) ) )
= ( E @ ( D @ ( C @ k1_binop_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_metric_1) ).
thf(13674,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( k1_numbers @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k1_metric_1 ) ) ) ) )
= ( E @ ( D @ ( C @ k1_binop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2167]) ).
thf(2057,axiom,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ p1_s1_funct_1 ) )
& ( B @ ( A @ p1_s1_funct_1 ) ) )
=> ( B = C ) )
=> ? [A: $i] :
( ! [B: $i,C: $i] :
( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
<=> ( ( C @ ( B @ p1_s1_funct_1 ) )
& ( f1_s1_funct_1 @ ( B @ r2_hidden ) ) ) )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_1) ).
thf(13076,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ p1_s1_funct_1 ) )
& ( B @ ( A @ p1_s1_funct_1 ) ) )
=> ( B = C ) )
=> ? [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ( C @ ( B @ p1_s1_funct_1 ) )
& ( f1_s1_funct_1 @ ( B @ r2_hidden ) ) )
=> ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
& ( ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) )
=> ( ( C @ ( B @ p1_s1_funct_1 ) )
& ( f1_s1_funct_1 @ ( B @ r2_hidden ) ) ) ) )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2057]) ).
thf(1661,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( A @ k2_setwiseo ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_setwiseo) ).
thf(10714,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( A @ k2_setwiseo ) @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1661]) ).
thf(1263,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ k1_tarski @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_subset_1) ).
thf(8679,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( B @ k1_tarski @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(1947,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ r2_hidden ) )
<=> ~ ( C @ ( D @ r2_hidden ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_subset_1) ).
thf(12424,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ~ ( C @ ( D @ r2_hidden ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( ( B @ ( D @ r2_hidden ) )
=> ~ ( C @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( C @ ( A @ k3_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1947]) ).
thf(2331,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_pre_topc ) )
= ( D @ ( C @ g1_pre_topc ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_pre_topc) ).
thf(14378,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_pre_topc ) )
= ( D @ ( C @ g1_pre_topc ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2331]) ).
thf(749,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ~ ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_4) ).
thf(5949,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ~ ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(297,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t89_xboole_1) ).
thf(3697,plain,
! [A: $i,B: $i] : ( B @ ( A @ k4_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(1736,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_binop_1 ) )
=> ( ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_funcop_1) ).
thf(11094,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_binop_1 ) )
=> ( ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1736]) ).
thf(1936,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m1_pboole ) )
=> ( ( C
= ( B @ ( A @ k2_altcat_1 ) ) )
<=> ! [D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ k1_multop_1 ) ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_altcat_1) ).
thf(12328,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m1_pboole ) )
=> ( ( ! [D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ k1_multop_1 ) ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) ) ) )
=> ( C
= ( B @ ( A @ k2_altcat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k2_altcat_1 ) ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ k1_multop_1 ) ) ) )
= ( F @ ( D @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1936]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ k1_setwiseo )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setwiseo) ).
thf(2500,plain,
! [A: $i] :
( ( A @ k1_setwiseo )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1132,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_funct_2 ) )
= ( B @ ( A @ k2_funcop_1 ) @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_funct_5) ).
thf(7876,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_funct_2 ) )
= ( B @ ( A @ k2_funcop_1 ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(1754,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_pboole ) )
=> ( ! [E: $i,F: $i] :
( ( ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( ( F @ ( E @ ( C @ k1_binop_1 ) ) )
= ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_altcat_1) ).
thf(11181,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_pboole ) )
=> ( ! [E: $i,F: $i] :
( ( ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( ( F @ ( E @ ( C @ k1_binop_1 ) ) )
= ( F @ ( E @ ( D @ k1_binop_1 ) ) ) ) )
=> ( C @ ( D @ ( B @ ( A @ k2_zfmisc_1 ) @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1754]) ).
thf(1031,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_sysrel) ).
thf(7466,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k3_xboole_0 ) @ k1_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(242,axiom,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v1_setwiseo ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_setwiseo) ).
thf(3415,plain,
! [A: $i] : ( A @ k5_finsub_1 @ ( A @ k9_setwiseo @ v1_setwiseo ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(1861,axiom,
! [A: $i] :
( ( A @ v1_fraenkel )
<=> ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_fraenkel) ).
thf(11835,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) )
=> ( A @ v1_fraenkel ) )
& ( ( A @ v1_fraenkel )
=> ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1861]) ).
thf(1806,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_finseq_1) ).
thf(11486,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1806]) ).
thf(1631,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_2) ).
thf(10531,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( A @ ( k1_xboole_0 @ ( B @ m2_relset_1 ) ) )
& ( A @ ( k1_xboole_0 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1631]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_xboole_1) ).
thf(3493,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(2326,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( B @ ( C @ ( A @ k4_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(14359,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_subset_1 ) ) )
= ( B @ ( C @ ( A @ k4_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2326]) ).
thf(2101,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= ( C @ ( D @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_binop_1) ).
thf(13299,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= ( C @ ( D @ ( B @ k1_binop_1 ) ) ) ) ) )
=> ( A @ ( B @ v1_binop_1 ) ) )
& ( ( A @ ( B @ v1_binop_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ k1_binop_1 ) ) )
= ( C @ ( D @ ( B @ k1_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2101]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m2_fraenkel ) ) ) )
<=> ( C @ ( D @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
thf(3356,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( C @ ( D @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ ( D @ m2_fraenkel ) ) ) ) )
& ( ( C @ ( B @ ( A @ ( D @ m2_fraenkel ) ) ) )
=> ( C @ ( D @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(1605,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_1_domain_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_domain_1) ).
thf(10415,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_1_domain_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_1_domain_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1605]) ).
thf(839,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ r6_pboole ) ) )
=> ( B @ ( C @ ( A @ r6_pboole ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r6_pboole) ).
thf(6369,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_pboole ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( ( C @ ( B @ ( A @ r6_pboole ) ) )
=> ( B @ ( C @ ( A @ r6_pboole ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(1713,axiom,
~ ( k1_numbers @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_numbers) ).
thf(10992,plain,
~ ( k1_numbers @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1713]) ).
thf(1114,axiom,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( A @ ( B @ k3_xboole_0 ) @ v2_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc30_membered) ).
thf(7797,plain,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( A @ ( B @ k3_xboole_0 ) @ v2_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(1369,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k1_funct_2 ) @ ( A @ ( C @ k1_funct_2 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_funct_5) ).
thf(9247,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k1_funct_2 ) @ ( A @ ( C @ k1_funct_2 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).
thf(1887,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_4) ).
thf(12014,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( D @ ( C @ k1_funct_4 ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1887]) ).
thf(1018,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( A @ k1_funct_4 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k1_funct_4) ).
thf(7391,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ ( A @ k1_funct_4 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(565,axiom,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(4991,plain,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(1156,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ k6_relat_1 @ r1_tarski ) )
=> ( ( B
= ( C @ ( B @ ( A @ k5_relset_1 ) ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_relset_1) ).
thf(8061,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( B @ k6_relat_1 @ r1_tarski ) )
=> ( ( B
= ( C @ ( B @ ( A @ k5_relset_1 ) ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(2226,axiom,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ~ ( B @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
thf(13951,plain,
! [A: $i] :
( ( A != k1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ~ ( B @ ( C @ r2_hidden ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2226]) ).
thf(989,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k8_relat_1 ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
<=> ( ( B @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
thf(7163,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ! [D: $i,E: $i] :
( ( ( ( B @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( ( B @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k8_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k8_relat_1 ) ) )
=> ! [D: $i,E: $i] :
( ( ( ( B @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ( ( B @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(1779,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ k1_binop_1 ) ) )
= D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_binop_1) ).
thf(11334,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ k1_binop_1 ) ) )
= D ) )
=> ( C @ ( B @ ( A @ r2_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ k1_binop_1 ) ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1779]) ).
thf(1017,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C
= ( A @ ( B @ k3_funct_5 @ k1_funct_1 ) ) )
& ( B @ k3_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( B @ k1_relat_1 @ ( D @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k4_tarski ) @ ( B @ k1_funct_1 ) ) ) ) )
& ( B @ k2_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ k2_funct_5 @ ( C @ k1_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ k2_funct_5 @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ k2_funct_5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_5) ).
thf(7374,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C
= ( A @ ( B @ k3_funct_5 @ k1_funct_1 ) ) )
& ( B @ k3_funct_5 @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( B @ k1_relat_1 @ ( D @ ( A @ k4_tarski ) @ r2_hidden ) )
& ( ( D @ ( C @ k1_funct_1 ) )
= ( D @ ( A @ k4_tarski ) @ ( B @ k1_funct_1 ) ) ) ) )
& ( B @ k2_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( B @ k1_relat_1 @ k2_funct_5 @ ( C @ k1_relat_1 @ r1_tarski ) )
& ( ( C @ k1_relat_1 )
= ( B @ k1_relat_1 @ k2_funct_5 @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ ( B @ k1_relat_1 @ k3_xboole_0 ) @ k2_funct_5 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(411,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
thf(4202,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ( ( A @ ( B @ k10_relat_1 ) )
= k1_xboole_0 )
& ( B @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
=> ( B @ ( C @ ( A @ r1_filter_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_filter_2) ).
thf(5226,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ r1_filter_2 ) ) )
=> ( B @ ( C @ ( A @ r1_filter_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(2038,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ g1_quantal1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ g1_quantal1 ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_quantal1) ).
thf(12952,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ g1_quantal1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ g1_quantal1 ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2038]) ).
thf(388,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B
= ( A @ ( C @ k7_relat_1 ) ) )
<=> ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
thf(4093,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) ) ) )
=> ( B
= ( A @ ( C @ k7_relat_1 ) ) ) )
& ( ( B
= ( A @ ( C @ k7_relat_1 ) ) )
=> ( ! [D: $i] :
( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ( ( D @ ( B @ k1_funct_1 ) )
= ( D @ ( C @ k1_funct_1 ) ) ) )
& ( ( B @ k1_relat_1 )
= ( A @ ( C @ k1_relat_1 @ k3_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(134,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k2_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_relat_1) ).
thf(2949,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k2_relat_1 @ ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_partfun1) ).
thf(4267,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) ) )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(2086,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_funct_2) ).
thf(13243,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k1_funct_2 ) @ ( C @ r2_hidden ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2086]) ).
thf(1608,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_relat_1) ).
thf(10432,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( A @ k6_relat_1 @ ( B @ k5_relat_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1608]) ).
thf(857,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_subset_1) ).
thf(6467,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= ( A @ k2_subset_1 @ ( A @ k3_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(1069,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ ( B @ k7_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).
thf(7595,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ ( B @ k7_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(1441,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k6_partfun1 @ ( C @ ( B @ ( A @ ( A @ k8_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funcop_1) ).
thf(9574,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k6_partfun1 @ ( C @ ( B @ ( A @ ( A @ k8_funcop_1 ) ) ) ) @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( C @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441]) ).
thf(1160,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k7_relat_1 ) )
= ( C @ ( A @ ( B @ k7_relat_1 ) @ k5_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_relat_1) ).
thf(8087,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ ( C @ ( B @ k5_relat_1 ) @ k7_relat_1 ) )
= ( C @ ( A @ ( B @ k7_relat_1 ) @ k5_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(536,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( D @ ( A @ k7_relat_1 ) )
= ( D @ ( B @ k7_relat_1 ) ) )
=> ( ( D @ ( C @ ( A @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) )
= ( D @ ( C @ ( B @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_funcop_1) ).
thf(4838,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ( ( ( D @ ( A @ k7_relat_1 ) )
= ( D @ ( B @ k7_relat_1 ) ) )
=> ( ( D @ ( C @ ( A @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) )
= ( D @ ( C @ ( B @ ( E @ k3_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(1880,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_eqrel_1 ) )
=> ( B @ ( C @ ( B @ ( A @ a_3_1_pua2mss1 ) ) @ m1_eqrel_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_pua2mss1) ).
thf(11957,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_eqrel_1 ) )
=> ( B @ ( C @ ( B @ ( A @ a_3_1_pua2mss1 ) ) @ m1_eqrel_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1880]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(2807,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(347,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( A @ ( B @ k9_relat_1 ) @ ( A @ r2_wellord2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_card_1) ).
thf(3914,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( B @ k1_relat_1 @ ( A @ r1_tarski ) ) )
=> ( A @ ( B @ k9_relat_1 ) @ ( A @ r2_wellord2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1739,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_3 ) ) @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_funct_2 ) ) ) @ ( B @ k5_setfam_1 ) )
= ( D @ ( A @ k5_setfam_1 ) @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_borsuk_1) ).
thf(11108,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_3 ) ) @ ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ k2_funct_2 ) ) ) @ ( B @ k5_setfam_1 ) )
= ( D @ ( A @ k5_setfam_1 ) @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1739]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( B @ ( C @ k9_funct_7 ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ ( C @ k9_funct_7 ) @ v1_funct_2 ) ) )
& ( B @ ( C @ k9_funct_7 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_7) ).
thf(3520,plain,
! [A: $i,B: $i] :
( ( k5_numbers @ ( k1_numbers @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( B @ ( C @ k9_funct_7 ) @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ ( C @ k9_funct_7 ) @ v1_funct_2 ) ) )
& ( B @ ( C @ k9_funct_7 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(1772,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( ~ ( C @ ( B @ ( A @ ( D @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ ( D @ ( C @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) )
& ~ ( A @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) )
& ~ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_mcart_1) ).
thf(11280,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( ~ ( C @ ( B @ ( A @ ( D @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) )
& ~ ( B @ ( A @ ( D @ ( C @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) )
& ~ ( A @ ( D @ ( C @ ( B @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) )
& ~ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1772]) ).
thf(110,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( A @ k4_finseq_1 @ ( A @ k4_finseq_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ k4_finseq_1 @ ( A @ k4_finseq_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_finseq_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_funct_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_finseq_2) ).
thf(2848,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( A @ k4_finseq_1 @ ( A @ k4_finseq_1 @ ( B @ m2_relset_1 ) ) )
& ( A @ k4_finseq_1 @ ( A @ k4_finseq_1 @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_finseq_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_funct_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1871,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_subset_1) ).
thf(11906,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1871]) ).
thf(2154,axiom,
! [A: $i] :
( ( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [B: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_realset1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_tex_2) ).
thf(13595,plain,
! [A: $i] :
( ( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [B: $i] :
( ~ ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_realset1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2154]) ).
thf(239,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v1_setwiseo ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ k1_setwiseo @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= ( C @ ( A @ k3_binop_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_setwiseo) ).
thf(3398,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v1_setwiseo ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( B @ k1_setwiseo @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= ( C @ ( A @ k3_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(391,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_2) ).
thf(4111,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( B @ ( A @ k1_funct_2 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(1318,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).
thf(8982,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_1 ) )
= ( C @ ( B @ k1_funct_1 ) ) ) )
& ( ( A @ k1_relat_1 )
= ( B @ k1_relat_1 ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).
thf(294,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
=> ~ ( A @ v1_realset1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_realset1) ).
thf(3684,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) )
=> ~ ( A @ v1_realset1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(210,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ m1_eqrel_1 ) )
=> ( A @ ( B @ ( A @ a_2_1_pua2mss1 ) @ m1_eqrel_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_pua2mss1) ).
thf(3288,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ k1_relat_1 @ ( B @ m1_eqrel_1 ) )
=> ( A @ ( B @ ( A @ a_2_1_pua2mss1 ) @ m1_eqrel_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(891,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k6_enumset1 ) ) ) ) ) ) ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_enumset1) ).
thf(6622,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k6_enumset1 ) ) ) ) ) ) ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(998,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ ( B @ k15_funct_3 ) @ k5_relat_1 ) @ k2_funct_4 )
= ( A @ k2_funct_4 @ ( B @ ( C @ k15_funct_3 ) @ k5_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_altcat_2) ).
thf(7239,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ ( B @ k15_funct_3 ) @ k5_relat_1 ) @ k2_funct_4 )
= ( A @ k2_funct_4 @ ( B @ ( C @ k15_funct_3 ) @ k5_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(2362,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_eqrel_1) ).
thf(14554,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2362]) ).
thf(240,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A )
<=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(3401,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ r2_hidden ) )
=> ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A ) )
& ( ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= A )
=> ~ ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(519,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ k2_funcop_1 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( B @ ( A @ k10_relat_1 ) @ k2_funcop_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_funcop_1) ).
thf(4763,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ k2_funcop_1 ) @ ( A @ k5_relat_1 ) )
= ( C @ ( B @ ( A @ k10_relat_1 ) @ k2_funcop_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(115,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ ( E @ m2_relset_1 ) ) )
& ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ! [F: $i] :
( ( B @ k5_finsub_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ k5_finsub_1 @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( B @ k5_setwiseo ) ) @ ( E @ ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( F @ ( E @ ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( C @ k5_setwiseo ) ) ) ) ) )
& ( ( B @ k1_setwiseo @ ( E @ ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( C @ k1_setwiseo ) ) )
=> ! [F: $i] :
( ( A @ k5_finsub_1 @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( E @ ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( E @ ( D @ ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ ( A @ k7_funct_2 ) ) ) ) @ ( F @ ( C @ ( A @ k10_setwiseo ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_setwiseo) ).
thf(2865,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ ( E @ m2_relset_1 ) ) )
& ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ! [F: $i] :
( ( B @ k5_finsub_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ k5_finsub_1 @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( B @ k5_setwiseo ) ) @ ( E @ ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( G @ ( E @ ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( F @ ( E @ ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( C @ k5_setwiseo ) ) ) ) ) )
& ( ( B @ k1_setwiseo @ ( E @ ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( C @ k1_setwiseo ) ) )
=> ! [F: $i] :
( ( A @ k5_finsub_1 @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ ( B @ ( A @ k10_setwiseo ) ) ) @ ( E @ ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( E @ ( D @ ( C @ k5_finsub_1 @ ( B @ k5_finsub_1 @ ( A @ k7_funct_2 ) ) ) ) @ ( F @ ( C @ ( A @ k10_setwiseo ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_wellord2 ) )
=> ( A @ ( B @ r2_wellord2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r2_wellord2) ).
thf(3168,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_wellord2 ) )
=> ( A @ ( B @ r2_wellord2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(2337,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_mcart_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k13_mcart_1) ).
thf(14403,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k13_mcart_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2337]) ).
thf(1342,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_mcart_1) ).
thf(9119,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ r2_hidden ) )
& ( E @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ r1_xboole_0 ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342]) ).
thf(1622,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( D @ ( D @ ( B @ ( B @ k12_mcart_1 ) ) ) @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( C @ ( C @ ( C @ ( A @ ( A @ k12_mcart_1 ) ) ) @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_nattra_1 ) ) ) ) ) )
= ( F @ ( E @ k3_funct_4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_nattra_1) ).
thf(10496,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( D @ ( D @ ( B @ ( B @ k12_mcart_1 ) ) ) @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( C @ ( C @ ( C @ ( A @ ( A @ k12_mcart_1 ) ) ) @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_nattra_1 ) ) ) ) ) )
= ( F @ ( E @ k3_funct_4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1622]) ).
thf(429,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ v6_ordinal1 )
=> ( ( A @ k3_tarski @ ( A @ k3_tarski @ k2_zfmisc_1 ) )
= ( A @ a_1_0_lattice5 @ k3_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_lattice5) ).
thf(4289,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( A @ v6_ordinal1 )
=> ( ( A @ k3_tarski @ ( A @ k3_tarski @ k2_zfmisc_1 ) )
= ( A @ a_1_0_lattice5 @ k3_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(1864,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_relat_1 @ k9_relat_1 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t162_funct_1) ).
thf(11862,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k6_relat_1 @ k9_relat_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1864]) ).
thf(744,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ k5_funcop_1 ) ) @ v1_finseq_1 )
& ( B @ ( A @ ( C @ k5_funcop_1 ) ) @ v1_funct_1 )
& ( B @ ( A @ ( C @ k5_funcop_1 ) ) @ v1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_finseq_2) ).
thf(5873,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ k1_relat_1 @ ( B @ k2_relat_1 @ ( A @ k1_tarski @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ k5_funcop_1 ) ) @ v1_finseq_1 )
& ( B @ ( A @ ( C @ k5_funcop_1 ) ) @ v1_funct_1 )
& ( B @ ( A @ ( C @ k5_funcop_1 ) ) @ v1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(2221,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_funcop_1) ).
thf(13934,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( E @ m1_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2221]) ).
thf(671,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k5_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) @ ( B @ k5_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_relat_1) ).
thf(5490,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ k5_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) @ ( B @ k5_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(982,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( B @ ( C @ k3_xboole_0 ) @ ( A @ ( C @ k3_xboole_0 ) @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t76_xboole_1) ).
thf(7146,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_xboole_0 ) )
=> ( B @ ( C @ k3_xboole_0 ) @ ( A @ ( C @ k3_xboole_0 ) @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(2372,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(14586,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k6_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2372]) ).
thf(1378,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r1_lattice2 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattice2) ).
thf(9279,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) )
=> ( C @ ( B @ ( A @ r1_lattice2 ) ) ) )
& ( ( C @ ( B @ ( A @ r1_lattice2 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378]) ).
thf(1577,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ k1_fraenkel ) @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k1_fraenkel ) @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k1_funcsdom ) ) ) ) )
= ( E @ ( D @ ( C @ k1_binop_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_funcsdom) ).
thf(10241,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ k1_fraenkel ) @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k1_fraenkel ) @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k1_funcsdom ) ) ) ) )
= ( E @ ( D @ ( C @ k1_binop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1577]) ).
thf(1461,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) )
=> ( ( C @ ( A @ ( E @ ( D @ k5_funcop_1 ) ) @ k7_relat_1 ) )
= ( C @ ( B @ ( E @ ( D @ k5_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funcop_1) ).
thf(9686,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) )
=> ( ( C @ ( A @ ( E @ ( D @ k5_funcop_1 ) ) @ k7_relat_1 ) )
= ( C @ ( B @ ( E @ ( D @ k5_funcop_1 ) ) @ k7_relat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461]) ).
thf(1533,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D
= ( B @ ( C @ k1_realset1 ) ) )
=> ( ( ( A @ ( C @ v2_binop_1 ) )
=> ( B @ ( D @ v2_binop_1 ) ) )
& ( ( A @ ( C @ v3_binop_1 ) )
=> ( B @ ( D @ v3_binop_1 ) ) )
& ( ( A @ ( C @ v1_binop_1 ) )
=> ( B @ ( D @ v1_binop_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_filter_2) ).
thf(10018,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D
= ( B @ ( C @ k1_realset1 ) ) )
=> ( ( ( A @ ( C @ v2_binop_1 ) )
=> ( B @ ( D @ v2_binop_1 ) ) )
& ( ( A @ ( C @ v3_binop_1 ) )
=> ( B @ ( D @ v3_binop_1 ) ) )
& ( ( A @ ( C @ v1_binop_1 ) )
=> ( B @ ( D @ v1_binop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1533]) ).
thf(2312,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_relset_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relset_2) ).
thf(14306,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_relset_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2312]) ).
thf(48,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ r1_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
=> ( ! [E: $i] :
( ( D @ ( C @ k1_funct_2 ) @ ( E @ m1_subset_1 ) )
=> ? [F: $i] :
( ( ( C @ ( F @ k7_relat_1 ) )
= E )
& ( A @ ( B @ k1_fraenkel ) @ ( A @ ( B @ ( F @ m2_fraenkel ) ) ) ) ) )
| ( ( D @ ( C @ k1_funct_2 ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_fraenkel) ).
thf(2626,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ r1_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
=> ( ! [E: $i] :
( ( D @ ( C @ k1_funct_2 ) @ ( E @ m1_subset_1 ) )
=> ? [F: $i] :
( ( ( C @ ( F @ k7_relat_1 ) )
= E )
& ( A @ ( B @ k1_fraenkel ) @ ( A @ ( B @ ( F @ m2_fraenkel ) ) ) ) ) )
| ( ( D @ ( C @ k1_funct_2 ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1938,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ ( A @ r3_relat_2 ) )
<=> ! [C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_2) ).
thf(12343,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( B @ ( A @ r3_relat_2 ) ) )
& ( ( B @ ( A @ r3_relat_2 ) )
=> ! [C: $i,D: $i] :
( ( ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( D @ r2_hidden ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( A @ ( C @ ( D @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1938]) ).
thf(314,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k3_funct_3 @ m2_relset_1 ) ) )
& ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k3_funct_3 @ v1_funct_2 ) ) )
& ( A @ k3_funct_3 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_funct_3) ).
thf(3757,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k3_funct_3 @ m2_relset_1 ) ) )
& ( A @ k1_relat_1 @ k1_zfmisc_1 @ ( A @ k2_relat_1 @ k1_zfmisc_1 @ ( A @ k3_funct_3 @ v1_funct_2 ) ) )
& ( A @ k3_funct_3 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(2393,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_realset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_realset1) ).
thf(14678,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m2_realset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2393]) ).
thf(2295,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s3_subset_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ r2_hidden ) )
<=> ( B @ p1_s3_subset_1 ) ) )
& ( f1_s3_subset_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_subset_1) ).
thf(14242,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s3_subset_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ p1_s3_subset_1 )
=> ( A @ ( B @ r2_hidden ) ) )
& ( ( A @ ( B @ r2_hidden ) )
=> ( B @ p1_s3_subset_1 ) ) ) )
& ( f1_s3_subset_1 @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2295]) ).
thf(851,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ! [F: $i,G: $i] :
~ ( ( E @ ( C @ k3_xboole_0 ) @ ( G @ r2_hidden ) )
& ( D @ ( B @ k3_xboole_0 ) @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ k4_tarski ) ) ) )
& ( E @ ( D @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ k3_xboole_0 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_zfmisc_1) ).
thf(6447,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ! [F: $i,G: $i] :
~ ( ( E @ ( C @ k3_xboole_0 ) @ ( G @ r2_hidden ) )
& ( D @ ( B @ k3_xboole_0 ) @ ( F @ r2_hidden ) )
& ( A
= ( G @ ( F @ k4_tarski ) ) ) )
& ( E @ ( D @ k2_zfmisc_1 ) @ ( C @ ( B @ k2_zfmisc_1 ) @ k3_xboole_0 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(1508,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( D @ ( A @ ( C @ k4_funcop_1 ) ) @ ( B @ k6_partfun1 @ k5_relat_1 ) )
= ( D @ ( B @ ( A @ k7_relat_1 ) @ ( C @ k4_funcop_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_funcop_1) ).
thf(9912,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( D @ ( A @ ( C @ k4_funcop_1 ) ) @ ( B @ k6_partfun1 @ k5_relat_1 ) )
= ( D @ ( B @ ( A @ k7_relat_1 ) @ ( C @ k4_funcop_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1508]) ).
thf(488,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_zfmisc_1) ).
thf(4587,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( ( A @ k1_tarski @ ( B @ k3_xboole_0 ) )
= ( A @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(1747,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k5_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) @ ( A @ k3_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_tops_2) ).
thf(11150,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( ( B @ ( A @ k7_setfam_1 ) @ ( A @ k5_setfam_1 ) )
= ( B @ ( A @ k6_setfam_1 ) @ ( A @ k3_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1747]) ).
thf(971,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ k1_tarski @ ( A @ k10_relat_1 ) )
!= ( C @ k1_tarski ) )
& ( A @ k2_relat_1 @ ( B @ r2_hidden ) ) )
<=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_funct_1) ).
thf(7024,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ v2_funct_1 )
=> ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ k1_tarski @ ( A @ k10_relat_1 ) )
!= ( C @ k1_tarski ) )
& ( A @ k2_relat_1 @ ( B @ r2_hidden ) ) ) )
& ( ! [B: $i] :
~ ( ! [C: $i] :
( ( B @ k1_tarski @ ( A @ k10_relat_1 ) )
!= ( C @ k1_tarski ) )
& ( A @ k2_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k2_funcop_1 ) @ v1_funct_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v2_relat_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_funcop_1) ).
thf(3067,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k2_funcop_1 ) @ v1_funct_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v2_relat_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1697,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
thf(10873,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k9_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( B @ ( E @ r2_hidden ) )
& ( A @ ( D @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1697]) ).
thf(1646,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( D @ ( D @ ( B @ ( B @ k12_mcart_1 ) ) ) @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( C @ ( C @ ( C @ ( A @ ( A @ k12_mcart_1 ) ) ) @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k12_mcart_1 ) ) ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_nattra_1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_nattra_1 ) ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_nattra_1) ).
thf(10595,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( D @ ( D @ ( B @ ( B @ k12_mcart_1 ) ) ) @ ( F @ m1_relset_1 ) ) )
& ( F @ v1_funct_1 )
& ( C @ ( C @ ( C @ ( A @ ( A @ k12_mcart_1 ) ) ) @ ( E @ m1_relset_1 ) ) )
& ( E @ v1_funct_1 )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k12_mcart_1 ) ) ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_nattra_1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_nattra_1 ) ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1646]) ).
thf(2194,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k11_setwiseo @ ( A @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( B @ r2_hidden ) )
<=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_setwiseo) ).
thf(13812,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( ( B = C )
=> ( C @ ( A @ k11_setwiseo @ ( A @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k11_setwiseo @ ( A @ k5_finsub_1 @ ( A @ k8_funct_2 ) ) ) @ ( B @ r2_hidden ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2194]) ).
thf(1957,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_zfmisc_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(12467,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k2_zfmisc_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i] :
( ( D
= ( F @ ( E @ k4_tarski ) ) )
& ( B @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1957]) ).
thf(846,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
<=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ ( C @ k5_relat_1 ) ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funct_1) ).
thf(6408,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ ( C @ k5_relat_1 ) ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( B = C ) ) ) )
=> ( A @ v2_funct_1 ) )
& ( ( A @ v2_funct_1 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ k5_relat_1 ) )
= ( A @ ( C @ k5_relat_1 ) ) )
& ( ( B @ k1_relat_1 )
= ( C @ k1_relat_1 ) )
& ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) )
=> ( B = C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(1385,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ k2_funcop_1 ) @ ( C @ ( A @ k2_funcop_1 ) @ k15_funct_3 ) )
= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funcop_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_altcat_2) ).
thf(9306,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ k2_funcop_1 ) @ ( C @ ( A @ k2_funcop_1 ) @ k15_funct_3 ) )
= ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funcop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385]) ).
thf(1630,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(10526,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1630]) ).
thf(1475,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_funcop_1 ) )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_4) ).
thf(9760,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k1_tarski @ k2_funcop_1 ) )
= ( B @ ( A @ k4_tarski ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1475]) ).
thf(1019,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( A @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_partfun1) ).
thf(7395,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ ( A @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(1884,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_funct_2) ).
thf(11995,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( B @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1884]) ).
thf(1414,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( D @ k2_relat_1 @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_funct_2) ).
thf(9438,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( D @ k2_relat_1 @ ( C @ ( D @ k1_funct_1 ) @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414]) ).
thf(1400,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( F @ v1_funct_1 )
& ( F @ v1_relat_1 ) )
=> ( ( ( ( F @ k1_relat_1 )
= ( D @ ( C @ k2_zfmisc_1 ) ) )
& ( ( E @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
=> ( ( F @ ( E @ k3_funct_4 ) @ k1_relat_1 )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_4) ).
thf(9389,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( F @ v1_funct_1 )
& ( F @ v1_relat_1 ) )
=> ( ( ( ( F @ k1_relat_1 )
= ( D @ ( C @ k2_zfmisc_1 ) ) )
& ( ( E @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
=> ( ( F @ ( E @ k3_funct_4 ) @ k1_relat_1 )
= ( D @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400]) ).
thf(731,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) )
!= k1_xboole_0 )
=> ( ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( B @ ( A @ k10_funct_3 ) @ k1_funct_3 @ k1_funct_1 ) )
= D )
& ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( B @ ( A @ k9_funct_3 ) @ k1_funct_3 @ k1_funct_1 ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_borsuk_1) ).
thf(5777,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) )
!= k1_xboole_0 )
=> ( ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( B @ ( A @ k10_funct_3 ) @ k1_funct_3 @ k1_funct_1 ) )
= D )
& ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( B @ ( A @ k9_funct_3 ) @ k1_funct_3 @ k1_funct_1 ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(1073,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k3_funcop_1 ) ) )
= ( A @ ( C @ ( B @ k13_funct_3 ) @ k5_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_funcop_1) ).
thf(7606,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k3_funcop_1 ) ) )
= ( A @ ( C @ ( B @ k13_funct_3 ) @ k5_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(545,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( A @ k15_funct_3 ) @ ( D @ ( B @ k15_funct_3 ) @ k5_relat_1 ) )
= ( C @ ( D @ k5_relat_1 ) @ ( A @ ( B @ k5_relat_1 ) @ k15_funct_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_funct_3) ).
thf(4873,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( A @ k15_funct_3 ) @ ( D @ ( B @ k15_funct_3 ) @ k5_relat_1 ) )
= ( C @ ( D @ k5_relat_1 ) @ ( A @ ( B @ k5_relat_1 ) @ k15_funct_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(495,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i,D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ k5_finsub_1 @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ k5_finsub_1 @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( F @ ( D @ ( E @ ( B @ ( A @ k8_setwiseo ) ) ) @ ( C @ ( B @ k10_setwiseo ) ) ) )
= ( F @ ( E @ ( C @ k5_finsub_1 @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( D @ ( C @ ( A @ k10_setwiseo ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_setwiseo) ).
thf(4656,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i,D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( C @ k5_finsub_1 @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ k5_finsub_1 @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( F @ ( D @ ( E @ ( B @ ( A @ k8_setwiseo ) ) ) @ ( C @ ( B @ k10_setwiseo ) ) ) )
= ( F @ ( E @ ( C @ k5_finsub_1 @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ ( D @ ( C @ ( A @ k10_setwiseo ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(843,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ ( A @ k6_partfun1 @ k5_relat_1 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_functor0) ).
thf(6390,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ ( A @ k6_partfun1 @ k5_relat_1 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(1055,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( B @ ( C @ ( A @ r1_binop_1 ) ) )
<=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_binop_1) ).
thf(7547,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_binop_1 ) )
=> ( ( ( B @ ( C @ ( A @ r2_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r1_binop_1 ) ) ) )
& ( ( B @ ( C @ ( A @ r1_binop_1 ) ) )
=> ( B @ ( C @ ( A @ r2_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(1490,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) )
=> ( ( A @ ( C @ ( B @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_4) ).
thf(9819,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) )
=> ( ( A @ ( C @ ( B @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1490]) ).
thf(688,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( A @ ( B @ k7_relat_1 ) @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_funct_1) ).
thf(5573,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ v2_funct_1 )
=> ( A @ ( B @ k7_relat_1 ) @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(567,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( ( C @ ( A @ k9_relat_1 ) )
= B )
& ( C @ v1_finset_1 )
& ( A @ k1_relat_1 @ ( C @ r1_tarski ) ) )
& ( A @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t195_orders_1) ).
thf(4997,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( ( C @ ( A @ k9_relat_1 ) )
= B )
& ( C @ v1_finset_1 )
& ( A @ k1_relat_1 @ ( C @ r1_tarski ) ) )
& ( A @ k2_relat_1 @ ( B @ r1_tarski ) )
& ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(1568,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_domain_1 ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_enumset1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k11_domain_1) ).
thf(10199,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_domain_1 ) ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k4_enumset1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1568]) ).
thf(1835,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ m2_filter_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( ( B @ ( G @ ( F @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) )
& ( B @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) )
=> ( B @ ( G @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_filter_1) ).
thf(11681,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( ( B @ ( G @ ( F @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) )
& ( B @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) )
=> ( B @ ( G @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) )
=> ( B @ ( A @ ( C @ m2_filter_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_filter_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( ( B @ ( G @ ( F @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) )
& ( B @ ( E @ ( D @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) )
=> ( B @ ( G @ ( E @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( A @ ( A @ k1_domain_1 ) ) ) @ r2_hidden ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1835]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_6_0_domain_1 ) ) ) ) ) @ ( A @ r2_hidden ) )
<=> ? [H: $i,I: $i,J: $i] :
( ( G @ ( J @ r2_hidden ) )
& ( F @ ( I @ r2_hidden ) )
& ( E @ ( H @ r2_hidden ) )
& ( A
= ( J @ ( I @ ( H @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
& ( D @ ( J @ m1_subset_1 ) )
& ( C @ ( I @ m1_subset_1 ) )
& ( B @ ( H @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_6_0_domain_1) ).
thf(4738,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [H: $i,I: $i,J: $i] :
( ( G @ ( J @ r2_hidden ) )
& ( F @ ( I @ r2_hidden ) )
& ( E @ ( H @ r2_hidden ) )
& ( A
= ( J @ ( I @ ( H @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
& ( D @ ( J @ m1_subset_1 ) )
& ( C @ ( I @ m1_subset_1 ) )
& ( B @ ( H @ m1_subset_1 ) ) )
=> ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_6_0_domain_1 ) ) ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_6_0_domain_1 ) ) ) ) ) @ ( A @ r2_hidden ) )
=> ? [H: $i,I: $i,J: $i] :
( ( G @ ( J @ r2_hidden ) )
& ( F @ ( I @ r2_hidden ) )
& ( E @ ( H @ r2_hidden ) )
& ( A
= ( J @ ( I @ ( H @ ( D @ ( C @ ( B @ k4_domain_1 ) ) ) ) ) ) )
& ( D @ ( J @ m1_subset_1 ) )
& ( C @ ( I @ m1_subset_1 ) )
& ( B @ ( H @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(592,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= ( A @ ( B @ k1_funct_4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_funct_4) ).
thf(5115,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( B @ ( A @ k1_funct_4 ) )
= ( A @ ( B @ k1_funct_4 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(524,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k18_group_2 ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k18_group_2) ).
thf(4780,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k18_group_2 ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(42,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( k5_numbers @ ( k1_numbers @ ( A @ k3_finseq_1 @ m2_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_finseq_1) ).
thf(2611,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( k5_numbers @ ( k1_numbers @ ( A @ k3_finseq_1 @ m2_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(405,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ~ ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) )
& ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_relset_1) ).
thf(4185,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ~ ( ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ~ ( C @ ( A @ ( B @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) )
& ( C @ ( A @ ( B @ k5_relset_1 ) ) @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(2257,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( C @ k3_tarski ) )
=> ( ( D @ ( A @ k3_subset_1 ) )
= ( C @ ( B @ k3_subset_1 ) @ k3_tarski ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_borsuk_1) ).
thf(14098,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ! [C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D
= ( C @ k3_tarski ) )
=> ( ( D @ ( A @ k3_subset_1 ) )
= ( C @ ( B @ k3_subset_1 ) @ k3_tarski ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2257]) ).
thf(902,axiom,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_realset1) ).
thf(6674,plain,
! [A: $i,B: $i] :
( ( A @ v1_relat_1 )
=> ( B @ ( A @ k1_realset1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(1566,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ k6_relat_1 @ ( C @ k5_relat_1 ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_partfun1) ).
thf(10188,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( B @ k6_relat_1 @ ( C @ k5_relat_1 ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1566]) ).
thf(1194,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( B @ ( A @ k2_funcop_1 ) @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ k2_funcop_1 ) @ k1_relat_1 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funcop_1) ).
thf(8285,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( B @ ( A @ k2_funcop_1 ) @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ k2_funcop_1 ) @ k1_relat_1 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(1175,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( C @ k1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
thf(8153,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k4_relset_1 ) ) )
= ( C @ k1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(915,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C
= ( A @ ( B @ ( D @ k4_funcop_1 ) ) ) )
& ( D @ k1_relat_1 @ ( A @ k1_tarski @ ( B @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( ( C @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_finseq_2) ).
thf(6743,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_finseq_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( C
= ( A @ ( B @ ( D @ k4_funcop_1 ) ) ) )
& ( D @ k1_relat_1 @ ( A @ k1_tarski @ ( B @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) ) )
=> ( ( C @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(1703,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) ) )
=> ( ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) )
| ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_mcart_1) ).
thf(10928,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) ) )
=> ( ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) )
| ( ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1703]) ).
thf(1998,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_funct_2) ).
thf(12722,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1998]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k1_funct_2 ) @ ( D @ r2_hidden ) )
=> ( ( ( C @ ( A @ k1_funct_2 ) @ ( B @ k1_funct_2 ) @ ( D @ k5_funct_5 @ r2_hidden ) )
& ( C @ ( B @ k1_funct_2 ) @ ( A @ k1_funct_2 ) @ ( D @ k3_funct_5 @ r2_hidden ) ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_6) ).
thf(3056,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k1_funct_2 ) @ ( D @ r2_hidden ) )
=> ( ( ( C @ ( A @ k1_funct_2 ) @ ( B @ k1_funct_2 ) @ ( D @ k5_funct_5 @ r2_hidden ) )
& ( C @ ( B @ k1_funct_2 ) @ ( A @ k1_funct_2 ) @ ( D @ k3_funct_5 @ r2_hidden ) ) )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(1332,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i,D: $i] :
( ( B @ ( A @ k1_funct_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ~ ( D @ ( B @ ( A @ k3_pralg_3 ) @ k10_relat_1 ) @ ( C @ k1_tarski @ ( B @ ( A @ k3_pralg_3 ) @ k10_relat_1 ) @ r1_xboole_0 ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_yellow17) ).
thf(9078,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i,D: $i] :
( ( B @ ( A @ k1_funct_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ~ ( D @ ( B @ ( A @ k3_pralg_3 ) @ k10_relat_1 ) @ ( C @ k1_tarski @ ( B @ ( A @ k3_pralg_3 ) @ k10_relat_1 ) @ r1_xboole_0 ) )
=> ( D @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(1278,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k15_funct_3 ) @ v2_funct_1 )
& ( B @ ( A @ k15_funct_3 ) @ v1_funct_1 )
& ( B @ ( A @ k15_funct_3 ) @ v1_relat_1 )
& ( B @ ( A @ k15_funct_3 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_functor0) ).
thf(8761,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k15_funct_3 ) @ v2_funct_1 )
& ( B @ ( A @ k15_funct_3 ) @ v1_funct_1 )
& ( B @ ( A @ k15_funct_3 ) @ v1_relat_1 )
& ( B @ ( A @ k15_funct_3 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(1260,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ~ ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_xboole_0 ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t185_partfun1) ).
thf(8666,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ~ ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_xboole_0 ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k7_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k7_relat_1 ) @ v2_relat_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pre_circ) ).
thf(2658,plain,
! [A: $i,B: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v2_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k7_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k7_relat_1 ) @ v2_relat_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1939,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k4_tarski ) )
= ( D @ ( C @ k4_tarski ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(12355,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k4_tarski ) )
= ( D @ ( C @ k4_tarski ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1939]) ).
thf(353,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k15_funct_3 ) @ k2_funct_1 )
= ( B @ k2_funct_1 @ ( A @ k2_funct_1 @ k15_funct_3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_functor0) ).
thf(3929,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( ( B @ ( A @ k15_funct_3 ) @ k2_funct_1 )
= ( B @ k2_funct_1 @ ( A @ k2_funct_1 @ k15_funct_3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_2 ) @ ( A @ k1_funct_2 ) @ ( D @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_2 ) @ ( B @ k1_funct_2 ) @ ( D @ k10_funct_6 @ r2_hidden ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_6) ).
thf(2775,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( B @ k1_funct_2 ) @ ( A @ k1_funct_2 ) @ ( D @ r2_hidden ) )
=> ( ( C @ ( A @ k1_funct_2 ) @ ( B @ k1_funct_2 ) @ ( D @ k10_funct_6 @ r2_hidden ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(1789,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
<=> ( B
= ( A @ k2_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_subset_1) ).
thf(11383,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B
= ( A @ k2_subset_1 ) )
=> ( B @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) ) )
& ( ( B @ ( B @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( B
= ( A @ k2_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1789]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
thf(4061,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k5_relat_1 ) @ k1_funct_1 ) )
= ( A @ ( C @ k1_funct_1 ) @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_classes2) ).
thf(2907,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_classes2 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ k1_tarski @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1456,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_funct_4 )
= ( B @ ( A @ k2_funct_4 @ k5_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_altcat_2) ).
thf(9647,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_funct_4 )
= ( B @ ( A @ k2_funct_4 @ k5_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456]) ).
thf(483,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_tarski ) @ k3_tarski )
= ( B @ ( A @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_zfmisc_1) ).
thf(4574,plain,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ k1_tarski @ k2_tarski ) @ k3_tarski )
= ( B @ ( A @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(1090,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_1) ).
thf(7670,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ k2_relat_1 @ ( A @ ( B @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(141,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k5_funct_5 @ k1_relat_1 )
= ( A @ k1_relat_1 @ k2_funct_5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_funct_5) ).
thf(2988,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k5_funct_5 @ k1_relat_1 )
= ( A @ k1_relat_1 @ k2_funct_5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(530,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t176_relat_1) ).
thf(4806,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(2031,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ k2_funct_4 @ k2_funct_4 )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funct_4) ).
thf(12915,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ k2_funct_4 @ k2_funct_4 )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2031]) ).
thf(1563,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_relat_1) ).
thf(10169,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1563]) ).
thf(646,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( D @ k2_relat_1 @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_partfun1) ).
thf(5382,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( D @ k2_relat_1 @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(1722,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( C @ k1_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funct_3) ).
thf(11039,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( B @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r1_tarski ) )
=> ( C @ k1_relat_1 @ ( A @ ( B @ k9_relat_1 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1722]) ).
thf(1182,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_mcart_1) ).
thf(8197,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r2_hidden ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(734,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ( ( D @ k1_tarski @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= k1_xboole_0 )
& ( B @ ( D @ r2_hidden ) ) )
<=> ( ( C @ k2_relat_1 )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_funct_2) ).
thf(5813,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( ( C @ k2_relat_1 )
= B )
=> ! [D: $i] :
~ ( ( ( D @ k1_tarski @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= k1_xboole_0 )
& ( B @ ( D @ r2_hidden ) ) ) )
& ( ! [D: $i] :
~ ( ( ( D @ k1_tarski @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) )
= k1_xboole_0 )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( C @ k2_relat_1 )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(954,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( A @ ( B @ k3_tarski @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t177_orders_1) ).
thf(6910,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
( ( ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
=> ( ( A @ ( B @ k3_tarski @ r2_hidden ) )
| ( B = k1_xboole_0 ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(904,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( A @ k1_relat_1 )
= k1_xboole_0 )
<=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
thf(6694,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
=> ( ( A @ k1_relat_1 )
= k1_xboole_0 ) )
& ( ( ( A @ k1_relat_1 )
= k1_xboole_0 )
=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(1547,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_funct_5 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_5) ).
thf(10077,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) )
=> ( B
= ( A @ k1_funct_5 ) ) )
& ( ( B
= ( A @ k1_funct_5 ) )
=> ! [C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] : ( A @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1547]) ).
thf(1467,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_funct_1) ).
thf(9707,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k6_relat_1 @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ ( B @ k1_relat_1 @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467]) ).
thf(2276,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_mcart_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k14_mcart_1) ).
thf(14172,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_mcart_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k4_zfmisc_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2276]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_funct_2) ).
thf(4121,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( A @ ( C @ r2_hidden ) )
=> ( ( C @ ( D @ k1_funct_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(951,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( A @ k1_ens_1 @ ( C @ ( B @ k1_funct_2 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_ens_1) ).
thf(6903,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( A @ k1_ens_1 @ ( C @ ( B @ k1_funct_2 ) @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ ( C @ ( B @ ( A @ k3_funcsdom ) ) @ m2_fraenkel ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_funcsdom) ).
thf(3613,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ ( C @ ( B @ ( A @ k3_funcsdom ) ) @ m2_fraenkel ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(1556,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ k15_funct_3 ) @ k9_relat_1 ) )
= ( B @ ( D @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k2_zfmisc_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_funct_3) ).
thf(10135,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ k15_funct_3 ) @ k9_relat_1 ) )
= ( B @ ( D @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k2_zfmisc_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1556]) ).
thf(71,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( ( C @ ( A @ k1_funct_1 ) )
= D )
<=> ( ( D @ ( B @ k1_funct_1 ) )
= C ) ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k2_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_funct_1) ).
thf(2707,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ! [C: $i,D: $i] :
( ( ( B @ k1_relat_1 @ ( D @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( C @ r2_hidden ) ) )
=> ( ( ( ( D @ ( B @ k1_funct_1 ) )
= C )
=> ( ( C @ ( A @ k1_funct_1 ) )
= D ) )
& ( ( ( C @ ( A @ k1_funct_1 ) )
= D )
=> ( ( D @ ( B @ k1_funct_1 ) )
= C ) ) ) )
& ( ( A @ k2_relat_1 )
= ( B @ k1_relat_1 ) )
& ( ( A @ k1_relat_1 )
= ( B @ k2_relat_1 ) )
& ( A @ v2_funct_1 ) )
=> ( B
= ( A @ k2_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1572,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_oppcat_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k1_oppcat_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_oppcat_1) ).
thf(10220,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_oppcat_1 ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k1_oppcat_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1572]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ ( C @ k3_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_partfun1) ).
thf(2853,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ ( C @ k2_relat_1 @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( C
= ( B @ ( A @ ( C @ k3_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(1776,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( D @ ( B @ r1_binop_1 ) ) )
& ( E @ ( C @ ( A @ r1_binop_1 ) ) ) )
<=> ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_binop_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_filter_1) ).
thf(11319,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_binop_1 ) ) )
=> ( ( F @ ( D @ ( B @ r1_binop_1 ) ) )
& ( E @ ( C @ ( A @ r1_binop_1 ) ) ) ) )
& ( ( ( F @ ( D @ ( B @ r1_binop_1 ) ) )
& ( E @ ( C @ ( A @ r1_binop_1 ) ) ) )
=> ( F @ ( E @ ( B @ ( A @ k7_filter_1 ) ) ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ ( B @ ( A @ k2_zfmisc_1 ) @ r1_binop_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1776]) ).
thf(1303,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k2_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_relat_1) ).
thf(8882,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ~ ( ! [C: $i] :
~ ( B @ k2_relat_1 @ ( C @ r2_hidden ) )
& ( B @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(1996,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( D @ ( C @ r1_partfun1 ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_funct_2) ).
thf(12698,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( D @ ( C @ r1_partfun1 ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1996]) ).
thf(570,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t148_funct_1) ).
thf(5008,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ ( B @ k10_relat_1 ) @ ( B @ k9_relat_1 ) )
= ( B @ k1_relat_1 @ ( B @ k9_relat_1 ) @ ( A @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(1975,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( F @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_funcop_1) ).
thf(12574,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_funcop_1 ) ) ) ) @ ( A @ ( B @ k8_funct_2 ) ) ) )
= ( F @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1975]) ).
thf(1195,axiom,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_subset_1) ).
thf(8292,plain,
! [A: $i] :
( ( A @ k1_subset_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k10_relat_1 ) @ ( B @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( A @ ( B @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_setwiseo) ).
thf(3383,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ ( C @ k10_relat_1 ) @ ( B @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( A @ ( B @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1899,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) )
= ( D @ ( C @ k4_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
thf(12061,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) )
= ( D @ ( C @ k4_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1899]) ).
thf(2358,axiom,
( ! [A: $i] :
( ( f1_s2_filter_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s2_filter_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( f2_s2_filter_1 @ ( f1_s2_filter_1 @ k2_filter_1 ) ) @ ( A @ ( f2_s2_filter_1 @ ( f1_s2_filter_1 @ k2_filter_1 ) ) @ p1_s2_filter_1 ) ) ) )
=> ! [A: $i] :
( ( f2_s2_filter_1 @ ( f1_s2_filter_1 @ k8_eqrel_1 ) @ ( f1_s2_filter_1 @ k1_zfmisc_1 @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( f2_s2_filter_1 @ ( f1_s2_filter_1 @ k8_eqrel_1 ) @ ( f1_s2_filter_1 @ k1_zfmisc_1 @ ( B @ m2_subset_1 ) ) )
=> ( B @ ( A @ p1_s2_filter_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_filter_1) ).
thf(14503,plain,
( ! [A: $i] :
( ( f1_s2_filter_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s2_filter_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( f2_s2_filter_1 @ ( f1_s2_filter_1 @ k2_filter_1 ) ) @ ( A @ ( f2_s2_filter_1 @ ( f1_s2_filter_1 @ k2_filter_1 ) ) @ p1_s2_filter_1 ) ) ) )
=> ! [A: $i] :
( ( f2_s2_filter_1 @ ( f1_s2_filter_1 @ k8_eqrel_1 ) @ ( f1_s2_filter_1 @ k1_zfmisc_1 @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( f2_s2_filter_1 @ ( f1_s2_filter_1 @ k8_eqrel_1 ) @ ( f1_s2_filter_1 @ k1_zfmisc_1 @ ( B @ m2_subset_1 ) ) )
=> ( B @ ( A @ p1_s2_filter_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2358]) ).
thf(2023,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_domain_1) ).
thf(12880,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_domain_1 ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2023]) ).
thf(2290,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_relset_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relset_2) ).
thf(14224,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) )
=> ( A @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k3_relset_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2290]) ).
thf(654,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_yellow_3 ) ) ) ) ) )
= ( F @ ( E @ k1_yellow_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_yellow_3) ).
thf(5426,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_yellow_3 ) ) ) ) ) )
= ( F @ ( E @ k1_yellow_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(1296,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k10_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t182_relat_1) ).
thf(8854,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 @ ( A @ k10_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( ( C @ ( B @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) )
& ( ( C @ ( A @ k8_relat_1 ) @ ( B @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_funct_1) ).
thf(4042,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( ( ( C @ ( B @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) )
& ( ( C @ ( A @ k8_relat_1 ) @ ( B @ k8_relat_1 ) )
= ( C @ ( A @ k8_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(2384,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(14618,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2384]) ).
thf(1356,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_relat_1) ).
thf(9205,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k1_relat_1 @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(364,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ k2_funct_5 @ ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ k4_xboole_0 ) @ r1_tarski ) )
& ( B @ ( A @ k4_xboole_0 ) @ k1_funct_5 @ ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ k4_xboole_0 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_5) ).
thf(3991,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ k2_funct_5 @ ( B @ k2_funct_5 @ ( A @ k2_funct_5 @ k4_xboole_0 ) @ r1_tarski ) )
& ( B @ ( A @ k4_xboole_0 ) @ k1_funct_5 @ ( B @ k1_funct_5 @ ( A @ k1_funct_5 @ k4_xboole_0 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(2347,axiom,
( ! [A: $i] :
( ( f1_s4_filter_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f2_s4_filter_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s4_filter_1 @ ( f1_s4_filter_1 @ k1_domain_1 ) ) ) @ p1_s4_filter_1 ) ) )
=> ! [A: $i] :
( ( f2_s4_filter_1 @ ( f1_s4_filter_1 @ k2_zfmisc_1 ) @ ( A @ m1_subset_1 ) )
=> ( A @ p1_s4_filter_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_filter_1) ).
thf(14457,plain,
( ! [A: $i] :
( ( f1_s4_filter_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f2_s4_filter_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ ( f2_s4_filter_1 @ ( f1_s4_filter_1 @ k1_domain_1 ) ) ) @ p1_s4_filter_1 ) ) )
=> ! [A: $i] :
( ( f2_s4_filter_1 @ ( f1_s4_filter_1 @ k2_zfmisc_1 ) @ ( A @ m1_subset_1 ) )
=> ( A @ p1_s4_filter_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2347]) ).
thf(621,axiom,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t175_orders_1) ).
thf(5228,plain,
! [A: $i] :
~ ( ! [B: $i] :
~ ( ! [C: $i] :
~ ( ( C @ ( B @ r1_tarski ) )
& ( C != B )
& ( A @ ( C @ r2_hidden ) ) )
& ( A @ ( B @ r2_hidden ) ) )
& ! [B: $i] :
~ ( ! [C: $i] :
~ ( ! [D: $i] :
( ( B @ ( D @ r2_hidden ) )
=> ( C @ ( D @ r1_tarski ) ) )
& ( A @ ( C @ r2_hidden ) ) )
& ( B @ v6_ordinal1 )
& ( A @ ( B @ r1_tarski ) ) )
& ( A != k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(2286,axiom,
( ! [A: $i] :
( ( f1_s1_yellow_3 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s1_yellow_3 @ ( B @ m1_subset_1 ) )
=> ( f1_s1_yellow_3 @ ( B @ ( A @ f2_s1_yellow_3 ) @ r2_hidden ) ) ) )
=> ( f1_s1_yellow_3 @ k1_zfmisc_1 @ ( a_0_0_yellow_3 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_yellow_3) ).
thf(14204,plain,
( ! [A: $i] :
( ( f1_s1_yellow_3 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s1_yellow_3 @ ( B @ m1_subset_1 ) )
=> ( f1_s1_yellow_3 @ ( B @ ( A @ f2_s1_yellow_3 ) @ r2_hidden ) ) ) )
=> ( f1_s1_yellow_3 @ k1_zfmisc_1 @ ( a_0_0_yellow_3 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2286]) ).
thf(1420,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ ( B @ k5_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t93_relat_1) ).
thf(9459,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( A @ ( C @ k7_relat_1 ) @ ( B @ k5_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1420]) ).
thf(1802,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k10_funct_3 ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k10_funct_3 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k10_funct_3 ) @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_funct_3) ).
thf(11469,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k10_funct_3 ) @ m2_relset_1 ) ) )
& ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k10_funct_3 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k10_funct_3 ) @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1802]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ k2_tarski ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_zfmisc_1) ).
thf(3561,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) )
=> ( ( C @ ( B @ k2_tarski ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( C @ ( B @ k2_tarski ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ~ ( ( A
!= ( C @ ( B @ k2_tarski ) ) )
& ( A
!= ( C @ k1_tarski ) )
& ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(2128,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_cat_5 ) ) ) )
= ( D @ k18_mcart_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_cat_5) ).
thf(13441,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_cat_5 ) ) ) )
= ( D @ k18_mcart_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2128]) ).
thf(1095,axiom,
! [A: $i,B: $i] :
( ( B @ k3_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ ( A @ k1_tarski @ k3_setfam_1 ) @ k3_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_setfam_1) ).
thf(7700,plain,
! [A: $i,B: $i] :
( ( B @ k3_tarski @ ( A @ k3_xboole_0 ) )
= ( B @ ( A @ k1_tarski @ k3_setfam_1 ) @ k3_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(145,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_relat_1 )
<=> ! [B: $i] :
~ ( ( B @ ( A @ k1_funct_1 ) @ v1_xboole_0 )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15_funct_1) ).
thf(3003,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ! [B: $i] :
~ ( ( B @ ( A @ k1_funct_1 ) @ v1_xboole_0 )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( A @ v2_relat_1 ) )
& ( ( A @ v2_relat_1 )
=> ! [B: $i] :
~ ( ( B @ ( A @ k1_funct_1 ) @ v1_xboole_0 )
& ( A @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ k15_funct_3 ) @ v2_funct_1 )
& ( A @ ( B @ k15_funct_3 ) @ v1_funct_1 )
& ( A @ ( B @ k15_funct_3 ) @ v1_relat_1 )
& ( A @ ( B @ k15_funct_3 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_functor0) ).
thf(5394,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ k15_funct_3 ) @ v2_funct_1 )
& ( A @ ( B @ k15_funct_3 ) @ v1_funct_1 )
& ( A @ ( B @ k15_funct_3 ) @ v1_relat_1 )
& ( A @ ( B @ k15_funct_3 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(1820,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(11567,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1820]) ).
thf(1081,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ ( B @ ( A @ k8_relat_1 ) @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_partfun1) ).
thf(7638,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ ( B @ ( A @ k8_relat_1 ) @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(466,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_relat_1) ).
thf(4495,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k7_relat_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(2328,axiom,
( ! [A: $i] :
( ( f1_s3_filter_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s3_filter_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s3_filter_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( f2_s3_filter_1 @ ( f1_s3_filter_1 @ k2_filter_1 ) ) @ ( B @ ( f2_s3_filter_1 @ ( f1_s3_filter_1 @ k2_filter_1 ) ) @ ( A @ ( f2_s3_filter_1 @ ( f1_s3_filter_1 @ k2_filter_1 ) ) @ p1_s3_filter_1 ) ) ) ) ) )
=> ! [A: $i] :
( ( f2_s3_filter_1 @ ( f1_s3_filter_1 @ k8_eqrel_1 ) @ ( f1_s3_filter_1 @ k1_zfmisc_1 @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( f2_s3_filter_1 @ ( f1_s3_filter_1 @ k8_eqrel_1 ) @ ( f1_s3_filter_1 @ k1_zfmisc_1 @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( f2_s3_filter_1 @ ( f1_s3_filter_1 @ k8_eqrel_1 ) @ ( f1_s3_filter_1 @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) )
=> ( C @ ( B @ ( A @ p1_s3_filter_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_filter_1) ).
thf(14368,plain,
( ! [A: $i] :
( ( f1_s3_filter_1 @ ( A @ m1_subset_1 ) )
=> ! [B: $i] :
( ( f1_s3_filter_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( f1_s3_filter_1 @ ( C @ m1_subset_1 ) )
=> ( C @ ( f2_s3_filter_1 @ ( f1_s3_filter_1 @ k2_filter_1 ) ) @ ( B @ ( f2_s3_filter_1 @ ( f1_s3_filter_1 @ k2_filter_1 ) ) @ ( A @ ( f2_s3_filter_1 @ ( f1_s3_filter_1 @ k2_filter_1 ) ) @ p1_s3_filter_1 ) ) ) ) ) )
=> ! [A: $i] :
( ( f2_s3_filter_1 @ ( f1_s3_filter_1 @ k8_eqrel_1 ) @ ( f1_s3_filter_1 @ k1_zfmisc_1 @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ( f2_s3_filter_1 @ ( f1_s3_filter_1 @ k8_eqrel_1 ) @ ( f1_s3_filter_1 @ k1_zfmisc_1 @ ( B @ m2_subset_1 ) ) )
=> ! [C: $i] :
( ( f2_s3_filter_1 @ ( f1_s3_filter_1 @ k8_eqrel_1 ) @ ( f1_s3_filter_1 @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) )
=> ( C @ ( B @ ( A @ p1_s3_filter_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2328]) ).
thf(2064,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_domain_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ k3_enumset1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_domain_1) ).
thf(13128,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k10_domain_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ k3_enumset1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2064]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
<=> ( ( ( A = B )
| ( C @ ( B @ r2_hidden ) ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_zfmisc_1) ).
thf(3331,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( A = B )
| ( C @ ( B @ r2_hidden ) ) )
& ~ ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) ) )
& ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( ( ( A = B )
| ( C @ ( B @ r2_hidden ) ) )
& ~ ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(170,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_funct_1) ).
thf(3136,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
=> ( ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k1_relat_1 ) )
& ( ( A @ k2_funct_1 @ ( A @ k5_relat_1 ) @ k1_relat_1 )
= ( A @ k1_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(1251,axiom,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(8617,plain,
! [A: $i] :
( ( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( A @ k2_relat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(2236,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finset_1) ).
thf(13998,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 )
=> ( ( B @ v1_finset_1 )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2236]) ).
thf(1755,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_subset_1) ).
thf(11187,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
=> ( A @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1755]) ).
thf(2278,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k5_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(14177,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k5_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2278]) ).
thf(1735,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C != k1_xboole_0 )
=> ( ( D @ k2_funct_4 @ k2_funct_4 )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_4) ).
thf(11091,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C != k1_xboole_0 )
=> ( ( D @ k2_funct_4 @ k2_funct_4 )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1735]) ).
thf(1140,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( I
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_enumset1 ) ) ) ) ) ) ) ) )
<=> ! [J: $i] :
( ( I @ ( J @ r2_hidden ) )
<=> ~ ( ( J != H )
& ( J != G )
& ( J != F )
& ( J != E )
& ( J != D )
& ( J != C )
& ( J != B )
& ( J != A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_enumset1) ).
thf(7912,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( ! [J: $i] :
( ( ~ ( ( J != H )
& ( J != G )
& ( J != F )
& ( J != E )
& ( J != D )
& ( J != C )
& ( J != B )
& ( J != A ) )
=> ( I @ ( J @ r2_hidden ) ) )
& ( ( I @ ( J @ r2_hidden ) )
=> ~ ( ( J != H )
& ( J != G )
& ( J != F )
& ( J != E )
& ( J != D )
& ( J != C )
& ( J != B )
& ( J != A ) ) ) )
=> ( I
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_enumset1 ) ) ) ) ) ) ) ) ) )
& ( ( I
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_enumset1 ) ) ) ) ) ) ) ) )
=> ! [J: $i] :
( ( ~ ( ( J != H )
& ( J != G )
& ( J != F )
& ( J != E )
& ( J != D )
& ( J != C )
& ( J != B )
& ( J != A ) )
=> ( I @ ( J @ r2_hidden ) ) )
& ( ( I @ ( J @ r2_hidden ) )
=> ~ ( ( J != H )
& ( J != G )
& ( J != F )
& ( J != E )
& ( J != D )
& ( J != C )
& ( J != B )
& ( J != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( D @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( E @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ a_6_0_relset_2 ) ) ) ) ) @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_relset_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( D @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( E @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ a_6_0_relset_2 ) ) ) ) ) @ m1_subset_1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(2394,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i,E: $i,F: $i] :
( ( D @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( E @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ a_6_0_relset_2 ) ) ) ) ) @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1026,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ ( C @ k5_funcop_1 ) ) @ ( B @ k6_partfun1 @ k5_relat_1 ) )
= ( B @ ( A @ k7_relat_1 ) @ ( D @ ( C @ k5_funcop_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funcop_1) ).
thf(7437,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ ( C @ k5_funcop_1 ) ) @ ( B @ k6_partfun1 @ k5_relat_1 ) )
= ( B @ ( A @ k7_relat_1 ) @ ( D @ ( C @ k5_funcop_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(1570,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_binop_1) ).
thf(10210,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( D = E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1570]) ).
thf(1322,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
=> ( B @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_setfam_1) ).
thf(8997,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ r2_hidden ) )
& ( B @ ( A @ k3_tarski @ r1_tarski ) ) )
=> ( B @ ( C @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).
thf(651,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 ) )
=> ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_1) ).
thf(5408,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( A @ ( B @ k5_relat_1 ) @ k1_relat_1 )
= ( B @ k1_relat_1 ) )
=> ( A @ k1_relat_1 @ ( B @ k2_relat_1 @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k5_finsub_1 @ ( C @ ( B @ ( A @ k6_setwiseo ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setwiseo) ).
thf(2399,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) )
& ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k5_finsub_1 @ ( C @ ( B @ ( A @ k6_setwiseo ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(768,axiom,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_zfmisc_1) ).
thf(6018,plain,
! [A: $i,B: $i] :
( ( ( B @ k1_tarski @ ( A @ k1_tarski @ k3_xboole_0 ) )
= ( A @ k1_tarski ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(1024,axiom,
! [A: $i,B: $i,C: $i] : ( B @ k1_tarski @ ( C @ ( B @ ( A @ k2_funcop_1 ) @ k9_relat_1 ) @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_borsuk_1) ).
thf(7416,plain,
! [A: $i,B: $i,C: $i] : ( B @ k1_tarski @ ( C @ ( B @ ( A @ k2_funcop_1 ) @ k9_relat_1 ) @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(1982,axiom,
! [A: $i] :
( ( A @ v1_funct_1 )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_1) ).
thf(12620,plain,
! [A: $i] :
( ( ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) )
=> ( A @ v1_funct_1 ) )
& ( ( A @ v1_funct_1 )
=> ! [B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( C @ ( B @ k4_tarski ) @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1982]) ).
thf(616,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_funct_2) ).
thf(5211,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(633,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 @ k2_funct_5 )
= ( A @ k2_funct_4 @ k1_relat_1 @ k1_funct_5 ) )
& ( ( A @ k1_relat_1 @ k1_funct_5 )
= ( A @ k2_funct_4 @ k1_relat_1 @ k2_funct_5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_funct_5) ).
thf(5287,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ k1_relat_1 @ k2_funct_5 )
= ( A @ k2_funct_4 @ k1_relat_1 @ k1_funct_5 ) )
& ( ( A @ k1_relat_1 @ k1_funct_5 )
= ( A @ k2_funct_4 @ k1_relat_1 @ k2_funct_5 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(2377,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = k1_xboole_0 )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_relset_2) ).
thf(14596,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C = k1_xboole_0 )
=> ( ( D @ ( C @ ( B @ ( A @ k8_relset_2 ) ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2377]) ).
thf(754,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v2_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_1) ).
thf(5963,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v2_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(2165,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) )
<=> ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_mcart_1) ).
thf(13656,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
!= k1_xboole_0 )
=> ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) ) )
& ( ( ( C != k1_xboole_0 )
& ( B != k1_xboole_0 )
& ( A != k1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
!= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2165]) ).
thf(1762,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_funct_2) ).
thf(11210,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ k5_partfun1 ) ) @ ( D @ r2_hidden ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1762]) ).
thf(2027,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_subset_1) ).
thf(12900,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ( C @ ( D @ r2_hidden ) ) )
=> ( C @ ( B @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2027]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_membered )
& ( A @ ( B @ r2_hidden ) ) )
=> ( A @ k1_setfam_1 @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_membered) ).
thf(3694,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_membered )
& ( A @ ( B @ r2_hidden ) ) )
=> ( A @ k1_setfam_1 @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(2000,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_pcomps_1 @ ( A @ k1_pcomps_1 @ ( C @ m1_relset_1 ) ) )
& ( B @ k1_pcomps_1 @ ( A @ k1_pcomps_1 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k14_borsuk_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_borsuk_1) ).
thf(12730,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_pcomps_1 @ ( A @ k1_pcomps_1 @ ( C @ m1_relset_1 ) ) )
& ( B @ k1_pcomps_1 @ ( A @ k1_pcomps_1 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k14_borsuk_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2000]) ).
thf(1850,axiom,
! [A: $i] :
( ( A @ k1_pcomps_1 )
= ( A @ k1_zfmisc_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
thf(11780,plain,
! [A: $i] :
( ( A @ k1_pcomps_1 )
= ( A @ k1_zfmisc_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1850]) ).
thf(1395,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( A @ ( B @ k7_relat_1 ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t186_relat_1) ).
thf(9338,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ( B @ ( C @ r1_tarski ) )
& ( A @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( A @ ( B @ k7_relat_1 ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).
thf(409,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(4197,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(823,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i,D: $i] :
( ( ( ( D @ ( A @ k7_relat_1 ) )
= ( D @ ( B @ k7_relat_1 ) ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t188_relat_1) ).
thf(6305,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i,D: $i] :
( ( ( ( D @ ( A @ k7_relat_1 ) )
= ( D @ ( B @ k7_relat_1 ) ) )
& ( D @ ( C @ r1_tarski ) ) )
=> ( ( C @ ( A @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(1422,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_xboole_1) ).
thf(9470,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( B @ ( A @ r1_xboole_0 ) )
& ~ ( C @ ( B @ k3_xboole_0 ) @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422]) ).
thf(2283,axiom,
f1_s7_domain_1 @ k1_zfmisc_1 @ ( a_0_0_domain_1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s7_domain_1) ).
thf(14187,plain,
f1_s7_domain_1 @ k1_zfmisc_1 @ ( a_0_0_domain_1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2283]) ).
thf(1979,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_subset_1) ).
thf(12588,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1979]) ).
thf(2157,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r7_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d20_binop_1) ).
thf(13610,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r7_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r7_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) )
= ( E @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( D @ ( B @ ( A @ ( A @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2157]) ).
thf(712,axiom,
? [A: $i] :
~ ( A @ v2_setfam_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_setfam_1) ).
thf(5692,plain,
? [A: $i] :
~ ( A @ v2_setfam_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(204,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_xboole_1) ).
thf(3267,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(2341,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_6_0_relset_2 ) ) ) ) ) @ ( A @ r2_hidden ) )
<=> ? [H: $i] :
( ( D @ ( H @ r2_hidden ) )
& ( A
= ( H @ ( G @ ( F @ ( E @ k8_relset_2 ) ) ) ) )
& ( F @ ( E @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_6_0_relset_2) ).
thf(14418,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( E @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( ( ? [H: $i] :
( ( D @ ( H @ r2_hidden ) )
& ( A
= ( H @ ( G @ ( F @ ( E @ k8_relset_2 ) ) ) ) )
& ( F @ ( E @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) ) )
=> ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_6_0_relset_2 ) ) ) ) ) @ ( A @ r2_hidden ) ) )
& ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ a_6_0_relset_2 ) ) ) ) ) @ ( A @ r2_hidden ) )
=> ? [H: $i] :
( ( D @ ( H @ r2_hidden ) )
& ( A
= ( H @ ( G @ ( F @ ( E @ k8_relset_2 ) ) ) ) )
& ( F @ ( E @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2341]) ).
thf(740,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_partfun1) ).
thf(5837,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_tarski @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ k1_tarski @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(2375,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_mcart_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_mcart_1) ).
thf(14592,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( D @ k1_zfmisc_1 @ ( H @ m1_subset_1 ) )
& ( C @ k1_zfmisc_1 @ ( G @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_mcart_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2375]) ).
thf(2370,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ a_2_0_relset_2 ) @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_relset_2) ).
thf(14582,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ a_2_0_relset_2 ) @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2370]) ).
thf(2274,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(14165,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2274]) ).
thf(1992,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setwiseo) ).
thf(12675,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1992]) ).
thf(798,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i,F: $i,G: $i] :
~ ( ( A
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) )
& ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_mcart_1) ).
thf(6166,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ! [E: $i,F: $i,G: $i] :
~ ( ( A
= ( G @ ( F @ ( E @ k3_mcart_1 ) ) ) )
& ( D @ ( G @ r2_hidden ) )
& ( C @ ( F @ r2_hidden ) )
& ( B @ ( E @ r2_hidden ) ) )
& ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(1903,axiom,
! [A: $i] : ( A @ ( A @ ( A @ k1_eqrel_1 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_eqrel_1) ).
thf(12093,plain,
! [A: $i] : ( A @ ( A @ ( A @ k1_eqrel_1 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1903]) ).
thf(1050,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B @ ( D @ v2_binop_1 ) )
& ( A @ ( C @ v2_binop_1 ) ) )
<=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v2_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_filter_1) ).
thf(7530,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v2_binop_1 ) )
=> ( ( B @ ( D @ v2_binop_1 ) )
& ( A @ ( C @ v2_binop_1 ) ) ) )
& ( ( ( B @ ( D @ v2_binop_1 ) )
& ( A @ ( C @ v2_binop_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v2_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(1310,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_3 @ k1_funct_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_3) ).
thf(8953,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( k1_xboole_0 @ ( A @ k1_funct_3 @ k1_funct_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( D @ ( C @ r1_partfun1 ) )
<=> ! [E: $i] :
( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_2) ).
thf(4074,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( ( ! [E: $i] :
( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) )
=> ( D @ ( C @ r1_partfun1 ) ) )
& ( ( D @ ( C @ r1_partfun1 ) )
=> ! [E: $i] :
( ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) )
=> ( ( E @ ( C @ k1_funct_1 ) )
= ( E @ ( D @ k1_funct_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(2227,axiom,
? [A: $i] :
( ( A @ v1_fraenkel )
& ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_closure2) ).
thf(13954,plain,
? [A: $i] :
( ( A @ v1_fraenkel )
& ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2227]) ).
thf(876,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t170_relat_1) ).
thf(6569,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k10_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(1269,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(8721,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(676,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) )
=> ( E @ ( C @ k3_xboole_0 ) @ ( D @ ( B @ k3_xboole_0 ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_zfmisc_1) ).
thf(5517,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( D @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) )
=> ( E @ ( C @ k3_xboole_0 ) @ ( D @ ( B @ k3_xboole_0 ) @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(1550,axiom,
( ( a_0_0_card_fil @ ( f2_s1_card_fil @ r2_hidden ) )
=> ( f2_s1_card_fil @ p1_s1_card_fil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_card_fil) ).
thf(10109,plain,
( ( a_0_0_card_fil @ ( f2_s1_card_fil @ r2_hidden ) )
=> ( f2_s1_card_fil @ p1_s1_card_fil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1550]) ).
thf(597,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t77_funct_4) ).
thf(5128,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ ( A @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= ( C @ ( B @ k7_relat_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pboole) ).
thf(2739,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( C @ ( B @ k1_funct_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) )
=> ( ( A @ k1_setfam_1 @ ( B @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_setfam_1) ).
thf(2494,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( C @ ( B @ r1_tarski ) ) )
=> ( ( A @ k1_setfam_1 @ ( B @ r1_tarski ) )
| ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(850,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k6_enumset1 ) ) ) ) ) ) ) )
= ( B @ ( A @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_enumset1) ).
thf(6444,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k6_enumset1 ) ) ) ) ) ) ) )
= ( B @ ( A @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= k1_xboole_0 )
<=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).
thf(2917,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= k1_xboole_0 ) )
& ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
= k1_xboole_0 )
=> ( ( C @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ k9_relat_1 ) )
= ( C @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_partfun1) ).
thf(4372,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( A @ ( C @ k9_relat_1 ) )
= ( C @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(2137,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_1_card_fil ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k3_subset_1 ) ) )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_1_card_fil) ).
thf(13513,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k3_subset_1 ) ) )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_1_card_fil ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_1_card_fil ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( C @ ( D @ r2_hidden ) )
& ( A
= ( D @ ( B @ k3_subset_1 ) ) )
& ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2137]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_xboole_1) ).
thf(2623,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ ( B @ k4_xboole_0 ) @ ( A @ r1_xboole_0 ) )
& ( C @ ( A @ r1_xboole_0 ) )
& ~ ( B @ ( A @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(2118,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(13389,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2118]) ).
thf(1825,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
thf(11604,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1825]) ).
thf(715,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( C @ v1_binop_1 ) )
=> ( ( D @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_funcop_1) ).
thf(5704,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ( ( B @ ( C @ v1_binop_1 ) )
=> ( ( D @ ( E @ ( C @ ( A @ ( B @ k8_funcop_1 ) ) ) ) )
= ( E @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k8_relat_1 ) )
= ( C @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_relat_1) ).
thf(3552,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C @ ( B @ ( A @ k4_xboole_0 ) @ k8_relat_1 ) )
= ( C @ ( B @ k8_relat_1 ) @ ( C @ ( A @ k8_relat_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(1761,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(11208,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1761]) ).
thf(743,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d19_binop_1) ).
thf(5864,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) )
=> ( C @ ( B @ ( A @ r5_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r5_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( F @ ( D @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(2089,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_eqrel_1) ).
thf(13257,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_eqrel_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2089]) ).
thf(2181,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
<=> ( B
= ( A @ k1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_subset_1) ).
thf(13753,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B
= ( A @ k1_subset_1 ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) ) )
& ( ( B @ ( A @ k3_subset_1 ) @ ( B @ r1_tarski ) )
=> ( B
= ( A @ k1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2181]) ).
thf(2081,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ ( C @ k7_relat_1 ) )
= ( E @ ( D @ k7_relat_1 ) ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( E @ ( F @ r2_hidden ) )
=> ( ( F @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( F @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_fraenkel) ).
thf(13220,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( E @ ( C @ k7_relat_1 ) )
= ( E @ ( D @ k7_relat_1 ) ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ( E @ ( F @ r2_hidden ) )
=> ( ( F @ ( C @ ( B @ ( A @ k8_funct_2 ) ) ) )
= ( F @ ( D @ ( B @ ( A @ k8_funct_2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2081]) ).
thf(1523,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] : ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_finset_1) ).
thf(9976,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] : ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k5_enumset1 ) ) ) ) ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1523]) ).
thf(1397,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d17_binop_1) ).
thf(9361,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) )
=> ( C @ ( B @ ( A @ r2_binop_1 ) ) ) )
& ( ( C @ ( B @ ( A @ r2_binop_1 ) ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( D @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397]) ).
thf(130,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ~ ( A @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( A @ k7_funct_6 @ v2_funct_1 )
<=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( B @ r2_hidden ) )
=> ( B @ v2_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_6) ).
thf(2930,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ~ ( A @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( B @ r2_hidden ) )
=> ( B @ v2_funct_1 ) ) )
=> ( A @ k7_funct_6 @ v2_funct_1 ) )
& ( ( A @ k7_funct_6 @ v2_funct_1 )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( A @ k2_relat_1 @ ( B @ r2_hidden ) )
=> ( B @ v2_funct_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(547,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( B @ ( A @ k8_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_relat_1) ).
thf(4880,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) @ ( A @ k8_relat_1 ) )
= ( B @ ( A @ k8_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(1689,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finsub_1) ).
thf(10838,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k5_finsub_1 @ ( A @ k5_finsub_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1689]) ).
thf(376,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ ( B @ ( C @ k4_funcop_1 ) ) @ k5_relat_1 ) )
= ( D @ ( B @ ( A @ ( C @ k5_relat_1 ) @ k4_funcop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funcop_1) ).
thf(4039,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ ( B @ ( C @ k4_funcop_1 ) ) @ k5_relat_1 ) )
= ( D @ ( B @ ( A @ ( C @ k5_relat_1 ) @ k4_funcop_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(1053,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_2) ).
thf(7542,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ v2_funct_1 )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( B @ k1_funct_1 ) )
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) )
& ( A @ ( C @ r2_hidden ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(707,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( C @ k6_relat_1 @ r1_tarski ) )
=> ( ( D @ ( B @ ( A @ k5_relset_1 ) ) @ ( C @ r1_tarski ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relset_1) ).
thf(5677,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( D @ ( C @ k6_relat_1 @ r1_tarski ) )
=> ( ( D @ ( B @ ( A @ k5_relset_1 ) ) @ ( C @ r1_tarski ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( C @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(527,axiom,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(4794,plain,
( ( ( k1_xboole_0 @ k2_relat_1 )
= k1_xboole_0 )
& ( ( k1_xboole_0 @ k1_relat_1 )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(1907,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_subset_1) ).
thf(12108,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k3_subset_1 ) @ ( B @ ( A @ k4_subset_1 ) ) )
= ( A @ k2_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1907]) ).
thf(2244,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ k2_funct_5 @ ( C @ k1_funct_5 @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_yellow_3) ).
thf(14030,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ k2_funct_5 @ ( C @ k1_funct_5 @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2244]) ).
thf(2235,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_partfun1) ).
thf(13991,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 )
= k1_xboole_0 )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2235]) ).
thf(969,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_enumset1) ).
thf(7016,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ k4_enumset1 ) ) ) ) ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(1014,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k5_relat_1 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_relat_1) ).
thf(7355,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k5_relat_1 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(506,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( B @ k6_subset_1 ) ) @ ( D @ r2_hidden ) )
=> ( F @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( E @ ( A @ k6_subset_1 ) ) @ ( D @ ( C @ k2_funct_1 @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_funct_7) ).
thf(4706,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( B @ k6_subset_1 ) ) @ ( D @ r2_hidden ) )
=> ( F @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ ( E @ ( A @ k6_subset_1 ) ) @ ( D @ ( C @ k2_funct_1 @ k1_funct_1 ) @ r2_hidden ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(500,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v3_monoid_0 ) )
<=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( ( C @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D )
& ( A @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_monoid_0) ).
thf(4670,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( ( C @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D )
& ( A @ ( E @ m1_subset_1 ) ) ) ) )
=> ( A @ ( B @ v3_monoid_0 ) ) )
& ( ( A @ ( B @ v3_monoid_0 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ? [E: $i] :
( ( ( C @ ( E @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= D )
& ( A @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1079,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_zfmisc_1 ) @ ( B @ ( A @ k13_funct_3 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_funct_3) ).
thf(7634,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_zfmisc_1 ) @ ( B @ ( A @ k13_funct_3 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(1487,axiom,
! [A: $i] :
( ( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ v1_tex_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tex_2) ).
thf(9806,plain,
! [A: $i] :
( ( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k6_domain_1 ) @ v1_tex_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487]) ).
thf(2356,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( D @ ( C @ ( B @ ( A @ k17_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k17_domain_1) ).
thf(14499,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( C @ ( D @ ( C @ ( B @ ( A @ k17_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2356]) ).
thf(2333,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k1_cantor_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_cantor_1) ).
thf(14386,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ ( A @ k1_cantor_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2333]) ).
thf(756,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k15_funct_3 ) )
= ( B @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k10_funct_3 ) @ k5_relat_1 ) @ ( A @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k9_funct_3 ) @ k5_relat_1 ) @ k13_funct_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_funct_3) ).
thf(5971,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ ( A @ k15_funct_3 ) )
= ( B @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k10_funct_3 ) @ k5_relat_1 ) @ ( A @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k9_funct_3 ) @ k5_relat_1 ) @ k13_funct_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(1918,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(12162,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( C @ k2_zfmisc_1 ) @ r1_tarski ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ ( A @ k2_zfmisc_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1918]) ).
thf(1365,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_funct_1) ).
thf(9229,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k3_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] : ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_enumset1 ) ) ) ) ) ) ) @ v1_finset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_finset_1) ).
thf(4356,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] : ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k6_enumset1 ) ) ) ) ) ) ) @ v1_finset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_xboole_1) ).
thf(3997,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k3_xboole_0 ) )
= ( C @ ( B @ ( A @ k3_xboole_0 ) @ k4_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(344,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_pua2mss1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_pua2mss1) ).
thf(3907,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m2_pua2mss1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(2113,axiom,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r1_tarski ) )
=> ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_setwiseo) ).
thf(13349,plain,
! [A: $i,B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( C @ r1_tarski ) )
=> ( A @ k5_finsub_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2113]) ).
thf(1965,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_domain_1) ).
thf(12520,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k1_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1965]) ).
thf(2275,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(14170,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2275]) ).
thf(1876,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ~ ( ( A != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_2) ).
thf(11928,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ~ ( ( A != k1_xboole_0 )
& ( C != k1_xboole_0 )
& ( B = k1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1876]) ).
thf(568,axiom,
! [A: $i] :
( ( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_setfam_1) ).
thf(5004,plain,
! [A: $i] :
( ( ( A @ v1_setfam_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k19_pralg_1 ) ) )
= ( C @ k3_funct_5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k19_pralg_1) ).
thf(3733,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k19_pralg_1 ) ) )
= ( C @ k3_funct_5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(1276,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ k3_enumset1 ) ) ) ) )
= ( A @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_enumset1) ).
thf(8754,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ ( A @ ( A @ k3_enumset1 ) ) ) ) )
= ( A @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(985,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ v1_finset_1 )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finset_1) ).
thf(7153,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ v1_finset_1 )
=> ( A @ k2_relat_1 @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(2309,axiom,
k1_numbers @ k1_zfmisc_1 @ ( k5_urysohn1 @ m1_subset_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_urysohn1) ).
thf(14300,plain,
k1_numbers @ k1_zfmisc_1 @ ( k5_urysohn1 @ m1_subset_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2309]) ).
thf(1942,axiom,
? [A: $i] :
( ! [B: $i] :
( ( f1_s4_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s4_funct_2 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_funct_2) ).
thf(12374,plain,
? [A: $i] :
( ! [B: $i] :
( ( f1_s4_funct_2 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ k8_funct_2 ) ) ) )
= ( B @ f3_s4_funct_2 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ m2_relset_1 ) ) )
& ( f2_s4_funct_2 @ ( f1_s4_funct_2 @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1942]) ).
thf(874,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_funcop_1) ).
thf(6563,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( B @ ( C @ v2_binop_1 ) )
=> ( ( F @ ( E @ ( C @ ( B @ ( B @ ( B @ k2_binop_1 ) ) ) ) ) @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) @ ( C @ ( A @ ( B @ k7_funcop_1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(1135,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ~ ( ( ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ k16_funct_3 ) ) ) ) ) )
!= ( F @ ( C @ ( A @ k10_funct_3 ) @ k5_relat_1 ) @ ( E @ ( C @ ( A @ k9_funct_3 ) @ k5_relat_1 ) @ k13_funct_3 ) ) )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_funct_3) ).
thf(7883,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ~ ( ( ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ k16_funct_3 ) ) ) ) ) )
!= ( F @ ( C @ ( A @ k10_funct_3 ) @ k5_relat_1 ) @ ( E @ ( C @ ( A @ k9_funct_3 ) @ k5_relat_1 ) @ k13_funct_3 ) ) )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(1841,axiom,
~ ( k2_qc_lang1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_qc_lang1) ).
thf(11739,plain,
~ ( k2_qc_lang1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1841]) ).
thf(1214,axiom,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_realset1) ).
thf(8412,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m3_realset1 ) ) )
=> ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ k2_zfmisc_1 ) @ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ ( C @ k1_realset1 ) @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(1648,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(10601,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1648]) ).
thf(751,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t80_zfmisc_1) ).
thf(5954,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ ( A @ k1_tarski @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(999,axiom,
! [A: $i] :
( ( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( A = k35_binop_2 )
<=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k1_numbers @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k11_binop_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_binop_2) ).
thf(7242,plain,
! [A: $i] :
( ( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k1_numbers @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k11_binop_2 ) ) ) ) )
=> ( A = k35_binop_2 ) )
& ( ( A = k35_binop_2 )
=> ! [B: $i] :
( ( k1_numbers @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( k1_numbers @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_binop_1 ) ) ) ) ) )
= ( C @ ( B @ k11_binop_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(1099,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ k2_relat_1 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_pboole) ).
thf(7712,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ k2_relat_1 @ ( C @ m1_subset_1 ) )
=> ? [D: $i] :
( ( C
= ( D @ ( B @ k1_funct_1 ) ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(2319,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k12_domain_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_domain_1) ).
thf(14332,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( A @ ( H @ m1_subset_1 ) )
& ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k12_domain_1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2319]) ).
thf(135,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ ( A @ k7_relat_1 ) @ v1_finseq_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) )
<=> ? [C: $i] :
( ( ( A @ k4_finseq_1 @ ( B @ k3_xboole_0 ) )
= ( C @ k2_finseq_1 ) )
& ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_finseq_3) ).
thf(2951,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ? [C: $i] :
( ( ( A @ k4_finseq_1 @ ( B @ k3_xboole_0 ) )
= ( C @ k2_finseq_1 ) )
& ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) ) )
=> ( ( B @ ( A @ k7_relat_1 ) @ v1_finseq_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) ) )
& ( ( ( B @ ( A @ k7_relat_1 ) @ v1_finseq_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k7_relat_1 ) @ v1_relat_1 ) )
=> ? [C: $i] :
( ( ( A @ k4_finseq_1 @ ( B @ k3_xboole_0 ) )
= ( C @ k2_finseq_1 ) )
& ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(2149,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k1_cantor_1 ) @ ( B @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_cantor_1) ).
thf(13577,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ ( A @ k1_cantor_1 ) @ ( B @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2149]) ).
thf(2352,axiom,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).
thf(14475,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2352]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_partfun1) ).
thf(2815,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(853,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i,D: $i] :
( A
!= ( D @ ( C @ k4_tarski ) ) )
& ( B @ k2_funct_4 @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_funct_6) ).
thf(6456,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i,D: $i] :
( A
!= ( D @ ( C @ k4_tarski ) ) )
& ( B @ k2_funct_4 @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(537,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ m1_relset_1 ) ) )
=> ( ( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( k1_xboole_0 @ ( A @ v2_binop_1 ) )
& ( k1_xboole_0 @ ( A @ v1_binop_1 ) )
& ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_xboole_0 )
& ( A @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_binop_1) ).
thf(4841,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ m1_relset_1 ) ) )
=> ( ( ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_funct_1 ) )
=> ( ( k1_xboole_0 @ ( A @ v2_binop_1 ) )
& ( k1_xboole_0 @ ( A @ v1_binop_1 ) )
& ( k1_xboole_0 @ ( k1_xboole_0 @ ( k1_xboole_0 @ k2_zfmisc_1 ) @ ( A @ v1_funct_2 ) ) )
& ( A @ v1_xboole_0 )
& ( A @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1928,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ a_1_1_ens_1 @ ( A @ r2_hidden ) )
<=> ? [C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( D @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ ( B @ k1_domain_1 ) ) ) @ ( B @ k1_ens_1 @ ( B @ ( B @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) ) )
& ( B @ k1_ens_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_1_1_ens_1) ).
thf(12213,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ? [C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( D @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ ( B @ k1_domain_1 ) ) ) @ ( B @ k1_ens_1 @ ( B @ ( B @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) ) )
& ( B @ k1_ens_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( C @ m1_subset_1 ) ) )
=> ( B @ a_1_1_ens_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ a_1_1_ens_1 @ ( A @ r2_hidden ) )
=> ? [C: $i,D: $i,E: $i] :
( ( D @ ( C @ ( E @ m2_relset_1 ) ) )
& ( D @ ( C @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( ( D = k1_xboole_0 )
=> ( C = k1_xboole_0 ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ ( B @ k1_domain_1 ) ) ) @ ( B @ k1_ens_1 @ ( B @ ( B @ k2_zfmisc_1 ) @ k1_domain_1 ) ) ) ) )
& ( B @ k1_ens_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( C @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1928]) ).
thf(322,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(3790,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(747,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i,D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( D @ v3_binop_1 ) )
& ( A @ ( D @ v2_binop_1 ) )
& ( A @ ( D @ v1_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( C @ k5_finsub_1 @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ k5_finsub_1 @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( A @ ( C @ k5_finsub_1 @ ( G @ m2_relset_1 ) ) )
& ( A @ ( C @ k5_finsub_1 @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ! [H: $i] :
( ( C @ k5_finsub_1 @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ k5_finsub_1 @ ( I @ m1_subset_1 ) )
=> ( ( I @ ( H @ ( C @ k5_setwiseo ) ) @ ( G @ ( A @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( I @ ( G @ ( A @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( H @ ( G @ ( A @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( D @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( ( F @ ( E @ ( C @ ( B @ k10_setwiseo ) ) ) @ ( G @ ( A @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( G @ ( F @ ( A @ ( C @ k5_finsub_1 @ ( B @ k7_funct_2 ) ) ) ) @ ( E @ ( D @ ( A @ ( B @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_setwiseo) ).
thf(5884,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i,D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( D @ v3_binop_1 ) )
& ( A @ ( D @ v2_binop_1 ) )
& ( A @ ( D @ v1_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( C @ k5_finsub_1 @ ( B @ ( F @ m2_relset_1 ) ) )
& ( C @ k5_finsub_1 @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( A @ ( C @ k5_finsub_1 @ ( G @ m2_relset_1 ) ) )
& ( A @ ( C @ k5_finsub_1 @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ! [H: $i] :
( ( C @ k5_finsub_1 @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ k5_finsub_1 @ ( I @ m1_subset_1 ) )
=> ( ( I @ ( H @ ( C @ k5_setwiseo ) ) @ ( G @ ( A @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( I @ ( G @ ( A @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( H @ ( G @ ( A @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) @ ( D @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) )
=> ( ( F @ ( E @ ( C @ ( B @ k10_setwiseo ) ) ) @ ( G @ ( A @ ( C @ k5_finsub_1 @ k8_funct_2 ) ) ) )
= ( G @ ( F @ ( A @ ( C @ k5_finsub_1 @ ( B @ k7_funct_2 ) ) ) ) @ ( E @ ( D @ ( A @ ( B @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(1780,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_mssubfam) ).
thf(11341,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( k1_xboole_0 @ r2_hidden ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1780]) ).
thf(2223,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) )
=> ? [D: $i] :
( ( ( D @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k8_funct_2 ) ) ) )
= C )
& ( A @ ( D @ m1_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_borsuk_1) ).
thf(13941,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( B @ m1_eqrel_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_zfmisc_1 @ ( C @ m2_subset_1 ) ) )
=> ? [D: $i] :
( ( ( D @ ( B @ ( A @ k2_borsuk_1 ) @ ( B @ ( A @ k8_funct_2 ) ) ) )
= C )
& ( A @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2223]) ).
thf(1626,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k1_closure2 ) @ k5_subset_1 ) ) @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_closure2) ).
thf(10515,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k1_closure2 ) @ k5_subset_1 ) ) @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1626]) ).
thf(1246,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( A @ ( I @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k6_enumset1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_subset_1) ).
thf(8574,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( A @ ( I @ m1_subset_1 ) )
=> ( ( A != k1_xboole_0 )
=> ( A @ k1_zfmisc_1 @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ k6_enumset1 ) ) ) ) ) ) ) @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(1392,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 @ ( B @ k9_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_relat_1) ).
thf(9329,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k5_relat_1 ) @ k2_relat_1 )
= ( A @ k2_relat_1 @ ( B @ k9_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392]) ).
thf(253,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k4_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_funct_1) ).
thf(3496,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( A @ k9_relat_1 ) )
= ( C @ ( A @ k9_relat_1 ) @ ( B @ ( A @ k9_relat_1 ) @ k4_xboole_0 ) ) )
=> ( A @ v2_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(549,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C
= ( B @ ( A @ k3_funct_4 ) ) )
<=> ( ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( B @ k1_relat_1 @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( G @ ( E @ k4_tarski ) @ ( F @ ( D @ k4_tarski ) @ k4_tarski ) @ ( C @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( B @ k1_funct_1 ) @ ( E @ ( D @ k4_tarski ) @ ( A @ k1_funct_1 ) @ k4_tarski ) ) ) )
& ! [D: $i] :
( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
<=> ? [E: $i,F: $i,G: $i,H: $i] :
( ( B @ k1_relat_1 @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( D
= ( H @ ( F @ k4_tarski ) @ ( G @ ( E @ k4_tarski ) @ k4_tarski ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_funct_4) ).
thf(4885,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( B @ k1_relat_1 @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( G @ ( E @ k4_tarski ) @ ( F @ ( D @ k4_tarski ) @ k4_tarski ) @ ( C @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( B @ k1_funct_1 ) @ ( E @ ( D @ k4_tarski ) @ ( A @ k1_funct_1 ) @ k4_tarski ) ) ) )
& ! [D: $i] :
( ( ? [E: $i,F: $i,G: $i,H: $i] :
( ( B @ k1_relat_1 @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( D
= ( H @ ( F @ k4_tarski ) @ ( G @ ( E @ k4_tarski ) @ k4_tarski ) ) ) )
=> ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i,G: $i,H: $i] :
( ( B @ k1_relat_1 @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( D
= ( H @ ( F @ k4_tarski ) @ ( G @ ( E @ k4_tarski ) @ k4_tarski ) ) ) ) ) ) )
=> ( C
= ( B @ ( A @ k3_funct_4 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_funct_4 ) ) )
=> ( ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( B @ k1_relat_1 @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( G @ ( E @ k4_tarski ) @ ( F @ ( D @ k4_tarski ) @ k4_tarski ) @ ( C @ k1_funct_1 ) )
= ( G @ ( F @ k4_tarski ) @ ( B @ k1_funct_1 ) @ ( E @ ( D @ k4_tarski ) @ ( A @ k1_funct_1 ) @ k4_tarski ) ) ) )
& ! [D: $i] :
( ( ? [E: $i,F: $i,G: $i,H: $i] :
( ( B @ k1_relat_1 @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( D
= ( H @ ( F @ k4_tarski ) @ ( G @ ( E @ k4_tarski ) @ k4_tarski ) ) ) )
=> ( C @ k1_relat_1 @ ( D @ r2_hidden ) ) )
& ( ( C @ k1_relat_1 @ ( D @ r2_hidden ) )
=> ? [E: $i,F: $i,G: $i,H: $i] :
( ( B @ k1_relat_1 @ ( H @ ( G @ k4_tarski ) @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
& ( D
= ( H @ ( F @ k4_tarski ) @ ( G @ ( E @ k4_tarski ) @ k4_tarski ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(1472,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( C @ ( B @ r1_partfun1 ) ) )
=> ( ( A @ ( C @ ( B @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_4) ).
thf(9728,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
& ( C @ ( B @ r1_partfun1 ) ) )
=> ( ( A @ ( C @ ( B @ k1_funct_4 ) @ k1_funct_1 ) )
= ( A @ ( B @ k1_funct_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472]) ).
thf(572,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_3) ).
thf(5014,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ k3_tarski @ ( B @ k10_relat_1 ) @ ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(2011,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(12798,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2011]) ).
thf(1330,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k5_relat_1 ) )
= A )
& ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_funct_1) ).
thf(9070,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k5_relat_1 ) )
= A )
& ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ k5_relat_1 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(1857,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k19_pralg_1 ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k19_pralg_1) ).
thf(11807,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_pboole ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( A @ ( C @ ( B @ ( A @ k19_pralg_1 ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1857]) ).
thf(623,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r1_tarski ) )
=> ( D @ ( E @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_funct_7) ).
thf(5247,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( C @ v2_funct_1 )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ ( E @ r1_tarski ) )
=> ( D @ ( E @ ( C @ ( B @ ( A @ k3_funct_2 ) ) ) @ r1_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(1915,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
| ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t135_zfmisc_1) ).
thf(12140,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
| ( B @ ( A @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1915]) ).
thf(1873,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_2) ).
thf(11914,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( C @ ( A @ r1_tarski ) )
=> ( ( C @ ( D @ ( B @ ( A @ k2_partfun1 ) ) ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1873]) ).
thf(1644,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ m1_pboole ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_pboole) ).
thf(10590,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ m1_pboole ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644]) ).
thf(2100,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ ( A @ k4_zfmisc_1 ) ) ) )
= ( B @ ( B @ ( B @ ( B @ k4_zfmisc_1 ) ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_mcart_1) ).
thf(13294,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ ( A @ k4_zfmisc_1 ) ) ) )
= ( B @ ( B @ ( B @ ( B @ k4_zfmisc_1 ) ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2100]) ).
thf(2301,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k16_domain_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_domain_1) ).
thf(14278,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ k16_domain_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2301]) ).
thf(838,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ k8_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_relat_1) ).
thf(6366,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( C @ ( A @ k8_relat_1 ) @ k7_relat_1 ) )
= ( B @ ( C @ k7_relat_1 ) @ ( A @ k8_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_partfun1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_partfun1) ).
thf(3062,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( C @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ r1_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(920,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ k2_funcop_1 ) @ k5_relat_1 ) )
= ( C @ ( A @ k1_funct_1 ) @ ( B @ k2_funcop_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funcop_1) ).
thf(6782,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( A @ k1_relat_1 @ ( C @ r2_hidden ) )
=> ( ( A @ ( C @ ( B @ k2_funcop_1 ) @ k5_relat_1 ) )
= ( C @ ( A @ k1_funct_1 ) @ ( B @ k2_funcop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(2176,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ~ ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_2_domain_1) ).
thf(13701,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ~ ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_2_domain_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ~ ( C @ ( D @ r2_hidden ) )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2176]) ).
thf(1931,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_cat_5 ) ) ) )
= ( D @ k17_mcart_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_cat_5) ).
thf(12272,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k1_cat_5 ) ) ) )
= ( D @ k17_mcart_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1931]) ).
thf(1716,axiom,
( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k34_binop_2 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k34_binop_2 @ v1_funct_2 ) ) )
& ( k34_binop_2 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k34_binop_2) ).
thf(11009,plain,
( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k34_binop_2 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k34_binop_2 @ v1_funct_2 ) ) )
& ( k34_binop_2 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1716]) ).
thf(868,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k1_fraenkel ) )
= ( B @ ( A @ k1_funct_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_fraenkel) ).
thf(6535,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k1_fraenkel ) )
= ( B @ ( A @ k1_funct_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(96,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m2_finseq_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m2_finseq_1 ) )
=> ( C @ ( F @ ( E @ ( D @ k3_funcop_1 ) ) @ m2_finseq_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_finseq_2) ).
thf(2800,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( A @ ( E @ m2_finseq_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m2_finseq_1 ) )
=> ( C @ ( F @ ( E @ ( D @ k3_funcop_1 ) ) @ m2_finseq_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(2368,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_domain_1 ) ) ) ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_domain_1) ).
thf(14578,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( A @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ( A @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( A @ k1_zfmisc_1 @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k11_domain_1 ) ) ) ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2368]) ).
thf(372,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D @ ( D @ ( C @ ( B @ ( A @ k1_isocat_2 ) ) ) @ ( C @ ( B @ ( A @ k2_cat_2 ) ) ) @ ( C @ ( B @ k1_fraenkel ) @ ( A @ ( C @ ( B @ k1_fraenkel ) @ ( A @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_isocat_2) ).
thf(4024,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ m2_relset_1 ) ) )
& ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( D @ ( D @ ( C @ ( B @ ( A @ k1_isocat_2 ) ) ) @ ( C @ ( B @ ( A @ k2_cat_2 ) ) ) @ ( C @ ( B @ k1_fraenkel ) @ ( A @ ( C @ ( B @ k1_fraenkel ) @ ( A @ r4_nattra_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(2256,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ ( k1_xboole_0 @ k2_tarski ) ) )
=> ( ( ( B @ ( A @ k2_cantor_1 ) )
= B )
& ( ( B @ ( A @ k1_cantor_1 ) )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_yellow_9) ).
thf(14090,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B
= ( A @ ( k1_xboole_0 @ k2_tarski ) ) )
=> ( ( ( B @ ( A @ k2_cantor_1 ) )
= B )
& ( ( B @ ( A @ k1_cantor_1 ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2256]) ).
thf(1370,axiom,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc29_membered) ).
thf(9250,plain,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).
thf(824,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k1_multop_1 ) ) ) )
= ( D @ ( C @ ( B @ k3_mcart_1 ) ) @ ( A @ k1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_multop_1) ).
thf(6309,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ k1_multop_1 ) ) ) )
= ( D @ ( C @ ( B @ k3_mcart_1 ) ) @ ( A @ k1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(53,axiom,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ k2_finseq_1 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k2_finseq_1 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( C @ m2_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finseq_2) ).
thf(2651,plain,
! [A: $i] :
( ( k5_numbers @ ( k1_numbers @ ( A @ m2_subset_1 ) ) )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ k2_finseq_1 @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k2_finseq_1 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ ( C @ m2_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(685,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ! [E: $i] :
( ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ k1_relat_1 @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( B @ k1_funct_1 ) @ ( E @ ( A @ k1_funct_1 ) @ ( C @ k1_binop_1 ) ) ) ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ k1_relat_1 ) ) )
=> ( D
= ( B @ ( A @ ( C @ k3_funcop_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funcop_1) ).
thf(5559,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ! [E: $i] :
( ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ k1_relat_1 @ ( E @ r2_hidden ) )
=> ( ( E @ ( D @ k1_funct_1 ) )
= ( E @ ( B @ k1_funct_1 ) @ ( E @ ( A @ k1_funct_1 ) @ ( C @ k1_binop_1 ) ) ) ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ ( C @ k3_funcop_1 ) ) @ k1_relat_1 ) ) )
=> ( D
= ( B @ ( A @ ( C @ k3_funcop_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(1464,axiom,
! [A: $i] : ( A @ ( A @ k3_pua2mss1 @ m1_eqrel_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_pua2mss1) ).
thf(9697,plain,
! [A: $i] : ( A @ ( A @ k3_pua2mss1 @ m1_eqrel_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m2_fraenkel ) ) ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_fraenkel) ).
thf(2636,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m2_fraenkel ) ) ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(2028,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_partfun1) ).
thf(12904,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( D @ ( C @ r1_tarski ) )
=> ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2028]) ).
thf(1238,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k8_relat_1 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_relat_1) ).
thf(8542,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
=> ( ( B @ ( A @ k8_relat_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(374,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k6_relat_1 )
= ( A @ ( A @ k4_tarski ) @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_sysrel) ).
thf(4029,plain,
! [A: $i] :
( ( A @ k1_tarski @ k6_relat_1 )
= ( A @ ( A @ k4_tarski ) @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(1543,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k14_funct_3) ).
thf(10064,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k14_funct_3 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1543]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( ( C @ k2_relat_1 )
= B )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_2) ).
thf(4178,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ! [D: $i] :
~ ( ! [E: $i] :
~ ( ( D
= ( E @ ( C @ k1_funct_1 ) ) )
& ( A @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
=> ( ( ( C @ k2_relat_1 )
= B )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(3328,plain,
! [A: $i,B: $i] :
( ( A @ v1_finset_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(1124,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( E @ v1_partfun1 ) ) )
& ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_partfun1) ).
thf(7851,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ ( E @ v1_partfun1 ) ) )
& ( E @ ( D @ r1_partfun1 ) )
& ( E @ ( C @ r1_partfun1 ) ) )
=> ( D @ ( C @ r1_partfun1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(2195,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(13819,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2195]) ).
thf(379,axiom,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k1_relat_1 @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc17_finseq_1) ).
thf(4051,plain,
! [A: $i] :
( ( ( A @ v1_finset_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( A @ k1_relat_1 @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(1685,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) )
=> ( ( ( C = F )
& ( B = E )
& ( A = D ) )
| ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_mcart_1) ).
thf(10809,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= ( F @ ( E @ ( D @ k3_zfmisc_1 ) ) ) )
=> ( ( ( C = F )
& ( B = E )
& ( A = D ) )
| ( ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1685]) ).
thf(2305,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( C @ ( C @ ( B @ ( A @ k3_pre_circ ) ) @ m1_pboole ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_pre_circ) ).
thf(14288,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( C @ ( C @ ( B @ ( A @ k3_pre_circ ) ) @ m1_pboole ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2305]) ).
thf(1256,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_zfmisc_1 ) @ ( B @ ( A @ k3_funct_4 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_4) ).
thf(8653,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k2_zfmisc_1 ) @ ( B @ ( A @ k3_funct_4 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(1509,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_xboole_1) ).
thf(9915,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ~ ( ( A @ ( B @ r1_xboole_0 ) )
& ( A @ ( B @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1509]) ).
thf(603,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc17_membered) ).
thf(5159,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(1759,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B
= ( D @ ( C @ k2_tarski ) ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( D @ ( C @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_mssubfam) ).
thf(11199,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( B
= ( D @ ( C @ k2_tarski ) ) )
=> ( ( B @ ( A @ k8_setfam_1 ) )
= ( D @ ( C @ ( A @ k5_subset_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1759]) ).
thf(1597,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ r1_tarski ) )
<=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_subset_1) ).
thf(10340,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) )
=> ( C @ ( B @ r1_tarski ) ) )
& ( ( C @ ( B @ r1_tarski ) )
=> ( B @ ( A @ k3_subset_1 ) @ ( C @ ( A @ k3_subset_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1597]) ).
thf(1482,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_borsuk_1 ) ) )
= ( C @ ( B @ k2_funcop_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_borsuk_1) ).
thf(9788,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m1_subset_1 ) )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k1_borsuk_1 ) ) )
= ( C @ ( B @ k2_funcop_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482]) ).
thf(561,axiom,
! [A: $i] : ( A @ k6_relat_1 @ v2_funct_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_1) ).
thf(4981,plain,
! [A: $i] : ( A @ k6_relat_1 @ v2_funct_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(2316,axiom,
! [A: $i] :
( ( a_0_39_fraenkel @ ( A @ r2_hidden ) )
<=> ? [B: $i,C: $i] :
( ( f4_s22_fraenkel @ ( C @ r2_hidden ) )
& ( f3_s22_fraenkel @ ( B @ r2_hidden ) )
& ( A
= ( C @ ( B @ f5_s22_fraenkel ) ) )
& ( f2_s22_fraenkel @ ( C @ m1_subset_1 ) )
& ( f1_s22_fraenkel @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_39_fraenkel) ).
thf(14315,plain,
! [A: $i] :
( ( ? [B: $i,C: $i] :
( ( f4_s22_fraenkel @ ( C @ r2_hidden ) )
& ( f3_s22_fraenkel @ ( B @ r2_hidden ) )
& ( A
= ( C @ ( B @ f5_s22_fraenkel ) ) )
& ( f2_s22_fraenkel @ ( C @ m1_subset_1 ) )
& ( f1_s22_fraenkel @ ( B @ m1_subset_1 ) ) )
=> ( a_0_39_fraenkel @ ( A @ r2_hidden ) ) )
& ( ( a_0_39_fraenkel @ ( A @ r2_hidden ) )
=> ? [B: $i,C: $i] :
( ( f4_s22_fraenkel @ ( C @ r2_hidden ) )
& ( f3_s22_fraenkel @ ( B @ r2_hidden ) )
& ( A
= ( C @ ( B @ f5_s22_fraenkel ) ) )
& ( f2_s22_fraenkel @ ( C @ m1_subset_1 ) )
& ( f1_s22_fraenkel @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2316]) ).
thf(224,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_funct_3) ).
thf(3347,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( A @ ( B @ k1_funct_3 @ k10_relat_1 ) @ ( A @ ( B @ k3_funct_3 @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(787,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_domain_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k3_mcart_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_domain_1) ).
thf(6114,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( F @ m1_subset_1 ) )
& ( B @ ( E @ m1_subset_1 ) )
& ( A @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_domain_1 ) ) ) ) ) )
= ( F @ ( E @ ( D @ k3_mcart_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(428,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ k13_funct_3 ) @ k7_relat_1 ) )
= ( B @ ( C @ ( A @ k7_relat_1 ) @ k13_funct_3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_funcop_1) ).
thf(4286,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ k13_funct_3 ) @ k7_relat_1 ) )
= ( B @ ( C @ ( A @ k7_relat_1 ) @ k13_funct_3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(1758,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( E @ ( C @ ( A @ ( B @ k8_relset_2 ) ) ) @ ( D @ r2_hidden ) )
<=> ! [F: $i] :
( ( C @ ( F @ r2_hidden ) )
=> ( F @ k1_tarski @ ( E @ k9_relat_1 ) @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_2) ).
thf(11194,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ! [F: $i] :
( ( C @ ( F @ r2_hidden ) )
=> ( F @ k1_tarski @ ( E @ k9_relat_1 ) @ ( D @ r2_hidden ) ) )
=> ( E @ ( C @ ( A @ ( B @ k8_relset_2 ) ) ) @ ( D @ r2_hidden ) ) )
& ( ( E @ ( C @ ( A @ ( B @ k8_relset_2 ) ) ) @ ( D @ r2_hidden ) )
=> ! [F: $i] :
( ( C @ ( F @ r2_hidden ) )
=> ( F @ k1_tarski @ ( E @ k9_relat_1 ) @ ( D @ r2_hidden ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1758]) ).
thf(1146,axiom,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finseq_1) ).
thf(8019,plain,
? [A: $i] :
( ( A @ v1_finseq_1 )
& ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(1230,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( G @ k4_tarski ) @ ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ k16_funct_3 ) ) ) ) ) @ k1_funct_1 ) )
= ( H @ ( F @ ( D @ ( C @ k8_funct_2 ) ) ) @ ( G @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ k4_tarski ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_funct_3) ).
thf(8510,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( C @ ( H @ m1_subset_1 ) )
=> ( ( H @ ( G @ k4_tarski ) @ ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ k16_funct_3 ) ) ) ) ) @ k1_funct_1 ) )
= ( H @ ( F @ ( D @ ( C @ k8_funct_2 ) ) ) @ ( G @ ( E @ ( B @ ( A @ k8_funct_2 ) ) ) @ k4_tarski ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(1344,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ~ ( ( ( C @ ( B @ k1_funct_1 ) )
= A )
& ( B @ k4_finseq_1 @ ( C @ r2_hidden ) ) ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_finseq_2) ).
thf(9134,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ~ ( ( ( C @ ( B @ k1_funct_1 ) )
= A )
& ( B @ k4_finseq_1 @ ( C @ r2_hidden ) ) ) )
& ( B @ k2_relat_1 @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).
thf(1978,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k6_pralg_1 ) @ m2_relset_1 ) ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k6_pralg_1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k6_pralg_1 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pralg_1) ).
thf(12583,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k6_pralg_1 ) @ m2_relset_1 ) ) )
& ( A @ ( B @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ ( A @ k6_pralg_1 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ k6_pralg_1 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1978]) ).
thf(1792,axiom,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
thf(11401,plain,
! [A: $i] :
( ( A @ k2_subset_1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1792]) ).
thf(558,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( D @ ( G @ ( F @ ( E @ ( B @ k4_setwiseo ) ) ) @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= ( G @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_setwiseo) ).
thf(4968,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( D @ ( G @ ( F @ ( E @ ( B @ k4_setwiseo ) ) ) @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= ( G @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( F @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( E @ ( D @ ( A @ ( B @ k8_funct_2 ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r2_wellord2 ) )
& ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ r2_wellord2 ) )
& ( B @ ( A @ r2_wellord2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_card_1) ).
thf(4007,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r2_wellord2 ) )
& ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( ( C @ ( B @ r2_wellord2 ) )
& ( B @ ( A @ r2_wellord2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(1190,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
thf(8241,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k9_relat_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k9_relat_1 ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ k1_funct_1 ) ) )
& ( B @ ( E @ r2_hidden ) )
& ( A @ k1_relat_1 @ ( E @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(1829,axiom,
! [A: $i] :
( ( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ v1_realset1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_tex_2) ).
thf(11627,plain,
! [A: $i] :
( ( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ v1_realset1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ~ ( B @ v1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1829]) ).
thf(590,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F
= ( B @ ( D @ k1_realset1 ) ) )
& ( E
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( ( ( D @ ( C @ ( A @ r5_binop_1 ) ) )
=> ( F @ ( E @ ( B @ r5_binop_1 ) ) ) )
& ( ( D @ ( C @ ( A @ r4_binop_1 ) ) )
=> ( F @ ( E @ ( B @ r4_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_filter_2) ).
thf(5105,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ( ( F
= ( B @ ( D @ k1_realset1 ) ) )
& ( E
= ( B @ ( C @ k1_realset1 ) ) ) )
=> ( ( ( D @ ( C @ ( A @ r5_binop_1 ) ) )
=> ( F @ ( E @ ( B @ r5_binop_1 ) ) ) )
& ( ( D @ ( C @ ( A @ r4_binop_1 ) ) )
=> ( F @ ( E @ ( B @ r4_binop_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(1324,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B @ ( D @ v1_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) )
<=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_binop_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_filter_1) ).
thf(9002,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_binop_1 ) )
=> ( ( B @ ( D @ v1_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) ) )
& ( ( ( B @ ( D @ v1_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ ( C @ ( B @ ( A @ k7_filter_1 ) ) ) @ v1_binop_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(2378,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k8_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_setfam_1) ).
thf(14600,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k8_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2378]) ).
thf(2201,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( C @ ( H @ m1_subset_1 ) )
& ( B @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_multop_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k1_multop_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_multop_1) ).
thf(13842,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( C @ ( H @ m1_subset_1 ) )
& ( B @ ( G @ m1_subset_1 ) )
& ( A @ ( F @ m1_subset_1 ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m1_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ~ ( D @ v1_xboole_0 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k2_multop_1 ) ) ) ) ) ) ) )
= ( H @ ( G @ ( F @ ( E @ k1_multop_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2201]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( D
= ( A @ ( C @ k3_funct_5 @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( ( B @ ( D @ k1_funct_1 ) )
= ( B @ ( A @ k4_tarski ) @ ( C @ k1_funct_1 ) ) )
& ( D @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_5) ).
thf(3479,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( D
= ( A @ ( C @ k3_funct_5 @ k1_funct_1 ) ) )
& ( C @ k1_relat_1 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
=> ( ( ( B @ ( D @ k1_funct_1 ) )
= ( B @ ( A @ k4_tarski ) @ ( C @ k1_funct_1 ) ) )
& ( D @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1521,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ ( A @ k8_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
<=> ( ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_funct_1) ).
thf(9959,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) )
=> ( C @ ( A @ k8_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) ) )
& ( ( C @ ( A @ k8_relat_1 ) @ k1_relat_1 @ ( B @ r2_hidden ) )
=> ( ( A @ ( B @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( B @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( k1_numbers @ ( B @ m1_subset_1 ) )
& ( k1_numbers @ ( A @ m1_subset_1 ) ) )
=> ( ( B @ ( A @ k9_binop_2 ) )
= ( A @ ( B @ k9_binop_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k9_binop_2) ).
thf(2417,plain,
! [A: $i,B: $i] :
( ( ( k1_numbers @ ( B @ m1_subset_1 ) )
& ( k1_numbers @ ( A @ m1_subset_1 ) ) )
=> ( ( B @ ( A @ k9_binop_2 ) )
= ( A @ ( B @ k9_binop_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1618,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_finset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( A @ k1_zfmisc_1 @ k6_domain_1 ) @ ( C @ ( A @ k1_zfmisc_1 @ k6_subset_1 ) ) @ ( A @ k5_setfam_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( D @ r2_hidden ) ) ) )
& ( ( C @ ( A @ k5_setfam_1 ) )
= ( B @ ( A @ k5_setfam_1 ) ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( C @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_waybel14) ).
thf(10472,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ v1_finset_1 ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ~ ( ( D @ ( A @ k1_zfmisc_1 @ k6_domain_1 ) @ ( C @ ( A @ k1_zfmisc_1 @ k6_subset_1 ) ) @ ( A @ k5_setfam_1 ) @ ( D @ r1_tarski ) )
& ( C @ ( D @ r2_hidden ) ) ) )
& ( ( C @ ( A @ k5_setfam_1 ) )
= ( B @ ( A @ k5_setfam_1 ) ) )
& ( B @ ( C @ r1_tarski ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( C @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1618]) ).
thf(1994,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_4_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ( ( D @ ( E @ r2_hidden ) )
& ~ ( C @ ( E @ r2_hidden ) ) )
| ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_4_domain_1) ).
thf(12679,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ( ( D @ ( E @ r2_hidden ) )
& ~ ( C @ ( E @ r2_hidden ) ) )
| ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_4_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_4_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ( ( D @ ( E @ r2_hidden ) )
& ~ ( C @ ( E @ r2_hidden ) ) )
| ( ~ ( D @ ( E @ r2_hidden ) )
& ( C @ ( E @ r2_hidden ) ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1994]) ).
thf(911,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( F @ v1_funct_1 )
& ( F @ v1_relat_1 ) )
=> ( ( F @ ( E @ k3_funct_4 ) @ k1_relat_1 @ ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) @ r2_hidden ) )
<=> ( ( F @ k1_relat_1 @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( E @ k1_relat_1 @ ( C @ ( A @ k4_tarski ) @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_4) ).
thf(6729,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( ( F @ v1_funct_1 )
& ( F @ v1_relat_1 ) )
=> ( ( ( ( F @ k1_relat_1 @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( E @ k1_relat_1 @ ( C @ ( A @ k4_tarski ) @ r2_hidden ) ) )
=> ( F @ ( E @ k3_funct_4 ) @ k1_relat_1 @ ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) @ r2_hidden ) ) )
& ( ( F @ ( E @ k3_funct_4 ) @ k1_relat_1 @ ( D @ ( C @ k4_tarski ) @ ( B @ ( A @ k4_tarski ) @ k4_tarski ) @ r2_hidden ) )
=> ( ( F @ k1_relat_1 @ ( D @ ( B @ k4_tarski ) @ r2_hidden ) )
& ( E @ k1_relat_1 @ ( C @ ( A @ k4_tarski ) @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(2307,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( B @ ( C @ ( A @ k7_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k7_subset_1) ).
thf(14293,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k7_subset_1 ) ) )
= ( B @ ( C @ ( A @ k7_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2307]) ).
thf(1006,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_setfam_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_eqrel_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_borsuk_1) ).
thf(7278,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_setfam_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_eqrel_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(2237,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C = D )
=> ( ( C @ ( A @ k1_cantor_1 ) )
= ( D @ ( B @ k1_cantor_1 ) ) ) )
& ( ( D @ ( C @ r1_tarski ) )
=> ( D @ ( B @ k1_cantor_1 ) @ ( C @ ( A @ k1_cantor_1 ) @ r1_tarski ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_yellow_9) ).
thf(14001,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( C = D )
=> ( ( C @ ( A @ k1_cantor_1 ) )
= ( D @ ( B @ k1_cantor_1 ) ) ) )
& ( ( D @ ( C @ r1_tarski ) )
=> ( D @ ( B @ k1_cantor_1 ) @ ( C @ ( A @ k1_cantor_1 ) @ r1_tarski ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2237]) ).
thf(127,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( A @ k4_finseq_1 @ ( A @ k4_finseq_1 @ ( C @ m2_relset_1 ) ) )
& ( A @ k4_finseq_1 @ ( A @ k4_finseq_1 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B
= ( A @ ( C @ k5_relat_1 ) ) )
& ( ( C @ k2_relat_1 )
= ( A @ k4_finseq_1 ) ) )
=> ( ( B @ k3_finseq_1 )
= ( A @ k3_finseq_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_finseq_2) ).
thf(2913,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( A @ k4_finseq_1 @ ( A @ k4_finseq_1 @ ( C @ m2_relset_1 ) ) )
& ( A @ k4_finseq_1 @ ( A @ k4_finseq_1 @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B
= ( A @ ( C @ k5_relat_1 ) ) )
& ( ( C @ k2_relat_1 )
= ( A @ k4_finseq_1 ) ) )
=> ( ( B @ k3_finseq_1 )
= ( A @ k3_finseq_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(5,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ v9_monoid_0 ) )
<=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( B @ ( A @ k3_binop_1 ) ) )
=> ( ( D
= ( B @ ( A @ k3_binop_1 ) ) )
& ( C = D ) ) ) ) )
& ( A @ ( B @ v1_setwiseo ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_monoid_0) ).
thf(2404,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( B @ ( A @ k3_binop_1 ) ) )
=> ( ( D
= ( B @ ( A @ k3_binop_1 ) ) )
& ( C = D ) ) ) ) )
& ( A @ ( B @ v1_setwiseo ) ) )
=> ( A @ ( B @ v9_monoid_0 ) ) )
& ( ( A @ ( B @ v9_monoid_0 ) )
=> ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( B @ ( A @ k3_binop_1 ) ) )
=> ( ( D
= ( B @ ( A @ k3_binop_1 ) ) )
& ( C = D ) ) ) ) )
& ( A @ ( B @ v1_setwiseo ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1143,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( A @ k15_funct_3 ) @ ( D @ ( B @ k13_funct_3 ) @ k5_relat_1 ) )
= ( C @ ( D @ k5_relat_1 ) @ ( A @ ( B @ k5_relat_1 ) @ k13_funct_3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_funct_3) ).
thf(8002,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( C @ ( A @ k15_funct_3 ) @ ( D @ ( B @ k13_funct_3 ) @ k5_relat_1 ) )
= ( C @ ( D @ k5_relat_1 ) @ ( A @ ( B @ k5_relat_1 ) @ k13_funct_3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ ( A @ k4_relset_1 ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_2) ).
thf(4865,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( B @ k2_relat_1 @ r1_tarski ) )
& ( ( B @ ( A @ ( A @ k4_relset_1 ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(645,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k13_funct_3 ) @ v1_funct_1 )
& ( B @ ( A @ k13_funct_3 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k13_funct_3) ).
thf(5378,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k13_funct_3 ) @ v1_funct_1 )
& ( B @ ( A @ k13_funct_3 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(1407,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_relat_1) ).
thf(9414,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( A @ k2_relat_1 @ k3_xboole_0 ) @ ( B @ ( A @ k3_xboole_0 ) @ k2_relat_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1407]) ).
thf(2074,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k14_domain_1 ) ) ) )
= ( D @ k17_mcart_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k14_domain_1) ).
thf(13194,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_zfmisc_1 ) @ ( D @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k14_domain_1 ) ) ) )
= ( D @ k17_mcart_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2074]) ).
thf(1117,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( ( A @ ( C @ ( B @ k10_funct_3 ) @ k1_funct_3 @ k1_funct_1 ) )
= ( A @ ( C @ ( B @ k10_funct_3 ) @ ( C @ ( C @ ( B @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_borsuk_1) ).
thf(7808,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) )
=> ( ( A @ ( C @ ( B @ k10_funct_3 ) @ k1_funct_3 @ k1_funct_1 ) )
= ( A @ ( C @ ( B @ k10_funct_3 ) @ ( C @ ( C @ ( B @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(408,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( ( C @ ( B @ k13_funct_3 ) @ k1_relat_1 )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_3) ).
thf(4193,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( C @ k1_relat_1 )
= A )
& ( ( B @ k1_relat_1 )
= A ) )
=> ( ( C @ ( B @ k13_funct_3 ) @ k1_relat_1 )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(844,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( B = D )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_zfmisc_1) ).
thf(6393,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B = D )
& ( C @ ( A @ r2_hidden ) ) )
=> ( D @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ k1_tarski @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( B = D )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(773,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ k2_tarski ) @ ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( F @ ( D @ ( B @ k3_mcart_1 ) ) @ ( F @ ( C @ ( B @ k3_mcart_1 ) ) @ ( E @ ( D @ ( B @ k3_mcart_1 ) ) @ ( E @ ( C @ ( B @ k3_mcart_1 ) ) @ ( F @ ( D @ ( A @ k3_mcart_1 ) ) @ ( F @ ( C @ ( A @ k3_mcart_1 ) ) @ ( E @ ( D @ ( A @ k3_mcart_1 ) ) @ ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ k6_enumset1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_mcart_1) ).
thf(6040,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ k2_tarski ) @ ( D @ ( C @ k2_tarski ) @ ( B @ ( A @ k2_tarski ) @ k3_zfmisc_1 ) ) )
= ( F @ ( D @ ( B @ k3_mcart_1 ) ) @ ( F @ ( C @ ( B @ k3_mcart_1 ) ) @ ( E @ ( D @ ( B @ k3_mcart_1 ) ) @ ( E @ ( C @ ( B @ k3_mcart_1 ) ) @ ( F @ ( D @ ( A @ k3_mcart_1 ) ) @ ( F @ ( C @ ( A @ k3_mcart_1 ) ) @ ( E @ ( D @ ( A @ k3_mcart_1 ) ) @ ( E @ ( C @ ( A @ k3_mcart_1 ) ) @ k6_enumset1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(955,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k1_funct_2 ) @ v1_fraenkel ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_fraenkel) ).
thf(6929,plain,
! [A: $i,B: $i] : ( B @ ( A @ k1_funct_2 ) @ v1_fraenkel ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(257,axiom,
! [A: $i] :
( ( A @ k6_relat_1 @ k4_relat_1 )
= ( A @ k6_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_relat_1) ).
thf(3506,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ k4_relat_1 )
= ( A @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(333,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( A @ k1_relat_1 )
= ( A @ k4_relat_1 @ k2_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( A @ k4_relat_1 @ k1_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
thf(3843,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( A @ k1_relat_1 )
= ( A @ k4_relat_1 @ k2_relat_1 ) )
& ( ( A @ k2_relat_1 )
= ( A @ k4_relat_1 @ k1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(1620,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(10485,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( A @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1620]) ).
thf(1678,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_relat_1) ).
thf(10781,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1678]) ).
thf(1573,axiom,
! [A: $i] :
( ( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( B @ v1_realset1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_tex_2) ).
thf(10224,plain,
! [A: $i] :
( ( ~ ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ v1_tex_2 ) )
& ( B @ v1_realset1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1573]) ).
thf(818,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_cat_2 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_cat_2 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k2_cat_2 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_cat_2) ).
thf(6269,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_cat_2 ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( B @ k1_fraenkel ) @ ( A @ ( D @ ( C @ ( B @ ( A @ k2_cat_2 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k2_cat_2 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(861,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( C @ v3_binop_1 ) )
& ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( ( D @ ( E @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( F @ ( B @ k2_setwiseo ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) )
= F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_setwiseo) ).
thf(6503,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( B @ ( C @ v3_binop_1 ) )
& ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( ( D @ ( E @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( F @ ( B @ k2_setwiseo ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) )
= F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(1415,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) )
= ( C @ ( B @ k3_xboole_0 ) @ ( A @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_xboole_1) ).
thf(9441,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k3_xboole_0 ) @ k3_xboole_0 ) )
= ( C @ ( B @ k3_xboole_0 ) @ ( A @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415]) ).
thf(538,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
thf(4848,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ k2_relat_1 @ ( B @ ( A @ k8_relat_1 ) @ k2_relat_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ r2_wellord2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_card_1) ).
thf(3362,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ k1_tarski @ ( B @ k4_xboole_0 ) @ ( A @ k1_tarski @ ( B @ k4_xboole_0 ) @ r2_wellord2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1635,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_3_domain_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i,E: $i] :
( ( E @ ( D @ p1_s2_domain_1 ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_3_domain_1) ).
thf(10554,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i,E: $i] :
( ( E @ ( D @ p1_s2_domain_1 ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_3_domain_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_3_domain_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i,E: $i] :
( ( E @ ( D @ p1_s2_domain_1 ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ k1_domain_1 ) ) ) ) )
& ( C @ ( E @ m1_subset_1 ) )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1635]) ).
thf(1782,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_partfun1) ).
thf(11358,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1782]) ).
thf(546,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_funct_2) ).
thf(4876,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( ( D @ ( C @ ( A @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) )
= ( A @ k6_partfun1 ) )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( D
= ( C @ k2_funct_1 ) )
| ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(2068,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_ordinal1) ).
thf(13161,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) )
& ( C @ ( B @ r2_hidden ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2068]) ).
thf(2298,axiom,
! [A: $i] :
( ( a_0_32_fraenkel @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ( B @ p1_s17_fraenkel )
& ( f2_s17_fraenkel @ ( B @ f3_s17_fraenkel @ r2_hidden ) )
& ( A
= ( B @ f3_s17_fraenkel ) )
& ( f1_s17_fraenkel @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_32_fraenkel) ).
thf(14251,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ p1_s17_fraenkel )
& ( f2_s17_fraenkel @ ( B @ f3_s17_fraenkel @ r2_hidden ) )
& ( A
= ( B @ f3_s17_fraenkel ) )
& ( f1_s17_fraenkel @ ( B @ m1_subset_1 ) ) )
=> ( a_0_32_fraenkel @ ( A @ r2_hidden ) ) )
& ( ( a_0_32_fraenkel @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ( B @ p1_s17_fraenkel )
& ( f2_s17_fraenkel @ ( B @ f3_s17_fraenkel @ r2_hidden ) )
& ( A
= ( B @ f3_s17_fraenkel ) )
& ( f1_s17_fraenkel @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2298]) ).
thf(2197,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m2_relset_1 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( G @ m2_relset_1 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( B @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( C @ ( J @ m1_subset_1 ) )
=> ! [K: $i] :
( ( D @ ( K @ m1_subset_1 ) )
=> ( ( K @ ( J @ ( I @ ( H @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_multop_1 ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_multop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( F = G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_multop_1) ).
thf(13824,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ~ ( E @ v1_xboole_0 )
=> ! [F: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ m2_relset_1 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( G @ m2_relset_1 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k4_zfmisc_1 ) ) ) @ ( G @ v1_funct_2 ) ) )
& ( G @ v1_funct_1 ) )
=> ( ! [H: $i] :
( ( A @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( B @ ( I @ m1_subset_1 ) )
=> ! [J: $i] :
( ( C @ ( J @ m1_subset_1 ) )
=> ! [K: $i] :
( ( D @ ( K @ m1_subset_1 ) )
=> ( ( K @ ( J @ ( I @ ( H @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_multop_1 ) ) ) ) ) ) ) ) ) )
= ( K @ ( J @ ( I @ ( H @ ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ k4_multop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ( F = G ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2197]) ).
thf(847,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ? [E: $i] :
( ( ( E @ ( D @ k1_funct_1 ) )
!= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_funct_2) ).
thf(6424,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ~ ( ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ? [E: $i] :
( ( ( E @ ( D @ k1_funct_1 ) )
!= ( E @ ( C @ k1_funct_1 ) ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(1391,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_relset_1) ).
thf(9325,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( D @ ( C @ k9_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k3_funct_5 )
= ( D @ k3_funct_5 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_5) ).
thf(3244,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k3_funct_5 )
= ( D @ k3_funct_5 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( D @ k1_relat_1 @ r1_tarski ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ k1_relat_1 @ r1_tarski ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(1790,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ( A
!= ( E @ ( D @ k4_tarski ) ) ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_domain_1) ).
thf(11390,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ~ ( ! [D: $i] :
( ( B @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( C @ ( E @ m1_subset_1 ) )
=> ( A
!= ( E @ ( D @ k4_tarski ) ) ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1790]) ).
thf(1157,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( A @ k2_relat_1 )
= ( B @ k1_tarski ) )
=> ( A
= ( B @ ( A @ k1_relat_1 @ k2_funcop_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_funcop_1) ).
thf(8066,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( A @ k2_relat_1 )
= ( B @ k1_tarski ) )
=> ( A
= ( B @ ( A @ k1_relat_1 @ k2_funcop_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( ( A @ k6_relat_1 @ ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) )
=> ( ( B @ ( A @ k8_relat_1 ) )
= ( A @ k6_relat_1 ) ) )
& ( ( ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= k1_xboole_0 )
& ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) )
=> ( ( A @ ( B @ k7_relat_1 ) )
= ( A @ k6_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_sysrel) ).
thf(2966,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( ( A @ k6_relat_1 @ ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) )
=> ( ( B @ ( A @ k8_relat_1 ) )
= ( A @ k6_relat_1 ) ) )
& ( ( ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= k1_xboole_0 )
& ( B @ ( A @ k6_relat_1 @ r1_tarski ) ) )
=> ( ( A @ ( B @ k7_relat_1 ) )
= ( A @ k6_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(917,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( A @ ( D @ k9_relat_1 ) @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_partfun1) ).
thf(6750,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ~ ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ~ ( ( C
= ( E @ ( D @ k1_funct_1 ) ) )
& ( D @ ( B @ ( A @ k4_relset_1 ) ) @ ( E @ r2_hidden ) ) ) )
& ( A @ ( D @ k9_relat_1 ) @ ( C @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(267,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k4_relat_1 @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(3543,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( A @ k4_relat_1 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(1913,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 ) )
=> ( ( C
= ( E @ ( D @ ( B @ ( A @ a_4_1_yellow_9 ) ) ) ) )
=> ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k8_setfam_1 ) )
= ( E @ ( B @ k8_setfam_1 ) @ ( D @ ( A @ k8_setfam_1 ) @ ( B @ ( A @ k12_mcart_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_yellow_9) ).
thf(12134,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ~ ( D @ v1_xboole_0 ) )
=> ! [E: $i] :
( ( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ~ ( E @ v1_xboole_0 ) )
=> ( ( C
= ( E @ ( D @ ( B @ ( A @ a_4_1_yellow_9 ) ) ) ) )
=> ( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k8_setfam_1 ) )
= ( E @ ( B @ k8_setfam_1 ) @ ( D @ ( A @ k8_setfam_1 ) @ ( B @ ( A @ k12_mcart_1 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1913]) ).
thf(2010,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m1_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k16_funct_3) ).
thf(12793,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m1_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) @ m2_relset_1 ) ) )
& ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k2_zfmisc_1 ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) @ v1_funct_2 ) ) )
& ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2010]) ).
thf(1220,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( ( ( C @ ( C @ k2_funct_1 @ k5_relat_1 ) )
= ( B @ k6_partfun1 ) )
& ( ( C @ k2_funct_1 @ ( C @ k5_relat_1 ) )
= ( A @ k6_partfun1 ) ) )
| ( B = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_2) ).
thf(8444,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( ( C @ k2_relat_1 )
= B ) )
=> ( ( ( ( C @ ( C @ k2_funct_1 @ k5_relat_1 ) )
= ( B @ k6_partfun1 ) )
& ( ( C @ k2_funct_1 @ ( C @ k5_relat_1 ) )
= ( A @ k6_partfun1 ) ) )
| ( B = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(704,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ k3_tarski @ ( A @ k3_tarski @ k2_zfmisc_1 ) )
= ( B @ ( A @ a_2_0_lattice5 ) @ k3_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_lattice5) ).
thf(5668,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ k3_tarski @ ( A @ k3_tarski @ k2_zfmisc_1 ) )
= ( B @ ( A @ a_2_0_lattice5 ) @ k3_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(1746,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(11144,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1746]) ).
thf(1459,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ k1_tarski @ ( C @ ( B @ k3_xboole_0 ) @ k9_relat_1 ) )
= ( A @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ k1_tarski @ ( B @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_relset_2) ).
thf(9679,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( A @ k1_tarski @ ( C @ ( B @ k3_xboole_0 ) @ k9_relat_1 ) )
= ( A @ k1_tarski @ ( C @ k9_relat_1 ) @ ( A @ k1_tarski @ ( B @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459]) ).
thf(1065,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_funct_1) ).
thf(7584,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ v2_funct_1 )
& ( B @ ( A @ r1_xboole_0 ) ) )
=> ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ r1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(927,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( A @ k2_funct_5 )
= ( A @ k2_relat_1 ) )
& ( ( A @ k1_funct_5 )
= ( A @ k1_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_5) ).
thf(6807,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( A @ k2_funct_5 )
= ( A @ k2_relat_1 ) )
& ( ( A @ k1_funct_5 )
= ( A @ k1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(1535,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_realset1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_tex_2) ).
thf(10032,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_realset1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1535]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t133_funct_2) ).
thf(2600,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B = k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
=> ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1476,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_2) ).
thf(9763,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k1_tarski @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ k1_tarski @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ( B @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1476]) ).
thf(1044,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_setwiseo ) ) ) @ k3_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_setwiseo) ).
thf(7506,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ k5_finsub_1 @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ k5_finsub_1 @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ ( B @ ( A @ k10_setwiseo ) ) ) )
= ( D @ ( C @ ( B @ k5_finsub_1 @ ( A @ k8_setwiseo ) ) ) @ k3_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(600,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( C @ ( B @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_realset1) ).
thf(5140,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ m2_relset_1 ) ) )
& ( C @ ( C @ ( C @ k2_zfmisc_1 ) @ ( C @ ( B @ k1_realset1 ) @ v1_funct_2 ) ) )
& ( C @ ( B @ k1_realset1 ) @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(2155,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ m1_pboole ) )
& ( A @ ( D @ m1_pboole ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( F @ m1_functor0 ) ) ) ) ) )
=> ( A @ ( F @ m1_pboole ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_functor0) ).
thf(13601,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( E @ m1_pboole ) )
& ( A @ ( D @ m1_pboole ) )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [F: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( F @ m1_functor0 ) ) ) ) ) )
=> ( A @ ( F @ m1_pboole ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2155]) ).
thf(1839,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C
= ( B @ ( A @ k1_cantor_1 ) ) )
<=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( C @ ( D @ r2_hidden ) )
<=> ? [E: $i] :
( ( D
= ( E @ ( A @ k5_setfam_1 ) ) )
& ( B @ ( E @ r1_tarski ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_cantor_1) ).
thf(11707,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ! [C: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( D
= ( E @ ( A @ k5_setfam_1 ) ) )
& ( B @ ( E @ r1_tarski ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ k5_setfam_1 ) ) )
& ( B @ ( E @ r1_tarski ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) )
=> ( C
= ( B @ ( A @ k1_cantor_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_cantor_1 ) ) )
=> ! [D: $i] :
( ( A @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ? [E: $i] :
( ( D
= ( E @ ( A @ k5_setfam_1 ) ) )
& ( B @ ( E @ r1_tarski ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ k5_setfam_1 ) ) )
& ( B @ ( E @ r1_tarski ) )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1839]) ).
thf(1846,axiom,
f2_s17_fraenkel @ ( a_0_32_fraenkel @ r1_tarski ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s17_fraenkel) ).
thf(11764,plain,
f2_s17_fraenkel @ ( a_0_32_fraenkel @ r1_tarski ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1846]) ).
thf(470,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(4506,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(859,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( B
= ( A @ k2_relat_1 ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
thf(6473,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k2_relat_1 ) ) )
& ( ( B
= ( A @ k2_relat_1 ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( C
= ( D @ ( A @ k1_funct_1 ) ) )
& ( A @ k1_relat_1 @ ( D @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(202,axiom,
! [A: $i,B: $i] : ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t82_xboole_1) ).
thf(3259,plain,
! [A: $i,B: $i] : ( A @ ( B @ k4_xboole_0 ) @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(2006,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).
thf(12761,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finset_1 )
& ( A @ v1_finset_1 ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2006]) ).
thf(1102,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( C @ v3_binop_1 ) )
& ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ k5_finsub_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ k5_finsub_1 @ ( G @ m1_subset_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( G @ ( E @ ( B @ ( A @ k2_funct_2 ) ) ) ) )
=> ( ( ( D @ ( F @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) )
= ( E @ ( G @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) ) )
| ( F = k1_xboole_0 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_setwiseo) ).
thf(7740,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( ( B @ ( C @ v3_binop_1 ) )
& ( B @ ( C @ v2_binop_1 ) )
& ( B @ ( C @ v1_binop_1 ) ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( B @ ( A @ ( E @ m2_relset_1 ) ) )
& ( B @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( A @ k5_finsub_1 @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( A @ k5_finsub_1 @ ( G @ m1_subset_1 ) )
=> ( ( ( F @ ( D @ ( B @ ( A @ k2_funct_2 ) ) ) )
= ( G @ ( E @ ( B @ ( A @ k2_funct_2 ) ) ) ) )
=> ( ( ( D @ ( F @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) )
= ( E @ ( G @ ( C @ ( B @ ( A @ k7_setwiseo ) ) ) ) ) )
| ( F = k1_xboole_0 ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(631,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(5280,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_tarski )
= ( C @ ( B @ k2_tarski ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(1417,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m1_card_fil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_card_fil) ).
thf(9446,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] : ( A @ ( B @ m1_card_fil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_funct_1) ).
thf(3817,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k10_relat_1 ) )
= ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ k4_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ ( A @ k2_tarski ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( A @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_zfmisc_1) ).
thf(3965,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ ( A @ k2_tarski ) ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( B @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= ( A @ k1_tarski ) )
& ( ( C @ ( B @ ( A @ k2_tarski ) @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(708,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funcop_1 ) @ k2_funct_4 )
= ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ k2_funcop_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_6) ).
thf(5681,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funcop_1 ) @ k2_funct_4 )
= ( C @ ( A @ ( B @ k2_zfmisc_1 ) @ k2_funcop_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(583,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_pboole ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_pboole ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ ( F @ m1_functor0 ) ) ) ) ) )
<=> ( E @ ( C @ ( B @ ( A @ k7_pboole ) ) ) @ ( D @ ( A @ ( F @ m3_pboole ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_functor0) ).
thf(5060,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( A @ ( D @ m1_pboole ) )
=> ! [E: $i] :
( ( B @ ( E @ m1_pboole ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_pboole ) )
=> ( ( ( E @ ( C @ ( B @ ( A @ k7_pboole ) ) ) @ ( D @ ( A @ ( F @ m3_pboole ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ ( F @ m1_functor0 ) ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ ( F @ m1_functor0 ) ) ) ) ) )
=> ( E @ ( C @ ( B @ ( A @ k7_pboole ) ) ) @ ( D @ ( A @ ( F @ m3_pboole ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(1271,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_relset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(8730,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_relset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(149,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v1_setwiseo ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k5_finsub_1 @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ ( E @ ( B @ k5_setwiseo ) ) @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= ( D @ ( F @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( D @ ( E @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_setwiseo) ).
thf(3020,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( B @ ( D @ m2_relset_1 ) ) )
& ( A @ ( B @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v1_setwiseo ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ k5_finsub_1 @ ( F @ m1_subset_1 ) )
=> ( ( D @ ( F @ ( E @ ( B @ k5_setwiseo ) ) @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= ( D @ ( F @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( D @ ( E @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( C @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(418,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ m2_relset_1 ) ) )
& ( A @ ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( A @ ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( F @ m2_relset_1 ) ) )
& ( A @ ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ! [G: $i,H: $i,I: $i] :
( ( ( D @ ( I @ r2_hidden ) )
& ( C @ ( H @ r2_hidden ) )
& ( B @ ( G @ r2_hidden ) ) )
=> ( ( I @ ( H @ ( G @ k3_mcart_1 ) ) @ ( E @ k1_funct_1 ) )
= ( I @ ( H @ ( G @ k3_mcart_1 ) ) @ ( F @ k1_funct_1 ) ) ) )
=> ( E = F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_multop_1) ).
thf(4239,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ m2_relset_1 ) ) )
& ( A @ ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( A @ ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( F @ m2_relset_1 ) ) )
& ( A @ ( D @ ( C @ ( B @ k3_zfmisc_1 ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ! [G: $i,H: $i,I: $i] :
( ( ( D @ ( I @ r2_hidden ) )
& ( C @ ( H @ r2_hidden ) )
& ( B @ ( G @ r2_hidden ) ) )
=> ( ( I @ ( H @ ( G @ k3_mcart_1 ) ) @ ( E @ k1_funct_1 ) )
= ( I @ ( H @ ( G @ k3_mcart_1 ) ) @ ( F @ k1_funct_1 ) ) ) )
=> ( E = F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(782,axiom,
! [A: $i] :
( ( k1_numbers @ ( A @ m1_subset_1 ) )
=> ( ( A @ k7_binop_2 @ k7_binop_2 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_binop_2) ).
thf(6082,plain,
! [A: $i] :
( ( k1_numbers @ ( A @ m1_subset_1 ) )
=> ( ( A @ k7_binop_2 @ k7_binop_2 )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(1339,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) )
= ( A @ ( B @ k1_relat_1 @ k2_zfmisc_1 ) @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_relat_1) ).
thf(9110,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( B @ ( A @ k8_relat_1 ) )
= ( A @ ( B @ k1_relat_1 @ k2_zfmisc_1 ) @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339]) ).
thf(2303,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_relset_2 ) ) )
= ( C @ ( B @ k5_relset_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_relset_2) ).
thf(14283,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( B @ ( A @ k6_relset_2 ) ) )
= ( C @ ( B @ k5_relset_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2303]) ).
thf(2180,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( C
= ( B @ ( A @ k1_yellow_3 ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
<=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( B @ ( I @ ( G @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( H @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( E
= ( I @ ( H @ k4_tarski ) ) )
& ( D
= ( G @ ( F @ k4_tarski ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yellow_3) ).
thf(13720,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( ( ! [D: $i,E: $i] :
( ( ? [F: $i,G: $i,H: $i,I: $i] :
( ( B @ ( I @ ( G @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( H @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( E
= ( I @ ( H @ k4_tarski ) ) )
& ( D
= ( G @ ( F @ k4_tarski ) ) ) )
=> ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( B @ ( I @ ( G @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( H @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( E
= ( I @ ( H @ k4_tarski ) ) )
& ( D
= ( G @ ( F @ k4_tarski ) ) ) ) ) )
=> ( C
= ( B @ ( A @ k1_yellow_3 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_yellow_3 ) ) )
=> ! [D: $i,E: $i] :
( ( ? [F: $i,G: $i,H: $i,I: $i] :
( ( B @ ( I @ ( G @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( H @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( E
= ( I @ ( H @ k4_tarski ) ) )
& ( D
= ( G @ ( F @ k4_tarski ) ) ) )
=> ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( E @ ( D @ k4_tarski ) @ r2_hidden ) )
=> ? [F: $i,G: $i,H: $i,I: $i] :
( ( B @ ( I @ ( G @ k4_tarski ) @ r2_hidden ) )
& ( A @ ( H @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( E
= ( I @ ( H @ k4_tarski ) ) )
& ( D
= ( G @ ( F @ k4_tarski ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2180]) ).
thf(1804,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(11479,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1804]) ).
thf(1803,axiom,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_triang_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_triang_1) ).
thf(11477,plain,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_triang_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1803]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(4659,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(265,axiom,
! [A: $i] : ( A @ ( k1_xboole_0 @ m2_finseq_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finseq_1) ).
thf(3538,plain,
! [A: $i] : ( A @ ( k1_xboole_0 @ m2_finseq_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1925,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ a_3_6_domain_1 ) ) @ ( A @ r2_hidden ) )
<=> ? [E: $i] :
( ( ( C @ ( E @ r2_hidden ) )
<=> ~ ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_3_6_domain_1) ).
thf(12188,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [E: $i] :
( ( ~ ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ~ ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) )
=> ( D @ ( C @ ( B @ a_3_6_domain_1 ) ) @ ( A @ r2_hidden ) ) )
& ( ( D @ ( C @ ( B @ a_3_6_domain_1 ) ) @ ( A @ r2_hidden ) )
=> ? [E: $i] :
( ( ~ ( D @ ( E @ r2_hidden ) )
=> ( C @ ( E @ r2_hidden ) ) )
& ( ( C @ ( E @ r2_hidden ) )
=> ~ ( D @ ( E @ r2_hidden ) ) )
& ( A = E )
& ( B @ ( E @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1925]) ).
thf(1110,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_tarski ) @ ( B @ k1_tarski @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( D @ ( B @ ( A @ k3_mcart_1 ) ) @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_mcart_1) ).
thf(7780,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_tarski ) @ ( B @ k1_tarski @ ( A @ k1_tarski @ k3_zfmisc_1 ) ) )
= ( D @ ( B @ ( A @ k3_mcart_1 ) ) @ ( C @ ( B @ ( A @ k3_mcart_1 ) ) @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(1801,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m1_pboole ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( F @ ( E @ ( D @ ( B @ k1_multop_1 ) ) ) )
= ( F @ ( E @ ( D @ ( C @ k1_multop_1 ) ) ) ) ) )
=> ( B @ ( C @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ r6_pboole ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_altcat_1) ).
thf(11462,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ ( C @ m1_pboole ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( A @ ( F @ r2_hidden ) )
& ( A @ ( E @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( ( F @ ( E @ ( D @ ( B @ k1_multop_1 ) ) ) )
= ( F @ ( E @ ( D @ ( C @ k1_multop_1 ) ) ) ) ) )
=> ( B @ ( C @ ( A @ ( A @ ( A @ k3_zfmisc_1 ) ) @ r6_pboole ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1801]) ).
thf(1655,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( C @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
<=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_t_0topsp) ).
thf(10642,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ m1_subset_1 ) )
=> ! [F: $i] :
( ( B @ ( F @ m1_subset_1 ) )
=> ( ( ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( C @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
& ( ( C @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1655]) ).
thf(355,axiom,
! [A: $i,B: $i] :
( ( B @ k1_tarski @ ( A @ r2_wellord2 ) )
<=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_card_1) ).
thf(3939,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ k1_tarski ) )
=> ( B @ k1_tarski @ ( A @ r2_wellord2 ) ) )
& ( ( B @ k1_tarski @ ( A @ r2_wellord2 ) )
=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(1394,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_funct_4) ).
thf(9335,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( B @ ( A @ k1_funct_4 ) @ k7_relat_1 ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394]) ).
thf(554,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( C @ v3_binop_1 ) )
=> ( ( D @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_funcop_1) ).
thf(4955,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B @ ( C @ v3_binop_1 ) )
=> ( ( D @ ( D @ ( C @ ( A @ ( B @ k6_funcop_1 ) ) ) ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(503,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
<=> ( ( B @ k1_relat_1 @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
thf(4691,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( ( B @ k1_relat_1 @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) )
=> ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) ) )
& ( ( B @ ( C @ k5_relat_1 ) @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( ( B @ k1_relat_1 @ ( A @ ( C @ k1_funct_1 ) @ r2_hidden ) )
& ( C @ k1_relat_1 @ ( A @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ~ ( B @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_pboole) ).
thf(2699,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ m1_pboole ) )
& ( B @ v2_relat_1 ) )
=> ~ ( B @ k2_relat_1 @ ( k1_xboole_0 @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1301,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_zfmisc_1) ).
thf(8876,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k3_tarski @ ( A @ k3_tarski @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).
thf(326,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( A @ k4_finseq_1 @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k1_funct_1 ) @ r2_hidden ) ) ) )
=> ( B @ ( A @ m2_finseq_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finseq_2) ).
thf(3812,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ( ( A @ k4_finseq_1 @ ( C @ r2_hidden ) )
=> ( B @ ( C @ ( A @ k1_funct_1 ) @ r2_hidden ) ) ) )
=> ( B @ ( A @ m2_finseq_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(2172,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(13689,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2172]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ ( A @ k3_enumset1 ) ) ) ) )
= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t78_enumset1) ).
thf(4345,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ ( A @ k3_enumset1 ) ) ) ) )
= ( C @ ( B @ ( A @ k1_enumset1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(2261,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k12_mcart_1) ).
thf(14114,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2261]) ).
thf(468,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ( B @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_card_fil) ).
thf(4501,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_card_fil ) )
=> ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(1642,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( A @ k1_ens_1 @ ( B @ k1_ens_1 @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ens_1) ).
thf(10586,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( A @ k1_ens_1 @ ( B @ k1_ens_1 @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1642]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m1_nat_lat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_nat_lat) ).
thf(4271,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m1_nat_lat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(349,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 )
& ( ( A @ k2_relat_1 )
= ( B @ k2_relat_1 ) ) )
=> ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_finseq_1) ).
thf(3918,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( ( B @ v2_funct_1 )
& ( A @ v2_funct_1 )
& ( ( A @ k2_relat_1 )
= ( B @ k2_relat_1 ) ) )
=> ( ( A @ k3_finseq_1 )
= ( B @ k3_finseq_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(1787,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_waybel_7) ).
thf(11373,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1787]) ).
thf(1297,axiom,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A = k1_xboole_0 )
<=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finseq_1) ).
thf(8857,plain,
! [A: $i] :
( ( ( A @ v1_finseq_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( ( ( A @ k2_relat_1 )
= k1_xboole_0 )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ( ( A @ k2_relat_1 )
= k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297]) ).
thf(1317,axiom,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_membered ) )
=> ( A @ k3_tarski @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_membered) ).
thf(8978,plain,
! [A: $i] :
( ! [B: $i] :
( ( A @ ( B @ r2_hidden ) )
=> ( B @ v1_membered ) )
=> ( A @ k3_tarski @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(1309,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m1_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) )
= ( F @ ( E @ k15_funct_3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k16_funct_3) ).
thf(8950,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ ( F @ m1_relset_1 ) ) )
& ( D @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 )
& ( C @ ( A @ ( E @ m1_relset_1 ) ) )
& ( C @ ( A @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k16_funct_3 ) ) ) ) ) )
= ( F @ ( E @ k15_funct_3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(577,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
thf(5029,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( A @ k1_relat_1 @ ( A @ k9_relat_1 ) )
= ( A @ k2_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(1734,axiom,
( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k35_binop_2 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k35_binop_2 @ v1_funct_2 ) ) )
& ( k35_binop_2 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k35_binop_2) ).
thf(11086,plain,
( ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k35_binop_2 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k1_numbers @ k2_zfmisc_1 ) @ ( k35_binop_2 @ v1_funct_2 ) ) )
& ( k35_binop_2 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734]) ).
thf(399,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(4161,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ k1_tarski @ ( A @ k1_tarski @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(1384,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ a_4_0_relset_2 ) ) ) @ k3_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_relset_2) ).
thf(9303,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ( ( C @ ( D @ ( B @ ( A @ k10_relset_1 ) ) ) )
= ( D @ ( C @ ( B @ ( A @ a_4_0_relset_2 ) ) ) @ k3_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).
thf(1708,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(10949,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1708]) ).
thf(285,axiom,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_classes2) ).
thf(3637,plain,
! [A: $i] :
( ( ( A @ v1_classes2 )
& ~ ( A @ v1_xboole_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(948,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_fraenkel ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_fraenkel) ).
thf(6896,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_fraenkel ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(342,axiom,
! [A: $i] :
( ( A @ k6_relat_1 @ k2_funct_1 )
= ( A @ k6_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_1) ).
thf(3901,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ k2_funct_1 )
= ( A @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(2002,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( k1_xboole_0 @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( k1_xboole_0 @ k5_relat_1 ) )
= k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_relat_1) ).
thf(12749,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( k1_xboole_0 @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( ( A @ ( k1_xboole_0 @ k5_relat_1 ) )
= k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2002]) ).
thf(1439,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ ( B @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( C @ ( B @ ( A @ k3_funcop_1 ) ) @ k1_relat_1 )
= ( C @ k1_relat_1 @ ( B @ k1_relat_1 @ k3_xboole_0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t84_funcop_1) ).
thf(9568,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( A @ k1_relat_1 @ ( C @ k2_relat_1 @ ( B @ k2_relat_1 @ k2_zfmisc_1 ) @ r1_tarski ) )
=> ( ( C @ ( B @ ( A @ k3_funcop_1 ) ) @ k1_relat_1 )
= ( C @ k1_relat_1 @ ( B @ k1_relat_1 @ k3_xboole_0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1439]) ).
thf(1265,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k3_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(8685,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k3_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k3_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(606,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_relat_1) ).
thf(5172,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ v1_relat_1 )
=> ( ( B @ ( A @ r1_tarski ) )
=> ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(2345,axiom,
! [A: $i] :
( ( a_0_0_group_5 @ ( A @ r2_hidden ) )
<=> ? [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ p1_s1_group_5 ) ) )
& ( A
= ( D @ ( C @ ( B @ f4_s1_group_5 ) ) ) )
& ( f3_s1_group_5 @ ( D @ m1_subset_1 ) )
& ( f2_s1_group_5 @ ( C @ m1_subset_1 ) )
& ( f1_s1_group_5 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_0_group_5) ).
thf(14443,plain,
! [A: $i] :
( ( ? [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ p1_s1_group_5 ) ) )
& ( A
= ( D @ ( C @ ( B @ f4_s1_group_5 ) ) ) )
& ( f3_s1_group_5 @ ( D @ m1_subset_1 ) )
& ( f2_s1_group_5 @ ( C @ m1_subset_1 ) )
& ( f1_s1_group_5 @ ( B @ m1_subset_1 ) ) )
=> ( a_0_0_group_5 @ ( A @ r2_hidden ) ) )
& ( ( a_0_0_group_5 @ ( A @ r2_hidden ) )
=> ? [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ p1_s1_group_5 ) ) )
& ( A
= ( D @ ( C @ ( B @ f4_s1_group_5 ) ) ) )
& ( f3_s1_group_5 @ ( D @ m1_subset_1 ) )
& ( f2_s1_group_5 @ ( C @ m1_subset_1 ) )
& ( f1_s1_group_5 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2345]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k1_setfam_1 @ r1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_setfam_1) ).
thf(3461,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ r1_xboole_0 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( B @ k1_setfam_1 @ r1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(2217,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( ( ( C @ ( B @ ( A @ k15_funct_3 ) @ k9_relat_1 ) @ k2_funct_5 )
= ( C @ k2_funct_5 @ ( B @ k9_relat_1 ) ) )
& ( ( C @ ( B @ ( A @ k15_funct_3 ) @ k9_relat_1 ) @ k1_funct_5 )
= ( C @ k1_funct_5 @ ( A @ k9_relat_1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_waybel20) ).
thf(13922,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ! [B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ! [C: $i] :
( ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k2_zfmisc_1 ) @ ( C @ r1_tarski ) )
=> ( ( ( C @ ( B @ ( A @ k15_funct_3 ) @ k9_relat_1 ) @ k2_funct_5 )
= ( C @ k2_funct_5 @ ( B @ k9_relat_1 ) ) )
& ( ( C @ ( B @ ( A @ k15_funct_3 ) @ k9_relat_1 ) @ k1_funct_5 )
= ( C @ k1_funct_5 @ ( A @ k9_relat_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2217]) ).
thf(2029,axiom,
( ( k1_xboole_0 @ k6_relat_1 )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_relat_1) ).
thf(12908,plain,
( ( k1_xboole_0 @ k6_relat_1 )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2029]) ).
thf(963,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( A @ r6_binop_1 ) ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( A @ ( B @ ( F @ m2_relset_1 ) ) )
& ( A @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( G @ ( D @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( G @ ( D @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ ( E @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_setwiseo) ).
thf(6961,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( C @ ( D @ ( A @ r6_binop_1 ) ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) )
& ( A @ ( C @ v3_binop_1 ) ) )
=> ! [E: $i] :
( ( B @ k5_finsub_1 @ ( E @ m1_subset_1 ) )
=> ( ( E != k1_xboole_0 )
=> ! [F: $i] :
( ( ( A @ ( B @ ( F @ m2_relset_1 ) ) )
& ( A @ ( B @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ( ( F @ ( E @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) @ ( G @ ( D @ ( A @ ( A @ ( A @ k2_binop_1 ) ) ) ) ) )
= ( F @ ( G @ ( D @ ( B @ ( A @ k8_funcop_1 ) ) ) ) @ ( E @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(1665,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(10723,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1665]) ).
thf(1553,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k3_cat_5 ) ) )
= ( C @ k2_mcart_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_cat_5) ).
thf(10118,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) @ ( C @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( C @ ( B @ ( A @ k3_cat_5 ) ) )
= ( C @ k2_mcart_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1553]) ).
thf(1242,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ ( A @ ( B @ k1_funct_1 ) @ ( A @ k1_tarski @ k2_funcop_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_4) ).
thf(8553,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ( ( B @ k1_relat_1 @ ( A @ r2_hidden ) )
=> ( B @ ( A @ ( B @ k1_funct_1 ) @ ( A @ k1_tarski @ k2_funcop_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(2080,axiom,
( ( k1_numbers @ ( k1_numbers @ ( k32_binop_2 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k32_binop_2 @ v1_funct_2 ) ) )
& ( k32_binop_2 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k32_binop_2) ).
thf(13215,plain,
( ( k1_numbers @ ( k1_numbers @ ( k32_binop_2 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( k1_numbers @ ( k32_binop_2 @ v1_funct_2 ) ) )
& ( k32_binop_2 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2080]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ ( A @ ( A @ ( B @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_funct_2) ).
thf(3924,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ m2_relset_1 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( A @ ( A @ ( A @ ( A @ ( B @ k3_partfun1 ) ) @ v1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(638,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ r1_tarski ) )
<=> ( B @ k1_orders_1 @ ( A @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_orders_1) ).
thf(5312,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( ( B @ k1_orders_1 @ ( A @ r2_hidden ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_orders_1 @ ( A @ r2_hidden ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(1403,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k3_xboole_0 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) ) )
& ( ( ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k3_xboole_0 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_sysrel) ).
thf(9399,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( ( ( ( A @ ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( ( A @ k1_relat_1 @ k6_relat_1 @ ( A @ k3_xboole_0 ) )
= ( A @ k1_relat_1 @ k6_relat_1 ) ) )
& ( ( ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k4_xboole_0 ) @ ( A @ k5_relat_1 ) )
= k1_xboole_0 )
& ( A @ ( A @ k5_relat_1 ) @ ( A @ r1_tarski ) ) )
=> ( ( A @ k2_relat_1 @ k6_relat_1 @ ( A @ k3_xboole_0 ) )
= ( A @ k2_relat_1 @ k6_relat_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403]) ).
thf(716,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k7_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_relat_1) ).
thf(5707,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k7_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_partfun1) ).
thf(3212,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( A @ ( B @ ( A @ ( C @ k3_partfun1 ) ) @ v1_partfun1 ) ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1433,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_funct_4 @ v1_funct_1 )
& ( A @ k2_funct_4 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_4) ).
thf(9536,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k2_funct_4 @ v1_funct_1 )
& ( A @ k2_funct_4 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1433]) ).
thf(2121,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_zfmisc_1) ).
thf(13400,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ k1_zfmisc_1 @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2121]) ).
thf(160,axiom,
! [A: $i] :
( ( k5_numbers @ ( A @ m1_subset_1 ) )
=> ( k1_numbers @ k1_zfmisc_1 @ ( A @ k3_urysohn1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_urysohn1) ).
thf(3096,plain,
! [A: $i] :
( ( k5_numbers @ ( A @ m1_subset_1 ) )
=> ( k1_numbers @ k1_zfmisc_1 @ ( A @ k3_urysohn1 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(700,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v3_binop_1 ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( D @ ( G @ r2_hidden ) )
=> ( ( G @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) )
= F ) ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= F ) ) )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_setwiseo) ).
thf(5618,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( B @ k5_finsub_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( ( A @ ( B @ ( E @ m2_relset_1 ) ) )
& ( A @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( A @ ( C @ v3_binop_1 ) )
& ( A @ ( C @ v2_binop_1 ) )
& ( A @ ( C @ v1_binop_1 ) ) )
=> ( ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ( ! [G: $i] :
( ( B @ ( G @ m1_subset_1 ) )
=> ( ( D @ ( G @ r2_hidden ) )
=> ( ( G @ ( E @ ( A @ ( B @ k8_funct_2 ) ) ) )
= F ) ) )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ k7_setwiseo ) ) ) ) )
= F ) ) )
| ( D = k1_xboole_0 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(1598,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ! [D: $i,E: $i] :
( ( E @ ( D @ k4_tarski ) )
!= A )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_zfmisc_1) ).
thf(10344,plain,
! [A: $i,B: $i,C: $i] :
~ ( ! [D: $i,E: $i] :
( ( E @ ( D @ k4_tarski ) )
!= A )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1598]) ).
thf(553,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) )
!= k1_xboole_0 )
=> ( ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( B @ ( A @ k10_funct_3 ) @ ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) )
= D )
& ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( B @ ( A @ k9_funct_3 ) @ ( A @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_borsuk_1) ).
thf(4949,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) )
!= k1_xboole_0 )
=> ( ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( B @ ( A @ k10_funct_3 ) @ ( B @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) )
= D )
& ( ( D @ ( C @ ( B @ ( A @ k12_mcart_1 ) ) ) @ ( B @ ( A @ k9_funct_3 ) @ ( A @ ( B @ ( A @ k2_zfmisc_1 ) @ k2_funct_2 ) ) ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(2182,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( C @ ( D @ k9_relat_1 ) @ ( E @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_funct_2) ).
thf(13760,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( B != k1_xboole_0 )
=> ! [E: $i] :
( ? [F: $i] :
( ( E
= ( F @ ( D @ k1_funct_1 ) ) )
& ( C @ ( F @ r2_hidden ) )
& ( A @ ( F @ r2_hidden ) ) )
=> ( C @ ( D @ k9_relat_1 ) @ ( E @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2182]) ).
thf(1374,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ k1_fraenkel ) @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k1_fraenkel ) @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_funcsdom ) ) ) ) @ m2_fraenkel ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funcsdom) ).
thf(9267,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ k1_fraenkel ) @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k1_fraenkel ) @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ k1_fraenkel ) @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( B @ ( A @ k1_fraenkel ) @ ( B @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k1_funcsdom ) ) ) ) @ m2_fraenkel ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).
thf(1830,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(11631,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1830]) ).
thf(2084,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ( ( I @ ( H @ ( G @ ( C @ ( B @ ( A @ k4_domain_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k8_funct_2 ) ) ) )
= ( I @ ( H @ ( G @ ( C @ ( B @ ( A @ k4_domain_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k8_funct_2 ) ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_multop_1) ).
thf(13230,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ~ ( D @ v1_xboole_0 )
=> ! [E: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ! [F: $i] :
( ( ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( F @ m2_relset_1 ) ) )
& ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ ( F @ v1_funct_2 ) ) )
& ( F @ v1_funct_1 ) )
=> ( ! [G: $i] :
( ( A @ ( G @ m1_subset_1 ) )
=> ! [H: $i] :
( ( B @ ( H @ m1_subset_1 ) )
=> ! [I: $i] :
( ( C @ ( I @ m1_subset_1 ) )
=> ( ( I @ ( H @ ( G @ ( C @ ( B @ ( A @ k4_domain_1 ) ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k8_funct_2 ) ) ) )
= ( I @ ( H @ ( G @ ( C @ ( B @ ( A @ k4_domain_1 ) ) ) ) ) @ ( F @ ( D @ ( C @ ( B @ ( A @ k3_zfmisc_1 ) ) @ k8_funct_2 ) ) ) ) ) ) ) )
=> ( E = F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2084]) ).
thf(64,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t79_xboole_1) ).
thf(2690,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( A @ k4_xboole_0 ) @ r1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ k2_tarski ) )
= ( D @ ( C @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(5261,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ k2_tarski ) )
= ( D @ ( C @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(658,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finseq_1 )
& ( B @ v1_finset_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ ( k5_numbers @ ( B @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_finseq_1) ).
thf(5436,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_finseq_1 )
& ( B @ v1_finset_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ ( k5_numbers @ ( B @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(1698,axiom,
! [A: $i] :
( ( k1_numbers @ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ k5_metric_1 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ k5_metric_1 @ v1_funct_2 ) ) )
& ( A @ k5_metric_1 @ v1_funct_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_metric_1) ).
thf(10900,plain,
! [A: $i] :
( ( k1_numbers @ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ k5_metric_1 @ m2_relset_1 ) ) )
& ( k1_numbers @ ( A @ ( A @ k2_zfmisc_1 ) @ ( A @ k5_metric_1 @ v1_funct_2 ) ) )
& ( A @ k5_metric_1 @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1698]) ).
thf(12,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k3_funct_5 @ v1_funct_1 )
& ( A @ k3_funct_5 @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_funct_5) ).
thf(2436,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ k3_funct_5 @ v1_funct_1 )
& ( A @ k3_funct_5 @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1126,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k10_relat_1 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t171_relat_1) ).
thf(7861,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ( ( k1_xboole_0 @ ( A @ k10_relat_1 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(2323,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g2_struct_0 ) )
= ( D @ ( C @ g2_struct_0 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g2_struct_0) ).
thf(14340,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g2_struct_0 ) )
= ( D @ ( C @ g2_struct_0 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2323]) ).
thf(1399,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_xboole_1) ).
thf(9385,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_xboole_0 ) )
& ( C @ ( A @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399]) ).
thf(516,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k7_relat_1 ) )
= k1_xboole_0 )
<=> ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_relat_1) ).
thf(4752,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) )
=> ( ( A @ ( B @ k7_relat_1 ) )
= k1_xboole_0 ) )
& ( ( ( A @ ( B @ k7_relat_1 ) )
= k1_xboole_0 )
=> ( A @ ( B @ k1_relat_1 @ r1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(1995,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i] :
( ( A @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( D @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_zfmisc_1) ).
thf(12694,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i] :
( ( A @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) )
=> ( D @ ( F @ ( E @ k4_tarski ) @ r2_hidden ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ r1_tarski ) ) )
=> ( D @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1995]) ).
thf(626,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ~ ( ( A
= ( C @ ( B @ k1_funct_1 ) @ ( C @ k4_tarski ) ) )
& ( B @ k4_finseq_1 @ ( C @ r2_hidden ) ) ) )
& ( B @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_finseq_1) ).
thf(5255,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_finseq_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) )
=> ~ ( ! [C: $i] :
( ( k5_numbers @ ( k1_numbers @ ( C @ m2_subset_1 ) ) )
=> ~ ( ( A
= ( C @ ( B @ k1_funct_1 ) @ ( C @ k4_tarski ) ) )
& ( B @ k4_finseq_1 @ ( C @ r2_hidden ) ) ) )
& ( B @ ( A @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ( k1_numbers @ ( B @ m1_subset_1 ) )
& ( k1_numbers @ ( A @ m1_subset_1 ) ) )
=> ( k1_numbers @ ( B @ ( A @ k10_binop_2 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_binop_2) ).
thf(2615,plain,
! [A: $i,B: $i] :
( ( ( k1_numbers @ ( B @ m1_subset_1 ) )
& ( k1_numbers @ ( A @ m1_subset_1 ) ) )
=> ( k1_numbers @ ( B @ ( A @ k10_binop_2 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(2228,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
<=> ? [H: $i] :
( ( E @ ( G @ ( H @ k4_tarski ) @ r2_hidden ) )
& ( D @ ( H @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( H @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_relset_1) ).
thf(13962,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ~ ( C @ v1_xboole_0 )
=> ! [D: $i] :
( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
=> ! [E: $i] :
( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
=> ! [F: $i] :
( ( A @ ( F @ m1_subset_1 ) )
=> ! [G: $i] :
( ( C @ ( G @ m1_subset_1 ) )
=> ( ( ? [H: $i] :
( ( E @ ( G @ ( H @ k4_tarski ) @ r2_hidden ) )
& ( D @ ( H @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( H @ m1_subset_1 ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) @ ( G @ ( F @ k4_tarski ) @ r2_hidden ) )
=> ? [H: $i] :
( ( E @ ( G @ ( H @ k4_tarski ) @ r2_hidden ) )
& ( D @ ( H @ ( F @ k4_tarski ) @ r2_hidden ) )
& ( B @ ( H @ m1_subset_1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2228]) ).
thf(1686,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relset_1) ).
thf(10817,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( k1_xboole_0 @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1686]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( E @ v2_funct_1 )
& ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C ) )
=> ( ( ( D @ k2_relat_1 )
= B )
| ( C = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_funct_2) ).
thf(4423,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) )
=> ! [E: $i] :
( ( ( C @ ( B @ ( E @ m2_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 ) )
=> ( ( ( E @ v2_funct_1 )
& ( ( E @ ( D @ ( C @ ( B @ ( B @ ( A @ k1_partfun1 ) ) ) ) ) @ k2_relat_1 )
= C ) )
=> ( ( ( D @ k2_relat_1 )
= B )
| ( C = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(218,axiom,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_relat_1) ).
thf(3316,plain,
! [A: $i] :
( ( A @ v1_relat_1 )
=> ! [B: $i] :
( ( B @ v1_relat_1 )
=> ( B @ ( A @ k4_xboole_0 ) @ k1_relat_1 @ ( B @ k1_relat_1 @ ( A @ k1_relat_1 @ k4_xboole_0 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( A @ k6_relat_1 @ ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k2_relat_1 )
= ( A @ k6_relat_1 @ k2_relat_1 @ ( B @ k2_relat_1 @ k4_xboole_0 ) ) ) )
& ( ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k1_relat_1 )
= ( A @ k6_relat_1 @ k1_relat_1 @ ( B @ k1_relat_1 @ k4_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_sysrel) ).
thf(2834,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ( ( ( ( A @ k6_relat_1 @ ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k2_relat_1 )
= ( A @ k6_relat_1 @ k2_relat_1 @ ( B @ k2_relat_1 @ k4_xboole_0 ) ) ) )
& ( ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ ( A @ k6_relat_1 @ k5_relat_1 ) )
= k1_xboole_0 )
=> ( ( A @ k6_relat_1 @ ( B @ k4_xboole_0 ) @ k1_relat_1 )
= ( A @ k6_relat_1 @ k1_relat_1 @ ( B @ k1_relat_1 @ k4_xboole_0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(406,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( B @ ( A @ ( B @ ( A @ k1_fraenkel ) @ m1_fraenkel ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_fraenkel) ).
thf(4189,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( B @ ( A @ ( B @ ( A @ k1_fraenkel ) @ m1_fraenkel ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_funct_1) ).
thf(2993,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( C @ v2_funct_1 )
=> ( ( B @ ( A @ k4_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( C @ k9_relat_1 ) @ ( A @ ( C @ k9_relat_1 ) @ k4_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(186,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k2_funcop_1 ) @ v1_funct_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v2_relat_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_cantor_1) ).
thf(3200,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ( ( B @ ( A @ k2_funcop_1 ) @ v1_funct_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v2_relat_1 )
& ( B @ ( A @ k2_funcop_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(1854,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k10_funcop_1) ).
thf(11799,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1854]) ).
thf(1812,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_funcop_1) ).
thf(11511,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ m1_relset_1 ) ) )
& ( C @ ( B @ k2_zfmisc_1 ) @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( C @ v1_xboole_0 )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ m2_relset_1 ) ) )
& ( B @ ( C @ k2_zfmisc_1 ) @ ( A @ ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ v1_funct_2 ) ) )
& ( D @ ( C @ ( B @ ( A @ k10_funcop_1 ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1812]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_funct_2) ).
thf(5293,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
& ( C @ v1_funct_1 ) )
=> ! [D: $i] :
( ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( D @ v1_funct_1 ) )
=> ( ( ( D @ ( B @ ( A @ k5_partfun1 ) ) @ ( C @ ( B @ ( A @ k5_partfun1 ) ) @ r1_tarski ) )
& ( C @ ( B @ ( A @ k4_relset_1 ) ) @ ( D @ ( B @ ( A @ k4_relset_1 ) ) @ r1_tarski ) ) )
=> ( C @ ( D @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(1672,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_lattices ) )
= ( D @ ( C @ g1_lattices ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_lattices) ).
thf(10750,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_lattices ) )
= ( D @ ( C @ g1_lattices ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1672]) ).
thf(2103,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_setwiseo) ).
thf(13311,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ k5_finsub_1 @ ( B @ m1_subset_1 ) )
=> ~ ( ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ~ ( B @ ( C @ r2_hidden ) ) )
& ( B != k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2103]) ).
thf(1953,axiom,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ( C @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_triang_1) ).
thf(12456,plain,
! [A: $i,B: $i] :
( ( ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( C @ m1_subset_1 ) )
=> ( C @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1953]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k5_funct_5 )
= ( D @ k5_funct_5 ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_5) ).
thf(2470,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ( ( ( ( C @ k5_funct_5 )
= ( D @ k5_funct_5 ) )
& ( ( D @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) )
& ( ( C @ k1_relat_1 )
= ( B @ ( A @ k2_zfmisc_1 ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(2134,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_0_cantor_1 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( A
= ( D @ ( B @ k8_setfam_1 ) ) )
& ( C @ ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_cantor_1) ).
thf(13478,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ~ ( C @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ( A
= ( D @ ( B @ k8_setfam_1 ) ) )
& ( C @ ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) ) )
=> ( C @ ( B @ a_2_0_cantor_1 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_cantor_1 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( A
= ( D @ ( B @ k8_setfam_1 ) ) )
& ( C @ ( B @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( D @ m2_subset_1 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2134]) ).
thf(402,axiom,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ ( B @ k7_relat_1 ) @ k5_relat_1 ) @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_relat_1) ).
thf(4174,plain,
! [A: $i,B: $i] :
( ( B @ v1_relat_1 )
=> ! [C: $i] :
( ( C @ v1_relat_1 )
=> ( C @ ( B @ k5_relat_1 ) @ ( C @ ( A @ ( B @ k7_relat_1 ) @ k5_relat_1 ) @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(967,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_funct_1) ).
thf(7003,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( ( C @ k2_relat_1 @ ( A @ r1_tarski ) )
& ( B @ ( C @ k10_relat_1 ) @ ( A @ ( C @ k10_relat_1 ) @ r1_tarski ) ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(2258,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_setfam_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_triang_1) ).
thf(14102,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_setfam_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k5_finsub_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2258]) ).
thf(1675,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_realset1) ).
thf(10768,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_realset1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1675]) ).
thf(1313,axiom,
! [A: $i] :
? [B: $i] :
( ( A @ ( B @ r2_wellord1 ) )
& ( B @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_wellord2) ).
thf(8961,plain,
! [A: $i] :
? [B: $i] :
( ( A @ ( B @ r2_wellord1 ) )
& ( B @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(1773,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_2) ).
thf(11294,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( B @ k1_zfmisc_1 @ ( D @ ( C @ ( B @ ( A @ k2_funct_2 ) ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1773]) ).
thf(908,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_funct_1) ).
thf(6722,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) @ ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(1833,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
<=> ( B @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_subset_1) ).
thf(11648,plain,
! [A: $i,B: $i] :
( ( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ m1_subset_1 ) )
=> ( B @ ( A @ ( C @ m2_subset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_subset_1 ) ) )
=> ( B @ ( C @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1833]) ).
thf(212,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ~ ( A @ v1_realset1 )
<=> ! [B: $i] :
~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_realset1) ).
thf(3296,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ( ( ! [B: $i] :
~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 )
=> ~ ( A @ v1_realset1 ) )
& ( ~ ( A @ v1_realset1 )
=> ! [B: $i] :
~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1224,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t150_funct_1) ).
thf(8465,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 ) )
=> ( ( B @ ( C @ k10_relat_1 ) @ ( A @ k3_xboole_0 ) @ ( C @ k9_relat_1 ) )
= ( B @ ( A @ ( C @ k9_relat_1 ) @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(2266,axiom,
! [A: $i] :
( ( a_0_0_altcat_2 @ ( A @ r2_hidden ) )
<=> ? [B: $i] :
( ( B @ p1_s1_altcat_2 )
& ( A
= ( B @ f2_s1_altcat_2 @ ( B @ k4_tarski ) ) )
& ( f1_s1_altcat_2 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_0_0_altcat_2) ).
thf(14129,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ p1_s1_altcat_2 )
& ( A
= ( B @ f2_s1_altcat_2 @ ( B @ k4_tarski ) ) )
& ( f1_s1_altcat_2 @ ( B @ m1_subset_1 ) ) )
=> ( a_0_0_altcat_2 @ ( A @ r2_hidden ) ) )
& ( ( a_0_0_altcat_2 @ ( A @ r2_hidden ) )
=> ? [B: $i] :
( ( B @ p1_s1_altcat_2 )
& ( A
= ( B @ f2_s1_altcat_2 @ ( B @ k4_tarski ) ) )
& ( f1_s1_altcat_2 @ ( B @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2266]) ).
thf(2140,axiom,
! [A: $i,B: $i] :
( ( ( k1_numbers @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( k1_numbers @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_metric_1 ) )
= ( D @ ( C @ g1_metric_1 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_metric_1) ).
thf(13537,plain,
! [A: $i,B: $i] :
( ( ( k1_numbers @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( k1_numbers @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_metric_1 ) )
= ( D @ ( C @ g1_metric_1 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2140]) ).
thf(957,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( C @ ( B @ k1_closure2 ) @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( ( F
= ( E @ ( D @ k2_tarski ) ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( A @ ( F @ ( C @ ( B @ k4_closure2 ) ) @ k1_funct_1 ) )
= ( A @ ( E @ k1_funct_1 ) @ ( A @ ( D @ k1_funct_1 ) @ k2_tarski ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_closure2) ).
thf(6933,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ m1_pboole ) )
=> ! [D: $i] :
( ( ( D @ v1_funct_1 )
& ( D @ v1_relat_1 ) )
=> ! [E: $i] :
( ( ( E @ v1_funct_1 )
& ( E @ v1_relat_1 ) )
=> ! [F: $i] :
( ( C @ ( B @ k1_closure2 ) @ k1_zfmisc_1 @ ( F @ m1_subset_1 ) )
=> ( ( ( F
= ( E @ ( D @ k2_tarski ) ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( ( A @ ( F @ ( C @ ( B @ k4_closure2 ) ) @ k1_funct_1 ) )
= ( A @ ( E @ k1_funct_1 ) @ ( A @ ( D @ k1_funct_1 ) @ k2_tarski ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(2061,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(13107,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2061]) ).
thf(1047,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( A @ k6_relat_1 )
= ( A @ ( B @ k6_relat_1 @ k7_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_funct_3) ).
thf(7521,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
=> ( ( A @ k6_relat_1 )
= ( A @ ( B @ k6_relat_1 @ k7_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(32823,plain,
$false,
inference(e,[status(thm)],[5659,9405,6387,13199,8114,2876,2463,13405,6566,14181,5509,13052,6085,13266,7766,13024,4447,13321,5088,4835,10259,4450,10785,2778,13402,11192,8663,3661,11895,12526,10577,13643,4729,12975,14574,9485,3979,9731,11581,6855,10743,2787,6317,6512,2480,3969,12148,9076,10944,14139,5999,11998,10363,9411,8828,6014,5131,6374,6162,5224,10294,13845,3680,12500,13869,4931,7601,12458,14296,5454,8005,6791,8417,12634,4714,2512,12030,3072,10149,9791,8129,8044,7358,11635,7409,5718,13007,13110,6868,3762,13177,13351,8082,12666,3230,9604,10673,3549,6463,3417,3509,6619,10567,9901,6813,3153,2590,14570,8682,2947,6796,13548,3912,3098,10061,10705,5878,6798,6323,7368,7253,10244,4711,6830,5982,3012,13796,13586,5265,4215,6602,8988,10463,14078,11881,11080,4479,7813,9950,4105,4090,7573,5701,6046,4543,5550,9956,5120,9933,10775,9184,8182,9644,14602,3429,8335,5565,8551,12590,11072,5589,2607,9978,8635,13317,14124,4647,6246,3648,8568,4011,13457,4870,6665,10358,8622,4026,7524,11014,13095,4110,8747,9428,9565,11917,9813,6727,10138,5316,6655,11075,7345,12522,3781,4440,12511,9218,5163,4650,8370,5674,8947,8210,12421,7188,14478,6759,2901,7871,7452,9801,6117,13557,2844,11055,4435,14025,8204,14301,13764,7748,11786,3717,5192,6640,9540,7220,11449,8539,6887,12763,12757,10854,12009,6342,8224,9116,10351,12026,12447,3103,8851,10336,10230,9476,8848,5740,3545,2723,13626,2972,3634,5977,7064,2432,9292,9845,3502,11260,13970,10908,5123,13915,10599,13179,13552,4124,3947,10071,5825,5770,12770,7343,14644,4760,4665,13223,14188,4156,5750,13003,9394,3688,7628,4511,5024,4249,8610,3976,3425,4778,8069,3820,3891,5553,11426,5765,10619,10326,4546,10121,11949,10286,5429,3195,14474,4348,9287,11844,2735,3275,9067,13696,7696,9828,7418,6538,11203,4070,3116,7401,13429,6547,6274,5284,11025,9216,10053,9084,2755,9332,7683,14489,11431,9693,11299,5064,11944,3653,10719,14039,8834,6506,14141,14440,2682,8522,11111,9315,7867,10010,3749,8146,6662,3744,5712,6519,7000,11051,13273,13275,4766,7743,6208,10469,14228,2745,14007,6130,2703,14331,14611,4358,8571,10570,4460,8126,5091,7509,6071,8770,2420,5338,6253,3463,12920,4353,13307,6470,5605,13878,4862,14376,10003,6905,14455,7209,7803,8819,8468,11247,14109,14334,12443,4928,11378,11802,11115,5052,11741,9199,12180,13393,3312,5829,8384,3835,5727,8632,5020,8037,5493,6734,10292,11959,11363,11404,4302,4514,11139,4253,7500,12517,9768,12875,8870,9580,7226,13575,2829,5974,9425,11163,8956,3393,11500,11083,6841,6559,4432,7258,10454,14034,14339,4696,13771,5433,9854,4205,11821,3322,8190,3431,13863,10324,7786,7273,5892,12924,7492,11778,8379,11064,6227,12023,13987,11344,3075,5597,2996,9088,12828,6657,13325,8158,7818,14584,10271,14532,14061,2451,3527,7775,3983,6189,6135,9837,3525,6187,14408,11215,9860,14346,6964,3973,11691,8659,12436,13414,11748,5032,3290,6823,4115,13543,13290,7139,5457,4783,4556,9319,9779,4810,6204,3851,14209,9309,5834,11523,8274,11218,6631,3189,3712,7645,5169,7413,12090,7473,12504,10404,4055,10442,5448,9616,3421,6740,2483,8817,9452,14410,3808,9140,4364,12315,7909,14071,13072,12101,14658,6702,4825,6863,6700,14622,6021,10801,9368,9533,9236,11783,2750,10233,10574,14637,11505,5137,6616,10459,9007,7051,9272,7460,5328,8362,2982,13838,13248,10029,7230,5695,8742,13683,12559,2762,3378,9822,2473,9221,11791,5443,6058,8668,12365,6282,8751,9997,7657,11159,14558,9917,3899,5174,14462,4853,14588,13885,12732,7535,6529,10725,5406,5157,14308,9682,8999,4199,13337,5783,9571,3301,10593,8655,12895,13228,4962,9340,12275,13017,9090,5839,3720,5411,11550,13767,13104,6250,8959,7019,11324,3318,9009,6571,11069,5416,9164,5487,7005,5862,2641,6884,5519,12565,9785,4312,12127,12232,12673,11410,8712,9488,8343,6079,11587,10426,9207,12809,4785,8878,10133,8513,10099,9722,3261,11751,12613,5611,13423,8783,8168,7703,6328,10171,6820,14501,6550,14032,8994,2596,8329,10975,8476,7353,11619,6032,4375,12664,11037,6371,8888,4989,13572,13131,7881,5349,13949,5956,11865,14222,7834,10843,9618,14465,12970,9981,9126,2937,7640,4493,5754,11565,7984,5102,8714,11908,3250,6509,7906,7565,4021,12058,14280,10756,14477,3926,8577,3282,13158,10721,3958,4295,10263,9113,5826,11244,4280,2873,5302,6852,7555,13282,7576,12910,4053,4585,13639,7185,9671,6043,7449,3314,4994,3499,5177,3349,3578,13799,10116,5460,13789,14556,4553,7625,10765,3894,9626,13530,4327,12025,2609,7545,13359,9301,10794,6833,5113,10006,5201,12849,6402,12095,7853,10615,2741,11624,9080,9613,9885,13411,10543,9868,4732,11101,12991,11420,5993,4680,13269,5330,8518,3595,4316,6090,2653,14028,11762,7481,9936,7593,3916,3205,8138,12372,11961,11234,8238,8297,3731,4808,8354,5189,5626,3699,11736,12863,3615,13946,10848,3909,9493,6677,7142,3831,2840,5221,8545,12728,10748,13939,5145,14327,5098,6801,13347,6940,2685,5006,9016,5615,8282,4048,11221,4429,9444,10266,2692,14398,9244,8619,14147,3518,11435,3386,12950,3632,3119,3746,6360,4883,6111,3078,8149,6958,11189,3650,9904,6128,7874,5687,3176,11877,3018,8792,2798,14580,14153,9609,4191,9100,11097,8230,13928,4653,7898,3775,10946,11860,13883,9640,6967,10830,4582,8864,8555,7631,12967,4983,5181,6844,7717,4772,14313,3210,12818,14212,6363,8008,9419,12885,2455,5464,5253,5786,5547,6164,2613,8968,10688,7806,8390,3723,3643,4444,2666,6625,6541,3555,9392,2649,2781,6065,6724,14148,8326,3354,5639,6876,2465,3540,4804,13979,10919,6349,3703,11608,8458,7609,13205,8219,12632,7651,2519,5481,8351,3787,9149,14655,2598,3770,9893,9448,3390,7495,5058,13718,4717,7597,6346,10306,8732,9461,8896,13911,13680,10438,9990,9620,4231,7619,12946,5823,6908,8455,6465,3247,3409,2766,2697,14634,8425,8090,10588,3064,10513,10180,8144,14116,10075,13693,5026,12641,3364,4086,14249,12831,9942,3083,13699,12962,12138,9699,8796,8614,11368,11125,5737,14185,5249,13932,7193,13522,11031,3755,13398,8971,3802,5310,10366,8839,4644,3225,11153,10338,12577,9964,14180,4212,14590,3183,10740,9782,3173,10524,9269,9716,13026,3856,10656,8422,10069,8049,2748,6592,10819,6011,12553,9169,9171,11901,2440,6756,13137,7476,14362,9925,6931,5198,13968,11576,5295,10111,2617,10783,4004,2423,9562,12104,7527,4572,9256,12677,2909,9939,10310,4438,6598,3158,7160,14107,11516,9545,10862,6901,2729,13122,13444,14231,6637,8164,6314,14020,10840,3130,6053,5524,2677,9416,11179,4708,12168,13603,14388,13041,13331,2904,8095,13201,13989,14045,12982,7512,9502,10202,8531,3257,3607,9577,7155,12119,14469,13259,5960,10043,13579,10289,3738,7636,3375,3888,6454,3839,5016,4503,4577,3792,5882,5095,3111,8718,4017,9650,13618,2894,13031,3396,5400,11693,7567,3768,3599,14286,11006,12028,13710,7709,3372,4000,12441,10155,3741,4662,7590,9798,11396,3234,11455,2859,6870,3504,4283,3255,2791,12835,7497,10547,2789,6312,8814,3609,4159,12170,9733,8470,10963,11941,11703,7487,9543,11809,13060,10480,7223,6581,11804,12210,7440,3736,3081,14572,7751,2674,2514,8124,13569,6229,9719,9295,10700,4032,8027,7041,5050,2991,13363,6344,6898,14247,13809,3590,10435,3604,8092,6606,9852,4590,7763,13920,2817,13492,4758,4769,2695,13685,8872,11483,14384,3646,7719,13621,11968,9808,7579,12509,9224,8381,3223,5965,13197,13908,14508,8767,3023,13054,4558,9210,3773,5567,14074,5118,8549,6937,6357,2891,5011,10770,7689,9506,6532,5595,4171,3208,9178,14608,13380,12524,4822,10348,6794,8359,11919,10051,12759,10728,10938,5207,2442,2759,3487,8059,9496,13984,2457,3641,6123,2425,9290,4273,8524,14151,12825,5997,3304,11765,8387,12278,10505,7746,3170,13903,14042,6061,6585,7158,8419,10565,8042,12032,6024,14290,3101,9623,2721,3352,8452,4337,9422,2679,6942,13240,10236,10317,7783,5671,10910,4498,4369,12651,7643,3155,9592,3238,5244,11508,12131,5325,14119,13467,7837,10279,6500,12034,3515,6866,6197,9322,3270,13253,13670,13464,10000,7255,12182,13794,13588,10037,2669,13888,3710,4958,9702,11365,4154,2856,4176,4667,2802,5689,7470,10098,6604,6184,13836,3586,6737,4509,9890,6460,14053,12064,5267,14632,12882,6216,9931,2824,6087,3133,10579,12562,8473,7504,6004,8826,9857,10621,2812,2632,4541,13164,10957,14262,4420,7275,13930,9888,5730,8156,14311,4569,12049,11498,13857,13323,6849,4064,9830,10628,4264,7820,3932,5599,9263,2446,4277,12111,7033,12755,11156,2757,10942,7664,3165,7551,10732,13653,11569,6747,2785,7654,2593,4850,11640,5466,8032,7869,4726,3861,12381,12821,7066,2461,2974,10792,4684,13486,6956,11521,2911,8280,9143,11558,2620,12556,3142,7558,12178,5495,8990,13840,2770,11173,13867,10147,6255,12460,13593,7603,6574,13630,2401,5216,6609,7479,11041,12534,6628,12086,10925,11775,12465,13339,6223,11113,4362,6816,5575,14660,9106,2752,12409,12765,3310,11130,8676,4703,10424,3512,12308,6027,3178,12341,6614,13208,11493,8035,4965,10499,11361,2984,14427,4481,6785,2506,13806,7049,8965,10322,9227,7151,2927,11872,6719,10456,3009,12922,10517,10617,4426,4207,12207,13278,14190,6320,5538,6890,5587,13168,7490,3193,12021,14126,11654,7896,7296,11062,6276,14012,14349,10191,4580,7975,13852,9259,10488,7298,3161,8804,4735,10249,6659,9826,7562,7539,11077,2878,2503,8116,6191,5952,8505,4292,8789,9408,14175,14406,14438,4566,4859,8106,3921,14530,2846,4113,3278,5710,13454,9232,7137,9276,5763,8885,14240,6440,4986,9202,6132,13189,3849,6202,9317,11540,5125,5388,10856,3214,9710,9953,10521,7864,11230,2942,7283,14594,5047,14304,10797,9022,12266,12918,8725,14609,6120,7705,8772,12502,2863,11329,9794,5607,14374,4360,5514,10540,9153,9606,6266,5478,14336,4366,8890,12056,12648,3904,4922,14017,5484,6826,13285,5592,12807,5980,7045,13261,4641,5721,2821,9766,4971,9499,13713,4324,8364,9948,6596,10159,8295,7811,7586,2888,9473,2831,12659,8039,13823,4164,2656,7672,5684,10218,14036,14272,8612,12187,11823,13769,10048,5767,5431,10994,14604,9214,8111,10439,10952,7264,8377,13677,12720,3273,13089,12124,8428,12514,10055,3344,13560,5555,11297,4222,10717,7667,7796,10144,2429,12160,8216,12419,7149,13791,6298,7879,6125,5203,5995,12995,13320,3127,8528,11257,4351,6174,3828,5543,7351,2701,6436,2486,4800,11034,14143,10012,8757,14226,14179,12580,10613,10846,7398,5450,9690,6206,9435,2468,5277,12439,4976,14400,13674,13076,10714,8679,12424,14378,5949,3697,11094,12328,2500,7876,11181,7466,3415,11835,11486,10531,3493,14359,13299,3356,10415,6369,10992,7797,9247,12014,7391,4991,8061,13951,7163,11334,7374,4202,5226,12952,4093,2949,4267,13243,10432,6467,7595,9574,8087,4838,11957,2807,3914,11108,3520,11280,2848,11906,13595,3398,4111,8982,3684,3288,6622,7239,14554,3401,4763,2865,3168,14403,9119,10496,4289,11862,5873,13934,5490,7146,14586,9279,10241,9686,10018,14306,2626,12343,3757,14678,14242,6447,9912,4587,11150,7024,3067,10873,10595,13812,12467,6408,9306,10526,9760,7395,11995,9438,9389,5777,7606,4873,4656,6390,7547,9819,5573,4997,10199,11681,4738,5115,4780,2611,4185,14098,6674,10188,8285,8153,6743,10928,12722,3056,9078,8761,8666,2658,12355,3929,2775,11383,4061,2907,9647,4574,7670,2988,4806,12915,10169,5382,11039,8197,5813,6910,6694,10077,9707,14172,4121,6903,3613,10135,2707,10220,2853,11319,8882,12698,5008,12574,8292,3383,12061,14503,12880,14224,5426,8854,4042,14618,9205,3991,14457,5228,14204,9459,11469,3561,13441,7700,3003,5394,11567,7638,4495,14368,13128,3331,3136,8617,13998,11187,14177,11091,7912,2394,7437,10210,8997,5408,2399,6018,7416,12620,5211,5287,14596,5963,13656,11210,12900,3694,12730,11780,9338,4197,6305,9470,14187,12588,13610,5692,3267,14418,5837,14592,14582,14165,12675,6166,12093,7530,8953,4074,13954,6569,8721,5517,10109,5128,2739,2494,6444,2917,4372,13513,2623,13389,11604,5704,3552,11208,5864,13257,13753,13220,9976,9361,2930,4880,10838,4039,7542,5677,4794,12108,14030,13991,7016,7355,4706,4670,7634,9806,14499,14386,5971,12162,9229,4356,3997,3907,13349,12520,14170,11928,5004,3733,8754,7153,14300,12374,6563,7883,11739,8412,10601,5954,7242,7712,14332,2951,13577,14475,2815,6456,4841,12213,3790,5884,11341,13941,10515,8574,9329,3496,4885,9728,5014,12798,9070,11807,5247,12140,11914,10590,13294,14278,6366,3062,6782,13701,12272,11009,6535,2800,14578,4024,14090,9250,6309,2651,5559,9697,2636,12904,8542,4029,10064,4178,3328,7851,13819,4051,10809,14288,8653,9915,5159,11199,10340,9788,4981,14315,3347,6114,4286,11194,8019,8510,9134,12583,11401,4968,4007,8241,11627,5105,9002,14600,13842,3479,9959,2417,10472,12679,6729,14293,7278,14001,2913,2404,8002,4865,5378,9414,13194,7808,4193,6393,6040,6929,3506,3843,10485,10781,10224,6269,6503,9441,4848,3362,10554,11358,4876,13161,14251,13824,6424,9325,3244,11390,8066,2966,6750,3543,12134,12793,8444,5668,11144,9679,7584,6807,10032,2600,9763,7506,5140,13601,11707,11764,4506,6473,3259,12761,7740,5280,9446,3817,3965,5681,5060,8730,3020,4239,6082,9110,14283,13720,11479,11477,4659,3538,12188,7780,11462,10642,3939,9335,4955,4691,2699,8876,3812,13689,4345,14114,4501,10586,4271,3918,11373,8857,8978,8950,5029,11086,4161,9303,10949,3637,6896,3901,12749,9568,8685,5172,14443,3461,13922,12908,6961,10723,10118,8553,13215,3924,5312,9399,5707,3212,9536,13400,3096,5618,10344,4949,13760,9267,11631,13230,2690,5261,5436,10900,2436,7861,14340,9385,4752,12694,5255,2615,13962,10817,4423,3316,2834,4189,2993,3200,11799,11511,5293,10750,13311,12456,2470,13478,4174,7003,14102,10768,8961,11294,6722,11648,3296,8465,14129,13537,6933,13107,7521]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU435+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n007.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 09:48:10 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.89/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 7.64/3.19 % [INFO] Parsing done (2206ms).
% 7.73/3.21 % [INFO] Running in sequential loop mode.
% 8.16/3.58 % [INFO] eprover registered as external prover.
% 8.16/3.59 % [INFO] Scanning for conjecture ...
% 12.45/4.94 % [INFO] Found a conjecture (or negated_conjecture) and 19108 axioms. Running axiom selection ...
% 20.21/10.08 % [INFO] Axiom selection finished. Selected 2391 axioms (removed 16717 axioms).
% 24.29/11.46 % [INFO] Problem is first-order (TPTP FOF).
% 24.48/11.55 % [INFO] Type checking passed.
% 24.48/11.56 % [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 ...
% 115.87/39.86 % External prover 'e' found a proof!
% 115.87/39.86 % [INFO] Killing All external provers ...
% 115.87/39.86 % Time passed: 39330ms (effective reasoning time: 36644ms)
% 115.87/39.86 % 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)>
% 115.87/39.87 % 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
% 115.87/39.87 % No. of inferences in proof: 4786
% 115.87/39.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 39330 ms resp. 36644 ms w/o parsing
% 120.03/40.85 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 120.03/40.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------